Multilevel superposition for deciphering the conformational variability of protein ensembles

The dynamics and variability of protein conformations are directly linked to their functions. Many comparative studies of X-ray protein structures have been conducted to elucidate the relevant conformational changes, dynamics and heterogeneity. The rapid increase in the number of experimentally determined structures has made comparison an effective tool for investigating protein structures. For example, it is now possible to compare structural ensembles formed by enzyme species, variants or the type of ligands bound to them. In this study, the author developed a multilevel model for estimating two covariance matrices that represent inter- and intra-ensemble variability in the Cartesian coordinate space. Principal component analysis using the two estimated covariance matrices identified the inter-/intra-enzyme variabilities, which seemed to be important for the enzyme functions, with the illustrative examples of cytochrome P450 family 2 enzymes and class A $\beta$-lactamases. In P450, in which each enzyme has its own active site of a distinct size, an active-site motion shared universally between the enzymes was captured as the first principal mode of the intra-enzyme covariance matrix. In this case, the method was useful for understanding the conformational variability after adjusting for the differences between enzyme sizes. The developed method is advantageous in small ensemble-size problems and hence promising for use in comparative studies on experimentally determined structures where ensemble sizes are smaller than those generated, for example, by molecular dynamics simulations.

A fast algorithm to factorize high-dimensional tensor product matrices used in genetic models

Many genetic models (including models for epistatic effects as well as genetic-by-environment) involve covariance structures that are Hadamard products of lower rank matrices. Implementing these models requires factorizing large Hadamard product matrices. The available algorithms for factorization do not scale well for big data, making the use of some of these models not feasible with large sample sizes. Here, based on properties of Hadamard products and (related) Kronecker products, we propose an algorithm that produces an approximate decomposition that is orders of magnitude faster than the standard eigenvalue decomposition. In this article, we describe the algorithm, show how it can be used to factorize large Hadamard product matrices, present benchmarks, and illustrate the use of the method by presenting an analysis of data from the northern testing locations of the G × E project from the Genomes to Fields Initiative (n ∼ 60,000). We implemented the proposed algorithm in the open-source "tensorEVD" R package.

Determination of correlations in multivariate count data with informative observation times

We consider there are various types of recurrent events and the total number of occurrences are collected at the random observation times. It has concerned that the observation process may not be independent to the multivariate event processes, hence the total counts and observation times may be correlated and the dependence may exist among different types of the event processes as well. Many methods have developed nonparametric models to accommodate such unknown structures; however, it is difficult to assess and directly quantify their correlation relationships. A multivariate frailty model is proposed to this study, in which the event and observation processes are linked by frailty variables whose joint distribution can be implicitly specified through the multivariate normal distribution with some unknown covariance matrix. The Bayesian inference method is conducted to obtain the estimates of the regression coefficients and correlation parameters. We use a form of trigonometric functions to represent the covariance matrix, so that it meets the positive-definiteness condition efficiently during the estimation schemes. The simulation studies demonstrate the utility of the proposed models. We apply the model to a skin cancer prevention study, and aim to determine the covariate and association effects. We found treatment is significant in determining the duration of examination times; prior-counts, age and gender are significant variables on the occurrence rates of tumor counts. Using the covariance matrix to access the underlying dependent structure, the mutual correlations among them are all positive, and the basal cell counts are more related to the examination times.

Homogeneity tests of covariance for high-dimensional functional data with applications to event segmentation

We consider inference problems for high-dimensional (HD) functional data with a dense number of T repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal dependence, high dimensionality, and dense number of repeated measurements pose theoretical and computational challenges. This paper has two aims; our first aim is to solve the theoretical and computational challenges in testing equivalence among covariance matrices from HD functional data. The second aim is to provide computationally efficient and tuning-free tools with guaranteed stochastic error control. The weak convergence of the stochastic process formed by the test statistics is established under the "large p, large T, and small n" setting. If the null is rejected, we further show that the locations of the change points can be estimated consistently. The estimator's rate of convergence is shown to depend on the data dimension, sample size, number of repeated measurements, and signal-to-noise ratio. We also show that our proposed computation algorithms can significantly reduce the computation time and are applicable to real-world data with a large number of HD-repeated measurements (e.g., functional magnetic resonance imaging (fMRI) data). Simulation results demonstrate both the finite sample performance and computational effectiveness of our proposed procedures. We observe that the empirical size of the test is well controlled at the nominal level, and the locations of multiple change points can be accurately identified. An application to fMRI data demonstrates that our proposed methods can identify event boundaries in the preface of the television series Sherlock. Code to implement the procedures is available in an R package named TechPhD.

Moisture Detection in Tree Trunks in Semiarid Lands Using Low-Cost Non-Invasive Capacitive Sensors with Statistical Based Anomaly Detection Approach

This paper focuses on building a non-invasive, low-cost sensor that can be fitted over tree trunks growing in a semiarid land environment. It also proposes a new definition that characterizes tree trunks' water retention capabilities mathematically. The designed sensor measures the variations in capacitance across its probes. It uses amplification and filter stages to smooth the readings, requires little power, and is operational over a 100 kHz frequency. The sensor sends data via a Long Range (LoRa) transceiver through a gateway to a processing unit. Field experiments showed that the system provides accurate readings of the moisture content. As the sensors are non-invasive, they can be fitted to branches and trunks of various sizes without altering the structure of the wood tissue. Results show that the moisture content in tree trunks increases exponentially with respect to the measured capacitance and reflects the distinct differences between different tree types. Data of known healthy trees and unhealthy trees and defective sensor readings have been collected and analysed statistically to show how anomalies in sensor reading baseds on eigenvectors and eigenvalues of the fitted curve coefficient matrix can be detected.

James-Stein for the leading eigenvector

Recent research identifies and corrects bias, such as excess dispersion, in the leading sample eigenvector of a factor-based covariance matrix estimated from a high-dimension low sample size (HL) data set. We show that eigenvector bias can have a substantial impact on variance-minimizing optimization in the HL regime, while bias in estimated eigenvalues may have little effect. We describe a data-driven eigenvector shrinkage estimator in the HL regime called "James-Stein for eigenvectors" (JSE) and its close relationship with the James-Stein (JS) estimator for a collection of averages. We show, both theoretically and with numerical experiments, that, for certain variance-minimizing problems of practical importance, efforts to correct eigenvalues have little value in comparison to the JSE correction of the leading eigenvector. When certain extra information is present, JSE is a consistent estimator of the leading eigenvector.

Developmental instability in domesticated mammals

Measures of fluctuating asymmetry (FA) have been adopted widely as an estimate of developmental instability. Arising from various sources of stress, developmental instability is associated with an organism's capacity to maintain fitness. The process of domestication has been framed as an environmental stress with human-specified parameters, suggesting that FA may manifest to a larger degree among domesticates compared to their wild relatives. This study used three-dimensional geometric morphometric landmark data to (a) quantify the amount of FA in the cranium of six domestic mammal species and their wild relatives and, (b) provide novel assessment of the commonalities and differences across domestic/wild pairs concerning the extent to which random variation arising from the developmental system assimilates into within-population variation. The majority of domestic mammals showed greater disparity for asymmetric shape, however, only two forms (Pig, Dog) showed significantly higher disparity as well as a higher degree of asymmetry compared to their wild counterparts (Wild Boar, Wolf). Contra to predictions, most domestic and wild forms did not show a statistically significant correspondence between symmetric shape variation and FA, however, a moderate correlation value was recorded for most pairs (r-partial least squares >0.5). Within pairs, domestic and wild forms showed similar correlation magnitudes for the relationship between the asymmetric and symmetric components. In domesticates, new variation may therefore retain a general, conserved pattern in the gross structuring of the cranium, whilst also being a source for response to selection on specific features.

Estimating Quantum Mutual Information of Continuous-Variable Quantum States by Measuring Purity and Covariance Matrix

We derive accessible upper and lower bounds for continuous-variable (CV) quantum states on quantum mutual information. The derivations are based on the observation that some functions of purities bound the difference between quantum mutual information of a quantum state and its Gaussian reference. The bounds are efficiently obtainable by measuring purities and the covariance matrix without multimode quantum state reconstruction. We extend our approach to the upper and lower bounds for the quantum total correlation of CV multimode quantum states. Furthermore, we investigate the relations of the bounds for the quantum mutual information with the bounds for the quantum conditional entropy.

A novel channel selection scheme for olfactory EEG signal classification on Riemannian manifolds

OBJECTIVE

The classification of olfactory-induced electroencephalogram (olfactory EEG) signals has potential applications in disease diagnosis, emotion regulation, multimedia, and so on. To achieve high-precision classification, numerous EEG channels are usually used, but this also brings problems such as information redundancy, overfitting and high computational load. Consequently, channel selection is necessary to find and use the most effective channels.

APPROACH

In this study, we proposed a multi-strategy fusion binary harmony search (MFBHS) algorithm and combined it with the Riemannian geometry (RG) classification framework to select the optimal channel sets for olfactory EEG signal classification. MFBHS was designed by simultaneously integrating three strategies into the binary harmony search (BHS) algorithm, including an opposition-based learning strategy (OBL) for generating high-quality initial population, an adaptive parameter strategy (APS) for improving search capability, and a bitwise operation strategy (BOS) for maintaining population diversity. It performed channel selection directly on the covariance matrix of EEG signals, and used the number of selected channels and the classification accuracy computed by a Riemannian classifier to evaluate the newly generated subset of channels.

MAIN RESULTS

With five different classification protocols designed based on two public olfactory EEG datasets, the performance of MFBHS was evaluated and compared with some state-of-the-art algorithms. Experimental results reveal that our method can minimize the number of channels while achieving high classification accuracy compatible with using all the channels. In addition, cross-subject generalization tests of MFBHS channel selection show that subject-independent channels obtained through training can be directly used on untrained subjects without greatly compromising classification accuracy.

SIGNIFICANCE

The proposed MFBHS algorithm is a practical technique for effective use of EEG channels in olfactory recognition.

Eddy heat exchange at the boundary under white noise turbulence

We prove the existence of an eddy heat diffusion coefficient coming from an idealized model of turbulent fluid. A difficulty lies in the presence of a boundary, with also turbulent mixing and the eddy diffusion coefficient going to zero at the boundary. Nevertheless, enhanced diffusion takes place. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

CM-LSTM Based Spectrum Sensing

This paper presents spectrum sensing as a classification problem, and uses a spectrum-sensing algorithm based on a signal covariance matrix and long short-term memory network (CM-LSTM). We jointly exploited the spatial cross-correlation of multiple signals received by the antenna array and the temporal autocorrelation of single signals; we used the long short-term memory network (LSTM), which is good at extracting temporal correlation features, as the classification model; we then input the covariance matrix of the signals received by the array into the LSTM classification model to achieve the fusion learning of spatial correlation features and temporal correlation features of the signals, thus significantly improving the performance of spectrum sensing. Simulation analysis shows that the CM-LSTM-based spectrum-sensing algorithm shows better performance compared with support vector machine (SVM), gradient boosting machine (GBM), random forest (RF), and energy detection (ED) algorithm-based spectrum-sensing algorithms for different signal-to-noise ratios (SNRs) and different numbers of secondary users (SUs). Among them, SVM is a classical machine-learning algorithm, GBM and RF are two integrated learning methods with better generalization capability, and ED is a classical, traditional, and spectrum-sensing algorithm.

DOA Estimation Method Based on Improved Deep Convolutional Neural Network

For the multi-target DOA estimation problem of uniform linear arrays, this paper proposes a DOA estimation method based on the deep convolution neural network. The algorithm adopts the deep convolutional neural network, and the DOA estimation problem of the array signal is transformed into the inverse mapping problem of the array output covariance matrix to a binary sequence in which “1” indicates that there is a target incident in the corresponding angular direction at that position. The upper triangular array of the discrete covariance matrix is used as the data input to realize the DOA estimation of multiple sources. The simulation results show that the DOA estimation accuracy of the proposed algorithm is significantly better than that of the typical super-resolution estimation algorithm under the conditions of low SNR and small snapshot. Under the conditions of high SNR and large snapshot, the estimation accuracy of the proposed algorithm is basically the same as those of the MUSIC algorithm, ESPRIT algorithm, and ML algorithm, which are better than that of the deep fully connected neural network. The analysis of the simulation results shows that the algorithm is effective, and the time and space complexity can be further reduced by replacing the square array with the upper triangular array as the input.

Model-Protected Multi-Task Learning

Multi-task learning (MTL) refers to the paradigm of learning multiple related tasks together. In contrast, in single-task learning (STL) each individual task is learned independently. MTL often leads to better trained models because they can leverage the commonalities among related tasks. However, because MTL algorithms can "leak" information from different models across different tasks, MTL poses a potential security risk. Specifically, an adversary may participate in the MTL process through one task and thereby acquire the model information for another task. The previously proposed privacy-preserving MTL methods protect data instances rather than models, and some of them may underperform in comparison with STL methods. In this paper, we propose a privacy-preserving MTL framework to prevent information from each model leaking to other models based on a perturbation of the covariance matrix of the model matrix. We study two popular MTL approaches for instantiation, namely, learning the low-rank and group-sparse patterns of the model matrix. Our algorithms can be guaranteed not to underperform compared with STL methods. We build our methods based upon tools for differential privacy, and privacy guarantees, utility bounds are provided, and heterogeneous privacy budgets are considered. The experiments demonstrate that our algorithms outperform the baseline methods constructed by existing privacy-preserving MTL methods on the proposed model-protection problem.

Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors

Sensor placement is an important factor that may significantly affect the localization performance of a sensor network. This paper investigates the sensor placement optimization problem in three-dimensional (3D) space for angle of arrival (AOA) target localization with Gaussian priors. We first show that under the A-optimality criterion, the optimization problem can be transferred to be a diagonalizing process on the AOA-based Fisher information matrix (FIM). Secondly, we prove that the FIM follows the invariance property of the 3D rotation, and the Gaussian covariance matrix of the FIM can be diagonalized via 3D rotation. Based on this finding, an optimal sensor placement method using 3D rotation was created for when prior information exists as to the target location. Finally, several simulations were carried out to demonstrate the effectiveness of the proposed method. Compared with the existing methods, the mean squared error (MSE) of the maximum a posteriori (MAP) estimation using the proposed method is lower by at least 25% when the number of sensors is between 3 and 6, while the estimation bias remains very close to zero (smaller than 0.15 m).

Boosting automated sleep staging performance in big datasets using population subgrouping

Current approaches to automated sleep staging from the electroencephalogram (EEG) rely on constructing a large labeled training and test corpora by aggregating data from different individuals. However, many of the subjects in the training set may exhibit changes in the EEG that are very different from the subjects in the test set. Training an algorithm on such data without accounting for this diversity can cause underperformance. Moreover, test data may have unexpected sensor misplacement or different instrument noise and spectral responses. This work proposes a novel method to learn relevant individuals based on their similarities effectively. The proposed method embeds all training patients into a shared and robust feature space. Individuals who share strong statistical relationships and are similar based on their EEG signals are clustered in this feature space before being passed to a deep learning framework for classification. Using 994 patient EEGs from the 2018 Physionet Challenge (≈6,561 h of recording), we demonstrate that the clustering approach significantly boosts performance compared to state-of-the-art deep learning approaches. The proposed method improves, on average, a precision score from 0.72 to 0.81, a sensitivity score from 0.74 to 0.82, and a Cohen's Kappa coefficient from 0.64 to 0.75 under 10-fold cross-validation.

Radar Position Estimation by Sequential Irradiation of ESM Receivers

In this article, a new technique for determination of 2D signal source (target) position is proposed. This novel approach, called the Inscribed Angle (InA), is based on measuring the time difference of sequential irradiation by the main beam of the target antenna's radiation pattern, using Electronic Support Measures (ESM) receivers, assuming that the target antenna is rotating and that its angular velocity is constant. In addition, it is also assumed that the localization system operates in a LOS (Line of Sight) situation and that three time-synchronized sensors are placed arbitrarily across the area. The main contribution of the article is a complete description of the proposed localization method. That is, this paper demonstrates a geometric representation and an InA localization technique model. Analysis of the method's accuracy is also demonstrated. The time of irradiation of the receiving station corresponds to the direction in which the maximum received signal strength (RSS) was measured. In order to achieve a certain degree of accuracy of the proposed positioning technique, a method was derived to increase the accuracy of the irradiation time estimation. Finally, extensive simulation was conducted to demonstrate the performance and accuracy of our positioning method.

Mitigation of the convergence issues associated with semi-replicated bioequivalence data

Semi-replicated designs for investigation of bioequivalence constitute a challenge when mixed models are applied. With the commonly available packages and regardless of choice of covariance structure the software may force variance components into the covariance matrix that render it over-specified. This may give rise to arbitrary estimates of certain variance components, lack of convergence or warnings. Classically the covariance matrix is decomposed as V = ZGZ^t  + R, with G containing the between-subject variance components, Z being the design matrix for the random effects and R containing the within-subject variance components. By abandoning the definitions of G and R, and instead working directly in V, it is possible to specify a correct model with only the variance components of interest. Proof-of-concept for this idea is delivered with a script in the statistical language R. The script is available as supplementary material (Data S1).

Invariant Quantum States of Quadratic Hamiltonians

The problem of finding covariance matrices that remain constant in time for arbitrary multi-dimensional quadratic Hamiltonians (including those with time-dependent coefficients) is considered. General solutions are obtained.

Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini-Kossakowski-Lindblad-Sudarshan equation.

The impact of covariance priors on arm-based Bayesian network meta-analyses with binary outcomes

Bayesian analyses with the arm-based (AB) network meta-analysis (NMA) model require researchers to specify a prior distribution for the covariance matrix of the treatment-specific event rates in a transformed scale, for example, the treatment-specific log-odds when a logit transformation is used. The commonly used conjugate prior for the covariance matrix, the inverse-Wishart (IW) distribution, has several limitations. For example, although the IW distribution is often described as noninformative or weakly informative, it may in fact provide strong information when some variance components are small (eg, when the standard deviation of study-specific log-odds of a treatment is smaller than 1/2), as is common in NMAs with binary outcomes. In addition, the IW prior generally leads to underestimation of correlations between treatment-specific log-odds, which are critical for borrowing strength across treatment arms to estimate treatment effects efficiently and to reduce potential bias. Alternatively, several separation strategies (ie, separate priors on variances and correlations) can be considered. To study the IW prior's impact on NMA results and compare it with separation strategies, we did simulation studies under different missing-treatment mechanisms. A separation strategy with appropriate priors for the correlation matrix and variances performs better than the IW prior, and should be recommended as the default vague prior in the AB NMA approach. Finally, we reanalyzed three case studies and illustrated the importance, when performing AB-NMA, of sensitivity analyses with different prior specifications on variances.

Meta-Modal Information Flow: A Method for Capturing Multimodal Modular Disconnectivity in Schizophrenia

OBJECTIVE

Multimodal measurements of the same phenomena provide complementary information and highlight different perspectives, albeit each with their own limitations. A focus on a single modality may lead to incorrect inferences, which is especially important when a studied phenomenon is a disease. In this paper, we introduce a method that takes advantage of multimodal data in addressing the hypotheses of disconnectivity and dysfunction within schizophrenia (SZ).

METHODS

We start with estimating and visualizing links within and among extracted multimodal data features using a Gaussian graphical model (GGM). We then propose a modularity-based method that can be applied to the GGM to identify links that are associated with mental illness across a multimodal data set. Through simulation and real data, we show our approach reveals important information about disease-related network disruptions that are missed with a focus on a single modality. We use functional MRI (fMRI), diffusion MRI (dMRI), and structural MRI (sMRI) to compute the fractional amplitude of low frequency fluctuations (fALFF), fractional anisotropy (FA), and gray matter (GM) concentration maps. These three modalities are analyzed using our modularity method.

RESULTS

Our results show missing links that are only captured by the cross-modal information that may play an important role in disconnectivity between the components.

CONCLUSION

We identified multimodal (fALFF, FA and GM) disconnectivity in the default mode network area in patients with SZ, which would not have been detectable in a single modality.

SIGNIFICANCE

The proposed approach provides an important new tool for capturing information that is distributed among multiple imaging modalities.

[Detection algorithm of paroxysmal atrial fibrillation with sparse coding based on Riemannian manifold]

In order to solve the problem that the early onset of paroxysmal atrial fibrillation is very short and difficult to detect, a detection algorithm based on sparse coding of Riemannian manifolds is proposed. The proposed method takes into account that the nonlinear manifold geometry is closer to the real feature space structure, and the computational covariance matrix is used to characterize the heart rate variability (RR interval variation), so that the data is in the Riemannian manifold space. Sparse coding is applied to the manifold, and each covariance matrix is represented as a sparse linear combination of Riemann dictionary atoms. The sparse reconstruction loss is defined by the affine invariant Riemannian metric, and the Riemann dictionary is learned by iterative method. Compared with the existing methods, this method used shorter heart rate variability signal, the calculation was simple and had no dependence on the parameters, and the better prediction accuracy was obtained. The final classification on MIT-BIH AF database resulted in a sensitivity of 99.34%, a specificity of 95.41% and an accuracy of 97.45%. At the same time, a specificity of 95.18% was realized in MIT-BIH NSR database. The high precision paroxysmal atrial fibrillation detection algorithm proposed in this paper has a potential application prospect in the long-term monitoring of wearable devices.

Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States

In the differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and momentum operators or quadrature components. Specifically, we obtain in generic form the differential equations for the covariance matrix, the mean values, and the density matrix parameters of a multipartite Gaussian state, unitarily evolving according to a Hamiltonian H^. We also present the corresponding differential equations, which describe the nonunitary evolution of the subsystems. The resulting nonlinear equations are used to solve the dynamics of the system instead of the Schrödinger equation. The formalism elaborated allows us to define new specific invariant and quasi-invariant states, as well as states with invariant covariance matrices, i.e., states were only the mean values evolve according to the classical Hamilton equations. By using density matrices in the position and in the tomographic-probability representations, we study examples of these properties. As examples, we present novel invariant states for the two-mode frequency converter and quasi-invariant states for the bipartite parametric amplifier.

The Transition from Evaluation to Selection Involves Neural Subspace Reorganization in Core Reward Regions

Economic choice proceeds from evaluation, in which we contemplate options, to selection, in which we weigh options and choose one. These stages must be differentiated so that decision makers do not proceed to selection before evaluation is complete. We examined responses of neurons in two core reward regions, orbitofrontal (OFC) and ventromedial prefrontal cortex (vmPFC), during two-option choice with asynchronous offer presentation. Our data suggest that neurons selective during the first (presumed evaluation) and second (presumed comparison and selection) offer epochs come from a single pool. Stage transition is accompanied by a shift toward orthogonality in the low-dimensional population response manifold. Nonetheless, the relative position of each option in driving responses in the population subspace is preserved. The orthogonalization we observe supports the hypothesis that the transition from evaluation to selection leads to reorganization of response subspace and suggests a mechanism by which value-related signals are prevented from prematurely driving choice.

Multitemporal SAR Image Despeckling Based on a Scattering Covariance Matrix of Image Patch

This paper presents a despeckling method for multitemporal images acquired by synthetic aperture radar (SAR) sensors. The proposed method uses a scattering covariance matrix of each image patch as the basic processing unit, which can exploit both the amplitude information of each pixel and the phase difference between any two pixels in a patch. The proposed filtering framework consists of four main steps: (1) a prefiltering result of each image is obtained by a nonlocal weighted average using only the information of the corresponding time phase; (2) an adaptively temporal linear filter is employed to further suppress the speckle; (3) the final output of each patch is obtained by a guided filter using both the original speckled data and the filtering result of step 3; and (4) an aggregation step is used to tackle the multiple estimations problem for each pixel. The despeckling experiments conducted on both simulated and real multitemporal SAR datasets reveal the pleasing performance of the proposed method in both suppressing speckle and retaining details, when compared with both advanced single-temporal and multitemporal SAR despeckling techniques.

Analyzing community structure subject to incomplete sampling: hierarchical community model vs. canonical ordinations

Recently developing hierarchical community models (HCMs) accounting for incomplete sampling are promising approaches to understand community organization. However, pros and cons of incorporating incomplete sampling in the analysis and related design issues remain unknown. In this study, we compared HCM and canonical redundancy analysis (RDA) carried out with 10 different dissimilarity coefficients to evaluate how each approach restores true community abundance data sampled with imperfect detection. We conducted simulation experiments with varying numbers of sampling sites, visits, mean detectability and mean abundance. Performance of HCM was measured by estimates of "expected" (mean) abundance ( λ ^ ij ) and realized abundance ( N ^ ij : direct estimate of site- and species-specific abundance). We also compared HCM and different types of RDA (normal, partial, and weighted), all performed with the same ten different dissimilarity coefficients, with unequal number of visits to sampling sites. In addition, we applied the models to a virtual survey carried out on the Barro Colorado Island tree plot data for which we know true community abundance. Simulation experiments showed that N ^ ij yielded by HCM best restored the underlying abundance of constituent species among 12 abundance estimates by HCM and RDA regardless if the sampling was equal or unequal. Mean abundance predominantly affected the performance of HCM and RDA while λ ^ ij yielded by HCM had comparable performance to percentage difference and Gower dissimilarity coefficients of RDA. Relative performance of RDA types depended on the combination of dissimilarity coefficients and the distribution of sampling effort. Best performance of N ^ ij followed by λ ^ ij , percentage difference and Gower dissimilarity were also observed for the analysis of tree plot data, and graphical plots (triplots) based on λ ^ ij rather than N ^ ij clearly separated the effects of two environmental covariates on the abundance of constituent species. Under our conditions of model evaluation and the method, we concluded that, in terms of assessing the environmental dependence of abundance, HCMs and RDA can have comparable performance if we can choose appropriate dissimilarity coefficients for RDA. However, since HCMs provide straightforward biological interpretations of parameter estimates and flexibility of the analysis, HCMs would be useful in many situations as well as conventional canonical ordinations.

Backward sensitivity analysis and reduced-order covariance estimation in noninvasive parameter identification for cerebral arteries

Using a previously developed inversion platform for functional cerebral medical imaging with ensemble Kalman filters, this work analyzes the sensitivity of the results with respect to different parameters entering the physical model and inversion procedure, such as the inlet flow rate from the heart, the choice of the boundary conditions, and the nonsymmetry in the network terminations. It also proposes an alternative low complexity construction for the covariance matrix of the hemodynamic parameters of a network of arteries including the circle of Willis. The platform takes as input patient-specific blood flow rates extracted from magnetic resonance angiography and magnetic resonance imaging (dicom files) and is applied to several available patients data. The paper presents full analysis of the results for one of these patients, including a sensitivity study with respect to the proximal and distal boundary conditions. The results notably show that the uncertainties on the inlet flow rate led to uncertainties of the same order of magnitude in the estimated parameters (blood pressure and elastic parameters) and that three-lumped parameters boundary conditions are necessary for a correct retrieval of the target signals.

Noise Suppression for Direction of Arrival Estimation in Co-located MIMO Sonar

Noise suppression capacity in multiple-input multiple-output (MIMO) sonar signal processing is derived under the assumption of white Gaussian noise. However, underwater noise mainly includes white Gaussian noise and colored noise. There exists a certain correlation between the noise signals received by each MIMO sonar array element. The performance of traditional direction-of-arrival (DOA) estimation methods decreases obviously in complex marine noise. In this paper, we propose a marine environment noise suppression method for MIMO applied to multiple targets’ DOA estimation. The noise field can be decomposed into a symmetric noise component and an asymmetric noise component. We use the covariance matrix imaginary component to pre-estimate the signal sources, then use the dimension reduction transformation to reconstruct the real component of the covariance matrix. The Toeplitz technique is utilized to reduce the correlation of the reconstructed covariance matrix. Thus, the subspace decomposition-based techniques such as multiple signal classification (MUSIC) can be used for multiple targets’ DOA estimation. To reduce the computational complexity of the methods, search-free direction-finding techniques such as the estimation of signal parameters via rotational invariance techniques (ESPRIT) can be utilized. As a result, the proposed methods can achieve better direction-finding performance in the condition of limited snapshots with lower computational cost. The corresponding Cramer-Rao bound (CRB) is deduced and the signal-to-noise ratio (SNR) gain obtained by dimension reduction processing is discussed. Simulation results also show the superiority of the proposed method over the existing methods.

A Novel Device-Free Counting Method Based on Channel Status Information

Crowd counting is of significant importance for numerous applications, e.g., urban security, intelligent surveillance and crowd management. Existing crowd counting methods typically require specialized hardware deployment and strict operating conditions, thereby hindering their widespread application. To acquire a more effective crowd counting approach, a device-free counting method based on Channel Status Information (CSI) is proposed. The wavelet domain denoising is introduced to mitigate environment noise. Furthermore, the amplitude or phase covariance matrix is extracted as the eigenmatrix. Moreover, both the spatial diversity and frequency diversity are leveraged to improve detection robustness. At the same experimental environment, the accuracy of the proposed CSI-based method is compared with a renowned crowd counting one, i.e., Electronic Frog Eye: Counting Crowd Using WiFi (FCC). The experimental results reveal an accuracy improvement of 30% over FCC.

Terahertz Imaging of Thin Film Layers with Matched Field Processing

Terahertz (THz) time of flight (TOF) tomography systems offer a new measurement modality for non-destructive evaluation (NDE) of the subsurface layers of protective coatings and/or laminated composite materials for industrial, security and biomedical applications. However, for thin film samples, the time-of-flight within a layer is less than the duration of the THz pulse and consequently there is insufficient range resolution for NDE of the sample under test. In this paper, matched field processing (MFP) techniques are applied to thickness estimation in THz TOF tomography applications, and these methods are demonstrated by using measured THz spectra to estimate the the thicknesses of a thin air gap and its depth below the surface. MFP methods have been developed over several decades in the underwater acoustics community for model-based inversion of geo-acoustic parameters. It is expected that this research will provide an important link for THz researchers to access and apply the robust methods available in the MFP literature.

A Closed-Form Error Model of Straight Lines for Improved Data Association and Sensor Fusing

Linear regression is a basic tool in mobile robotics, since it enables accurate estimation of straight lines from range-bearing scans or in digital images, which is a prerequisite for reliable data association and sensor fusing in the context of feature-based SLAM. This paper discusses, extends and compares existing algorithms for line fitting applicable also in the case of strong covariances between the coordinates at each single data point, which must not be neglected if range-bearing sensors are used. Besides, in particular, the determination of the covariance matrix is considered, which is required for stochastic modeling. The main contribution is a new error model of straight lines in closed form for calculating quickly and reliably the covariance matrix dependent on just a few comprehensible and easily-obtainable parameters. The model can be applied widely in any case when a line is fitted from a number of distinct points also without a priori knowledge of the specific measurement noise. By means of extensive simulations, the performance and robustness of the new model in comparison to existing approaches is shown.

Multi-Target Angle Tracking Algorithm for Bistatic Multiple-Input Multiple-Output (MIMO) Radar Based on the Elements of the Covariance Matrix

In this paper, we consider the problem of tracking the direction of arrivals (DOA) and the direction of departure (DOD) of multiple targets for bistatic multiple-input multiple-output (MIMO) radar. A high-precision tracking algorithm for target angle is proposed. First, the linear relationship between the covariance matrix difference and the angle difference of the adjacent moment was obtained through three approximate relations. Then, the proposed algorithm obtained the relationship between the elements in the covariance matrix difference. On this basis, the performance of the algorithm was improved by averaging the covariance matrix element. Finally, the least square method was used to estimate the DOD and DOA. The algorithm realized the automatic correlation of the angle and provided better performance when compared with the adaptive asymmetric joint diagonalization (AAJD) algorithm. The simulation results demonstrated the effectiveness of the proposed algorithm. The algorithm provides the technical support for the practical application of MIMO radar.

CAMERRA: An analysis tool for the computation of conformational dynamics by evaluating residue-residue associations

A computational method which extracts the dominant motions from an ensemble of biomolecular conformations via a correlation analysis of residue-residue contacts is presented. The algorithm first renders the structural information into contact matrices, then constructs the collective modes based on the correlated dynamics of a selected set of dynamic contacts. Associated programs can bridge the results for further visualization using graphics software. The aim of this method is to provide an analysis of conformations of biopolymers from the contact viewpoint. It may assist a systematical uncovering of conformational switching mechanisms existing in proteins and biopolymer systems in general by statistical analysis of simulation snapshots. In contrast to conventional correlation analyses of Cartesian coordinates (such as distance covariance analysis and Cartesian principal component analysis), this program also provides an alternative way to locate essential collective motions in general. Herein, we detail the algorithm in a stepwise manner and comment on the importance of the method as applied to decoding allosteric mechanisms. © 2018 Wiley Periodicals, Inc.

Estimation of surgical tool-tip tracking error distribution in coordinate reference frame involving pivot calibration uncertainty

Accurate understanding of surgical tool-tip tracking error is important for decision making in image-guided surgery. In this Letter, the authors present a novel method to estimate/model surgical tool-tip tracking error in which they take pivot calibration uncertainty into consideration. First, a new type of error that is referred to as total target registration error (TTRE) is formally defined in a single-rigid registration. Target localisation error (TLE) in two spaces to be registered is considered in proposed TTRE formulation. With first-order approximation in fiducial localisation error (FLE) or TLE magnitude, TTRE statistics (mean, covariance matrix and root-mean-square (RMS)) are then derived. Second, surgical tool-tip tracking error in optical tracking system (OTS) frame is formulated using TTRE when pivot calibration uncertainty is considered. Finally, TTRE statistics of tool-tip in OTS frame are then propagated relative to a coordinate reference frame (CRF) rigid-body. Monte Carlo simulations are conducted to validate the proposed error model. The percentage passing statistical tests that there is no difference between simulated and theoretical mean and covariance matrix of tool-tip tracking error in CRF space is more than 90% in all test cases. The RMS percentage difference between simulated and theoretical tool-tip tracking error in CRF space is within 5% in all test cases.

A New Low Complexity Angle of Arrival Algorithm for 1D and 2D Direction Estimation in MIMO Smart Antenna Systems

This paper proposes a new low complexity angle of arrival (AOA) method for signal direction estimation in multi-element smart wireless communication systems. The new method estimates the AOAs of the received signals directly from the received signals with significantly reduced complexity since it does not need to construct the correlation matrix, invert the matrix or apply eigen-decomposition, which are computationally expensive. A mathematical model of the proposed method is illustrated and then verified using extensive computer simulations. Both linear and circular sensors arrays are studied using various numerical examples. The method is systematically compared with other common and recently introduced AOA methods over a wide range of scenarios. The simulated results show that the new method has several advantages in terms of reduced complexity and improved accuracy under the assumptions of correlated signals and limited numbers of snapshots.

A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix

The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.

TESTING HIGH-DIMENSIONAL COVARIANCE MATRICES, WITH APPLICATION TO DETECTING SCHIZOPHRENIA RISK GENES

Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene "relationship" matrices that are of practical interest, such as the weighted adjacency matrices.

Considering Horn's Parallel Analysis from a Random Matrix Theory Point of View

Horn's parallel analysis is a widely used method for assessing the number of principal components and common factors. We discuss the theoretical foundations of parallel analysis for principal components based on a covariance matrix by making use of arguments from random matrix theory. In particular, we show that (i) for the first component, parallel analysis is an inferential method equivalent to the Tracy-Widom test, (ii) its use to test high-order eigenvalues is equivalent to the use of the joint distribution of the eigenvalues, and thus should be discouraged, and (iii) a formal test for higher-order components can be obtained based on a Tracy-Widom approximation. We illustrate the performance of the two testing procedures using simulated data generated under both a principal component model and a common factors model. For the principal component model, the Tracy-Widom test performs consistently in all conditions, while parallel analysis shows unpredictable behavior for higher-order components. For the common factor model, including major and minor factors, both procedures are heuristic approaches, with variable performance. We conclude that the Tracy-Widom procedure is preferred over parallel analysis for statistically testing the number of principal components based on a covariance matrix.

Concordance between stabilizing sexual selection, intraspecific variation, and interspecific divergence in Phymata

Empirical studies show that lineages typically exhibit long periods of evolutionary stasis and that relative levels of within-species trait covariance often correlate with the extent of between-species trait divergence. These observations have been interpreted by some as evidence of genetic constraints persisting for long periods of time. However, an alternative explanation is that both intra- and interspecific variation are shaped by the features of the adaptive landscape (e.g., stabilizing selection). Employing a genus of insects that are diverse with respect to a suite of secondary sex traits, we related data describing nonlinear phenotypic (sexual) selection to intraspecific trait covariances and macroevolutionary divergence. We found support for two key predictions (1) that intraspecific trait covariation would be aligned with stabilizing selection and (2) that there would be restricted macroevolutionary divergence in the direction of stabilizing selection. The observed alignment of all three matrices offers a point of caution in interpreting standing variability as metrics of evolutionary constraint. Our results also illustrate the power of sexual selection for determining variation observed at both short and long timescales and account for the apparently slow evolution of some secondary sex characters in this lineage.

A Comparison of Inverse-Wishart Prior Specifications for Covariance Matrices in Multilevel Autoregressive Models

Multilevel autoregressive models are especially suited for modeling between-person differences in within-person processes. Fitting these models with Bayesian techniques requires the specification of prior distributions for all parameters. Often it is desirable to specify prior distributions that have negligible effects on the resulting parameter estimates. However, the conjugate prior distribution for covariance matrices-the Inverse-Wishart distribution-tends to be informative when variances are close to zero. This is problematic for multilevel autoregressive models, because autoregressive parameters are usually small for each individual, so that the variance of these parameters will be small. We performed a simulation study to compare the performance of three Inverse-Wishart prior specifications suggested in the literature, when one or more variances for the random effects in the multilevel autoregressive model are small. Our results show that the prior specification that uses plug-in ML estimates of the variances performs best. We advise to always include a sensitivity analysis for the prior specification for covariance matrices of random parameters, especially in autoregressive models, and to include a data-based prior specification in this analysis. We illustrate such an analysis by means of an empirical application on repeated measures data on worrying and positive affect.

Inference for High-dimensional Differential Correlation Matrices

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.

EvolQG - An R package for evolutionary quantitative genetics

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.

EvolQG - An R package for evolutionary quantitative genetics

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.

Benefits of statistical molecular design, covariance analysis, and reference models in QSAR: a case study on acetylcholinesterase

Scientific disciplines such as medicinal- and environmental chemistry, pharmacology, and toxicology deal with the questions related to the effects small organic compounds exhort on biological targets and the compounds' physicochemical properties responsible for these effects. A common strategy in this endeavor is to establish structure-activity relationships (SARs). The aim of this work was to illustrate benefits of performing a statistical molecular design (SMD) and proper statistical analysis of the molecules' properties before SAR and quantitative structure-activity relationship (QSAR) analysis. Our SMD followed by synthesis yielded a set of inhibitors of the enzyme acetylcholinesterase (AChE) that had very few inherent dependencies between the substructures in the molecules. If such dependencies exist, they cause severe errors in SAR interpretation and predictions by QSAR-models, and leave a set of molecules less suitable for future decision-making. In our study, SAR- and QSAR models could show which molecular sub-structures and physicochemical features that were advantageous for the AChE inhibition. Finally, the QSAR model was used for the prediction of the inhibition of AChE by an external prediction set of molecules. The accuracy of these predictions was asserted by statistical significance tests and by comparisons to simple but relevant reference models.

Joint Estimation of Multiple Precision Matrices with Common Structures

Estimation of inverse covariance matrices, known as precision matrices, is important in various areas of statistical analysis. In this article, we consider estimation of multiple precision matrices sharing some common structures. In this setting, estimating each precision matrix separately can be suboptimal as it ignores potential common structures. This article proposes a new approach to parameterize each precision matrix as a sum of common and unique components and estimate multiple precision matrices in a constrained l₁ minimization framework. We establish both estimation and selection consistency of the proposed estimator in the high dimensional setting. The proposed estimator achieves a faster convergence rate for the common structure in certain cases. Our numerical examples demonstrate that our new estimator can perform better than several existing methods in terms of the entropy loss and Frobenius loss. An application to a glioblastoma cancer data set reveals some interesting gene networks across multiple cancer subtypes.

An efficient technique for Bayesian modeling of family data using the BUGS software

Linear mixed models have become a popular tool to analyze continuous data from family-based designs by using random effects that model the correlation of subjects from the same family. However, mixed models for family data are challenging to implement with the BUGS (Bayesian inference Using Gibbs Sampling) software because of the high-dimensional covariance matrix of the random effects. This paper describes an efficient parameterization that utilizes the singular value decomposition of the covariance matrix of random effects, includes the BUGS code for such implementation, and extends the parameterization to generalized linear mixed models. The implementation is evaluated using simulated data and an example from a large family-based study is presented with a comparison to other existing methods.

Meta-Analysis of the Factor Structures of the Beck Depression Inventory-II

Two meta-analyses examined the factor structure of the Beck Depression Inventory-II (BDI-II). Study 1, which meta-analyzed 51 studies comprising 62 samples (N = 20,475) providing pattern matrices, determined that the two-factor solution comprising Cognitive and Somatic-Affective factors was supported for the full sample. The two-factor solution was also supported for subgroups of studies. As the factor structure varied somewhat between subgroups of studies, the strength of relationships between scale items and their underlying depressive symptoms varied. Hence, comparisons of mean BDI-II scores across subgroups can be misleading. Study 2 meta-analyzed 13 studies consisting of 16 samples (N = 5,128) providing covariance matrices among the 21 BDI-II items. The two-factor solution was again supported in Study 2. Nevertheless, the existence of a general depression factor was supported by the good fit of the one-factor model.

Modeling and Control of Nonstationary Noise Characteristics in Filtered-Backprojection and Penalized Likelihood Image Reconstruction

Purpose

Nonstationarity of CT noise presents a major challenge to the assessment of image quality. This work presents models for imaging performance in both filtered backprojection (FBP) and penalized likelihood (PL) reconstruction that describe not only the dependence on the imaging chain but also the dependence on the object as well as the nonstationary characteristics of the signal and noise. The work furthermore demonstrates the ability to impart control over the imaging process by adjusting reconstruction parameters to exploit nonstationarity in a manner advantageous to a particular imaging task.

Methods

A cascaded systems analysis model was used to model the local noise-power spectrum (NPS) and modulation transfer function (MTF) for FBP reconstruction, with locality achieved by separate calculation of fluence and system gain for each view as a function of detector location. The covariance and impulse response function for PL reconstruction (quadratic penalty) were computed using the implicit function theorem and Taylor expansion. Detectability index was calculated under the assumption of local stationarity to show the variation in task-dependent image quality throughout the image for simple and complex, heterogeneous objects. Control of noise magnitude and correlation was achieved by applying a spatially varying roughness penalty in PL reconstruction in a manner that improved overall detectability.

Results

The models provide a foundation for task-based imaging performance assessment in FBP and PL image reconstruction. For both FBP and PL, noise is anisotropic and varies in a manner dependent on the path length of each view traversing the object. The anisotropy in turn affects task performance, where detectability is enhanced or diminished depending on the frequency content of the task relative to that of the NPS. Spatial variation of the roughness penalty can be exploited to control noise magnitude and correlation (and hence detectability).

Conclusions

Nonstationarity of image noise is a significant effect that can be modeled in both FBP and PL image reconstruction. Prevalent spatial-frequency-dependent metrics of spatial resolution and noise can be analyzed under assumptions of local stationarity, providing a means to analyze imaging performance as a function of location throughout the image. Knowledgeable selection of a spatially-varying roughness penalty in PL can potentially improve local noise and spatial resolution in a manner tuned to a particular imaging task.

Estimation of inferential uncertainty in assessing expert segmentation performance from STAPLE

The evaluation of the quality of segmentations of an image, and the assessment of intra- and inter-expert variability in segmentation performance, has long been recognized as a difficult task. For a segmentation validation task, it may be effective to compare the results of an automatic segmentation algorithm to multiple expert segmentations. Recently an expectation-maximization (EM) algorithm for simultaneous truth and performance level estimation (STAPLE) was developed to this end to compute both an estimate of the reference standard segmentation and performance parameters from a set of segmentations of an image. The performance is characterized by the rate of detection of each segmentation label by each expert in comparison to the estimated reference standard. This previous work provides estimates of performance parameters,but does not provide any information regarding the uncertainty of the estimated values. An estimate of this inferential uncertainty, if available, would allow the estimation of confidence intervals for the values of the parameters. This would facilitate the interpretation of the performance of segmentation generators and help determine if sufficient data size and number of segmentations have been obtained to precisely characterize the performance parameters. We present a new algorithm to estimate the inferential uncertainty of the performance parameters for binary and multi-category segmentations. It is derived for the special case of the STAPLE algorithm based on established theory for general purpose covariance matrix estimation for EM algorithms. The bounds on the performance parameters are estimated by the computation of the observed information matrix.We use this algorithm to study the bounds on performance parameters estimates from simulated images with specified performance parameters, and from interactive segmentations of neonatal brain MRIs. We demonstrate that confidence intervals for expert segmentation performance parameters can be estimated with our algorithm. We investigate the influence of the number of experts and of the segmented data size on these bounds, showing that it is possible to determine the number of image segmentations and the size of images necessary to achieve a chosen level of accuracy in segmentation performance assessment.

Dynamic conditionally linear mixed models for longitudinal data

We develop a new class of models, dynamic conditionally linear mixed models, for longitudinal data by decomposing the within-subject covariance matrix using a special Cholesky decomposition. Here 'dynamic' means using past responses as covariates and 'conditional linearity' means that parameters entering the model linearly may be random, but nonlinear parameters are nonrandom. This setup offers several advantages and is surprisingly similar to models obtained from the first-order linearization method applied to nonlinear mixed models. First, it allows for flexible and computationally tractable models that include a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, e.g., all standard linear mixed models, antedependence models, and Vonesh-Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited.