Estimating Mean Dimensionality of Analysis of Variance Decompositions

Global Sensitivity Analysis with Mixtures: A Generalized Functional ANOVA Approach

This work investigates aspects of the global sensitivity analysis of computer codes when alternative plausible distributions for the model inputs are available to the analyst. Analysts may decide to explore results under each distribution or to aggregate the distributions, assigning, for instance, a mixture. In the first case, we lose uniqueness of the sensitivity measures, and in the second case, we lose independence even if the model inputs are independent under each of the assigned distributions. Removing the unique distribution assumption impacts the mathematical properties at the basis of variance-based sensitivity analysis and has consequences on result interpretation as well. We analyze in detail the technical aspects. From this investigation, we derive corresponding recommendations for the risk analyst. We show that an approach based on the generalized functional ANOVA expansion remains theoretically grounded in the presence of a mixture distribution. Numerically, we base the construction of the generalized function ANOVA effects on the diffeomorphic modulation under observable response preserving homotopy regression. Our application addresses the calculation of variance-based sensitivity measures for the well-known Nordhaus' DICE model, when its inputs are assigned a mixture distribution. A discussion of implications for the risk analyst and future research perspectives closes the work.

Global Sensitivity Analysis of Various Numerical Schemes for the Heston Model

The pricing of financial options is usually based on statistical sampling of the evolution of the underlying under a chosen model, using a suitable numerical scheme. It is widely accepted that using low-discrepancy sequences instead of pseudorandom numbers in most cases increases the accuracy. It is important to understand and quantify the reasons for this effect. In this work, we use Global Sensitivity Analysis in order to study one widely used model for pricing of options, namely the Heston model. The Heston model is an important member of the family of the stochastic volatility models, which have been found to better describe the observed behaviour of option prices in the financial markets. By using a suitable numerical scheme, like those of Euler, Milstein, Kahl-Jäckel, Andersen, one has the flexibility needed to compute European, Asian or exotic options. In any case the problem of evaluating an option price can be considered as a numerical integration problem. For the purposes of modelling and complexity reduction, one should make the distinction between the model nominal dimension and its effective dimension. Another notion of “average dimension” has been found to be more practical from the computational point of view. The definitions and methods of evaluation of effective dimensions are based on computing Sobol’ sensitivity indices. A classification of functions based on their effective dimensions is also known. In the context of quantitative finance, Global Sensitivity Analysis (GSA) can be used to assess the efficiency of a particular numerical scheme. In this work we apply GSA based on Sobol sensitivity indices in order to assess the interactions of the various dimensions in using the above mentioned schemes. We observe that the GSA offers useful insight on how to maximize the advantages of using QMC in these schemes.

Short-Term Antiretroviral Treatment Recommendations Based on Sensitivity Analysis of a Mathematical Model for HIV Infection of CD₄⁺Τ Cells

HIV infection is one of the most difficult infections to control and manage. The most recent recommendations to control this infection vary according to the guidelines used (US, European, WHO) and are not patient-specific. Unfortunately, no two individuals respond to infection and treatment quite the same way. The purpose of this paper is to make use of the uncertainty and sensitivity analysis to investigate possible short-term treatment options that are patient-specific. We are able to identify the most significant parameters that are responsible for ART outcome and to formulate some insights into the ART success.

Combining Two Methods of Global Sensitivity Analysis to Investigate MRSA Nasal Carriage Model

We apply two different sensitivity techniques to a model of bacterial colonization of the anterior nares to better understand the dynamics of Staphylococcus aureus nasal carriage. Specifically, we use partial rank correlation coefficients to investigate sensitivity as a function of time and identify a reduced model with fewer than half of the parameters of the full model. The reduced model is used for the calculation of Sobol' indices to identify interacting parameters by their additional effects indices. Additionally, we found that the model captures an interesting characteristic of the biological phenomenon related to the initial population size of the infection; only two parameters had any significant additional effects, and these parameters have biological evidence suggesting they are connected but not yet completely understood. Sensitivity is often applied to elucidate model robustness, but we show that combining sensitivity measures can lead to synergistic insight into both model and biological structures.

Global sensitivity analysis used to interpret biological experimental results

Modeling host/pathogen interactions provides insight into immune defects that allow bacteria to overwhelm the host, mechanisms that allow vaccine strategies to be successful, and illusive interactions between immune components that govern the immune response to a challenge. However, even simplified models require a fairly high dimensional parameter space to be explored. Here we use global sensitivity analysis for parameters in a simple model for biofilm infections in mice. The results indicate which parameters are insignificant and are 'frozen' to yield a reduced model. The reduced model replicates the full model with high accuracy, using approximately half of the parameter space. We used the sensitivity to investigate the results of the combined biological and mathematical experiments for osteomyelitis. We are able to identify parts of the compartmentalized immune system that were responsible for each of the experimental outcomes. This model is one example for a technique that can be used generally.