Handling parametric assumptions in principal causal effect estimation using Gaussian mixtures

Given the latent stratum membership, principal stratification models with continuous outcomes naturally fit in the parametric estimation framework of Gaussian mixtures. However, with models that are not nonparametrically identified, relying on parametric mixture modeling has been mostly discouraged as a way of identifying principal effects. This study revisits this rather deserted use of parametric mixture modeling, which may open up various possibilities in principal stratification modeling. The main problem with using the parametric mixture modeling approach is that it is hard to assess the quality of principal effect estimates given its reliance on parametric conditions. As a way of assessing the estimation quality in this situation, this study proposes that we use parametric mixture modeling in two different ways, with and without the assurance of nonparametric identification. The key identifying assumption employed in this study is the moving exclusion restriction, a flexible version of the standard exclusion restriction assumption. This assumption is used as a temporary vehicle to help assess the quality of principal effect estimates obtained relying on parametric mixture modeling. The study presents promising results, showing the possibility of using parametric mixture modeling as an accessible tool for causal inference.

An investigation of higher order moments of empirical financial data and their implications to risk

Here, we analyse the behaviour of the higher order standardised moments of financial time series when we truncate a large data set into smaller and smaller subsets, referred to below as time windows. We look at the effect of the economic environment on the behaviour of higher order moments in these time windows. We observe two different scaling relations of higher order moments when the data sub sets' length decreases; one for longer time windows and another for the shorter time windows. These scaling relations drastically change when the time window encompasses a financial crisis. We also observe a qualitative change of higher order standardised moments compared to the gaussian values in response to a shrinking time window. Moreover, we model the observed scaling laws by analysing the hierarchy of rare events on higher order moments. We extend the analysis of the scaling relations to incorporate the effects these scaling relations have upon risk. We decompose the return series within these time windows and carry out a Value-at-Risk calculation. In doing so, we observe the manifestation of the scaling relations through the change in the Value-at-Risk level.

Within Reach? Habitat Availability as a Function of Individual Mobility and Spatial Structuring

Organisms need access to particular habitats for their survival and reproduction. However, even if all necessary habitats are available within the broader environment, they may not all be easily reachable from the position of a single individual. Many species distribution models consider populations in environmental (or niche) space, hence overlooking this fundamental aspect of geographical accessibility. Here, we develop a formal way of thinking about habitat availability in environmental spaces by describing how limitations in accessibility can cause animals to experience a more limited or simply different mixture of habitats than those more broadly available. We develop an analytical framework for characterizing constrained habitat availability based on the statistical properties of movement and environmental autocorrelation. Using simulation experiments, we show that our general statistical representation of constrained availability is a good approximation of habitat availability for particular realizations of landscape-organism interactions. We present two applications of our approach, one to the statistical analysis of habitat preference (using step-selection functions to analyze harbor seal telemetry data) and a second that derives theoretical insights about population viability from knowledge of the underlying environment. Analytical expressions for habitat availability, such as those we develop here, can yield gains in analytical speed, biological realism, and conceptual generality by allowing us to formulate models that are habitat sensitive without needing to be spatially explicit.

Developing of robust and high accurate ECG beat classification by combining Gaussian mixtures and wavelets features

Electrocardiogram (ECG) beat classification is a significant application in computer-aided analysis and diagnosis technologies. This paper proposed a method to detect, extract informative features, and classify ECG beats utilizing real ECG signals available in the standard MIT-BIH Arrhythmia database, with 10,502 beats had been extracted from it. The present study classifies the ECG beat into six classes, normal beat (N), Left bundle branch block beat, Right bundle branch block beat, Premature ventricular contraction, atrial premature beat, and aberrated atrial premature, using Gaussian mixture and wavelets features, and by applying principal component analysis for feature set reduction. The classification process is implemented utilizing two classifier techniques, the probabilistic neural network (PNN) algorithm and Random Forest (RF) algorithm. The achieved accuracy is 99.99%, and 99.97% for PNN and RF respectively. The precision is 99.99%, and 99.98% for PNN and RF respectively. The sensitivity is 99.99%, and 99.81% for PNN and RF respectively, while the specificity is 99.97%, 99.96% for PNN and RF respectively. It has been shown that the combination of Gaussian mixtures coefficients and the wavelets features have provided a valuable information about the heart performance and can be used significantly in arrhythmia classification.

Joint modeling of survival time and longitudinal outcomes with flexible random effects

Joint models with shared Gaussian random effects have been conventionally used in analysis of longitudinal outcome and survival endpoint in biomedical or public health research. However, misspecifying the normality assumption of random effects can lead to serious bias in parameter estimation and future prediction. In this paper, we study joint models of general longitudinal outcomes and survival endpoint but allow the underlying distribution of shared random effect to be completely unknown. For inference, we propose to use a mixture of Gaussian distributions as an approximation to this unknown distribution and adopt an Expectation-Maximization (EM) algorithm for computation. Either AIC and BIC criteria are adopted for selecting the number of mixtures. We demonstrate the proposed method via a number of simulation studies. We illustrate our approach with the data from the Carolina Head and Neck Cancer Study (CHANCE).

Sensor Fusion of Gaussian Mixtures for Ballistic Target Tracking in the Re-Entry Phase

A sensor fusion methodology for the Gaussian mixtures model is proposed for ballistic target tracking with unknown ballistic coefficients. To improve the estimation accuracy, a track-to-track fusion architecture is proposed to fuse tracks provided by the local interacting multiple model filters. During the fusion process, the duplicate information is removed by considering the first order redundant information between the local tracks. With extensive simulations, we show that the proposed algorithm improves the tracking accuracy in ballistic target tracking in the re-entry phase applications.

Bayesian random effects selection in mixed accelerated failure time model for interval-censored data

In many medical problems that collect multiple observations per subject, the time to an event is often of interest. Sometimes, the occurrence of the event can be recorded at regular intervals leading to interval-censored data. It is further desirable to obtain the most parsimonious model in order to increase predictive power and to obtain ease of interpretation. Variable selection and often random effects selection in case of clustered data become crucial in such applications. We propose a Bayesian method for random effects selection in mixed effects accelerated failure time (AFT) models. The proposed method relies on the Cholesky decomposition on the random effects covariance matrix and the parameter-expansion method for the selection of random effects. The Dirichlet prior is used to model the uncertainty in the random effects. The error distribution for the accelerated failure time model has been specified using a Gaussian mixture to allow flexible error density and prediction of the survival and hazard functions. We demonstrate the model using extensive simulations and the Signal Tandmobiel Study(®).