Methodology (stat.ME)

Abstract: Step-selection models are widely used to study animals' fine-scale habitat selection based on movement data. Resource preferences and movement patterns, however, can depend on the animal's unobserved behavioural states, such as resting or foraging. This is ignored in standard (integrated) step-selection analyses (SSA, iSSA). While different approaches have emerged to account for such states in the analysis, the performance of such approaches and the consequences of ignoring the states in the analysis have rarely been quantified. We evaluated the recent idea of combining hidden Markov chains and iSSA in a single modelling framework. The resulting Markov-switching integrated step-selection analysis (MS-iSSA) allows for a joint estimation of both the underlying behavioural states and the associated state-dependent habitat selection. In an extensive simulation study, we compared the MS-iSSA to both the standard iSSA and a classification-based iSSA (i.e., a two-step approach based on a separate prior state classification). We further illustrate the three approaches in a case study on fine-scale interactions of simultaneously tracked bank voles (Myodes glareolus). The results indicate that standard iSSAs can lead to erroneous conclusions due to both biased estimates and unreliable p-values when ignoring underlying behavioural states. We found the same for iSSAs based on prior state-classifications, as they ignore misclassifications and classification uncertainties. The MS-iSSA, on the other hand, performed well in parameter estimation and decoding of behavioural states. To facilitate its use, we implemented the MS-iSSA approach in the R package msissa available on GitHub.

Abstract: Precision medicine seeks to discover an optimal personalized treatment plan and thereby provide informed and principled decision support, based on the characteristics of individual patients. With recent advancements in medical imaging, it is crucial to incorporate patient-specific imaging features in the study of individualized treatment regimes. We propose a novel, data-driven method to construct interpretable image features which can be incorporated, along with other features, to guide optimal treatment regimes. The proposed method treats imaging information as a realization of a stochastic process, and employs smoothing techniques in estimation. We show that the proposed estimators are consistent under mild conditions. The proposed method is applied to a dataset provided by the Alzheimer's Disease Neuroimaging Initiative.

Abstract: In this paper, we show that the halfspace depth random variable for samples from a univariate distribution with a notion of center is distributed as a uniform distribution on the interval [0,1/2]. The simplicial depth random variable has a distribution that first-order stochastic dominates that of the halfspace depth random variable and relates to a Beta distribution. Depth-induced divergences between two univariate distributions can be defined using divergences on the distributions for the statistical depth random variables in-between these two distributions. We discuss the properties of such induced divergences, particularly the depth-induced TVD distance based on halfspace or simplicial depth functions, and how empirical two-sample estimators benefit from such transformations.

Abstract: We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators, and its hyperparameters can be decided using cross validation. We define our estimators by taking integral transforms of kernel-based distribution surrogates. We then use the iterated density estimation evolutionary algorithm, a variant of estimation of distribution algorithms, to fit the estimators. We also extend our method to estimate covariance functions for point-referenced data. Compared to alternative approaches, our method provides more reliable estimates for long-range dependence. Several numerical studies are performed to demonstrate the efficacy and performance of our method. Also, we illustrate our method using precipitation data from the Spatial Interpolation Comparison 97 project.

Abstract: We use a Stein identity to define a new class of parametric distributions which we call ``independent additive weighted bias distributions.'' We investigate related $L^2$-type discrepancy measures, empirical versions of which not only encompass traditional ODE-based procedures but also offer novel methods for conducting goodness-of-fit tests in composite hypothesis testing problems. We determine critical values for these new procedures using a parametric bootstrap approach and evaluate their power through Monte Carlo simulations. As an illustration, we apply these procedures to examine the compatibility of two real data sets with a compound Poisson Gamma distribution.