arXiv subjects

Dipak K. Dey

Publications and source records attributed to Dipak K. Dey.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Feature Extraction using Gaussian and Diffused-gamma Priors for High Dimensional Spatio-Temporal Data

High-dimensional data with sparse structure and spatio-temporal dependence arise in many scientific domains. We develop a Bayesian feature-extraction framework for spatio-temporal settings that employs Gaussian and Diffused-gamma priors to induce structured sparsity. The modeling framework specifies a general likelihood via Bregman divergence, enabling compatibility with a range of loss functions and measurement models. Posterior computation is carried out via Markov chain Monte Carlo (MCMC), and we introduce a two-stage feature-extraction procedure based on posterior samples to stabilize selection across space and time. We illustrate the method with a multi-subject electroencephalography (EEG) case study examining the relationship between chronic alcohol exposure and activity in different brain regions. We first fit binary classification models at each time point, then use false discovery rate-controlled screening and subsequent clustering in a two-stage feature-extraction pipeline to identify active brain regions. The analysis demonstrates that our proposed priors improve recovery of sparse features and enhance interpretability in the presence of spatio-temporal dependence. The framework is broadly applicable to high-dimensional, structured problems where accurate feature selection and inference are required. The code to implement the model is publicly available via GitHub.

stat.ME↗

arXiv2026

Robust Bayesian Predictive Model Selection using Bregman Divergence

Predictive Bayesian model comparison often relies on leave-one-out (LOO) cross-validation criteria such as the expected log predictive density (ELPD). However, model rankings can be overly sensitive to outliers and tail mismatch because ELPD is based on the log score. We propose a score-matched generalized ELPD framework that replaces the log score by a Bregman scoring rule to update model parameters through a generalized posterior and to evaluate LOO predictive utility. Candidate posterior predictive distributions are ranked by out-of-sample utility under the chosen scoring rule, yielding a direct proper-score generalization of standard ELPD. We focus especially on the $β$-divergence family, where $β$ controls the sensitivity of predictive comparison to low-density observations. Under model misspecification, the procedure asymptotically selects the model whose predictive distribution is closest to the data-generating process under the chosen Bregman divergence. A simulation study and applications to microbial and forensic data show that the generalized ELPD can change the selected model through reduced sensitivity to low-density observations.

stat.ME↗

arXiv2026

Scalable spatial point process models for forensic footwear analysis

Shoe print evidence recovered from crime scenes plays a key role in forensic investigations. By examining shoe prints, investigators can determine details of the footwear worn by suspects. However, establishing that a suspect's shoes match the make and model of a crime scene print may not be sufficient. Typically, thousands of shoes of the same size, make, and model are manufactured, any of which could be responsible for the print. Accordingly, a popular approach used by investigators is to examine the print for signs of ``accidentals,'' i.e., cuts, scrapes, and other features that accumulate on shoe soles after purchase due to wear. While some patterns of accidentals are common on certain types of shoes, others are highly distinctive, potentially distinguishing the suspect's shoe from all others. Quantifying the rarity of a pattern is thus essential to accurately measuring the strength of forensic evidence. In this study, we address this task by developing a hierarchical Bayesian model. Our improvement over existing methods primarily stems from two advancements. First, we frame our approach in terms of a latent Gaussian model, thus enabling inference to be efficiently scaled to large collections of annotated shoe prints via integrated nested Laplace approximations. Second, we incorporate spatially varying coefficients to model the relationship between shoes' tread patterns and accidental locations. We demonstrate these improvements through superior performance on held-out data, which enhances accuracy and reliability in forensic shoe print analysis.

cs.CV↗

arXiv2025

Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data

The Tweedie exponential dispersion family is a popular choice among many to model insurance losses that consist of zero-inflated semicontinuous data. In such data, it is often important to obtain credibility (inference) of the most important features that describe the endogenous variables. Post-selection inference is the standard procedure in statistics to obtain confidence intervals of model parameters after performing a feature extraction procedure. For a linear model, the lasso estimate often has non-negligible estimation bias for large coefficients corresponding to exogenous variables. To have valid inference on those coefficients, it is necessary to correct the bias of the lasso estimate. Traditional statistical methods, such as hypothesis testing or standard confidence interval construction might lead to incorrect conclusions during post-selection, as they are generally too optimistic. Here we discuss a few methodologies for constructing confidence intervals of the coefficients after feature selection in the Generalized Linear Model (GLM) family with application to insurance data.

stat.ME↗

arXiv2025

Distribution-free inference for LightGBM and GLM with Tweedie loss

Prediction uncertainty quantification is a key research topic in recent years scientific and business problems. In insurance industries (\cite{parodi2023pricing}), assessing the range of possible claim costs for individual drivers improves premium pricing accuracy. It also enables insurers to manage risk more effectively by accounting for uncertainty in accident likelihood and severity. In the presence of covariates, a variety of regression-type models are often used for modeling insurance claims, ranging from relatively simple generalized linear models (GLMs) to regularized GLMs to gradient boosting models (GBMs). Conformal predictive inference has arisen as a popular distribution-free approach for quantifying predictive uncertainty under relatively weak assumptions of exchangeability, and has been well studied under the classic linear regression setting. In this work, we propose new non-conformity measures for GLMs and GBMs with GLM-type loss. Using regularized Tweedie GLM regression and LightGBM with Tweedie loss, we demonstrate conformal prediction performance with these non-conformity measures in insurance claims data. Our simulation results favor the use of locally weighted Pearson residuals for LightGBM over other methods considered, as the resulting intervals maintained the nominal coverage with the smallest average width.

stat.ML↗

arXiv2024

Improving Opioid Use Disorder Risk Modelling through Behavioral and Genetic Feature Integration

Opioids are an effective analgesic for acute and chronic pain, but also carry a considerable risk of addiction leading to millions of opioid use disorder (OUD) cases and tens of thousands of premature deaths in the United States yearly. Estimating OUD risk prior to prescription could improve the efficacy of treatment regimens, monitoring programs, and intervention strategies, but risk estimation is typically based on self-reported data or questionnaires. We develop an experimental design and computational methods that combine genetic variants associated with OUD with behavioral features extracted from GPS and Wi-Fi spatiotemporal coordinates to assess OUD risk. Since both OUD mobility and genetic data do not exist for the same cohort, we develop algorithms to (1) generate mobility features from empirical distributions and (2) synthesize mobility and genetic samples assuming an expected level of disease co-occurrence. We show that integrating genetic and mobility modalities improves risk modelling using classification accuracy, area under the precision-recall and receiver operator characteristic curves, and $F_1$ score. Interpreting the fitted models suggests that mobility features have more influence on OUD risk, although the genetic contribution was significant, particularly in linear models. While there exist concerns with respect to privacy, security, bias, and generalizability that must be evaluated in clinical trials before being implemented in practice, our framework provides preliminary evidence that behavioral and genetic features may improve OUD risk estimation to assist with personalized clinical decision-making.

q-bio.QM↗

arXiv2023

A Mixed-Membership Model for Social Network Clustering

We propose a simple mixed membership model for social network clustering in this paper. A flexible function is adopted to measure affinities among a set of entities in a social network. The model not only allows each entity in the network to possess more than one membership, but also provides accurate statistical inference about network structure. We estimate the membership parameters using an MCMC algorithm. We evaluate the performance of the proposed algorithm by applying our model to two empirical social network data, the Zachary club data and the bottlenose dolphin network data. We also conduct some numerical studies based on synthetic networks for further assessing the effectiveness of our algorithm. In the end, some concluding remarks and future work are addressed briefly.

stat.AP↗

arXiv2023

Bayesian Variable Selection in Double Generalized Linear Tweedie Spatial Process Models

Double generalized linear models provide a flexible framework for modeling data by allowing the mean and the dispersion to vary across observations. Common members of the exponential dispersion family including the Gaussian, Poisson, compound Poisson-gamma (CP-g), Gamma and inverse-Gaussian are known to admit such models. The lack of their use can be attributed to ambiguities that exist in model specification under a large number of covariates and complications that arise when data display complex spatial dependence. In this work we consider a hierarchical specification for the CP-g model with a spatial random effect. The spatial effect is targeted at performing uncertainty quantification by modeling dependence within the data arising from location based indexing of the response. We focus on a Gaussian process specification for the spatial effect. Simultaneously, we tackle the problem of model specification for such models using Bayesian variable selection. It is effected through a continuous spike and slab prior on the model parameters, specifically the fixed effects. The novelty of our contribution lies in the Bayesian frameworks developed for such models. We perform various synthetic experiments to showcase the accuracy of our frameworks. They are then applied to analyze automobile insurance premiums in Connecticut, for the year of 2008.

stat.ME↗

arXiv2023

Spatial Clustering Regression of Count Value Data via Bayesian Mixture of Finite Mixtures

Investigating relationships between response variables and covariates in areas such as environmental science, geoscience, and public health is an important endeavor. Based on a Bayesian mixture of finite mixtures model, we present a novel spatially clustered coefficients regression model for count value data. The proposed method detects the spatial homogeneity of the Poisson regression coefficients. A Markov random field constrained mixture of finite mixtures prior provides a regularized estimator of the number of clusters of regression coefficients with geographical neighborhood information. As a by-product, we also provide the theoretical properties of our proposed method when the Markov random field is exchangeable. An efficient Markov chain Monte Carlo algorithm is developed by using the multivariate log gamma distribution as a base distribution. Simulation studies are carried out to examine the empirical performance of the proposed method. Additionally, we analyze Georgia's premature death data as an illustration of the effectiveness of our approach. The supplementary materials are provided on GitHub at \url{https://github.com/pengzhaostat/MLG_MFM}.

stat.ME↗

arXiv2023

Bayesian modeling with spatial curvature processes

Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as \emph{wombling} boundaries, occur in geographic space in the form of rivers in a flood plain, roads, mountains or plateaus or other topographic features leading to high gradients on the response surface. We demonstrate fully model based Bayesian inference on directional curvature processes to analyze differential behavior in responses along wombling boundaries. We illustrate our methodology with a number of simulated experiments followed by multiple applications featuring the Boston Housing data; Meuse river data; and temperature data from the Northeastern United States.

stat.ME↗

arXiv2021

Zero Inflated Poisson Model with Clustered Regression Coefficients: an Application to Heterogeneity Learning of Field Goal Attempts of Professional Basketball Players

Although basketball is a dynamic process sport, with 5 plus 5 players competing on both offense and defense simultaneously, learning some static information is predominant for professional players, coaches and team mangers. In order to have a deep understanding of field goal attempts among different players, we propose a zero inflated Poisson model with clustered regression coefficients to learn the shooting habits of different players over the court and the heterogeneity among them. Specifically, the zero inflated model recovers the large proportion of the court with zero field goal attempts, and the mixture of finite mixtures model learn the heterogeneity among different players based on clustered regression coefficients and inflated probabilities. Both theoretical and empirical justification through simulation studies validate our proposed method. We apply our proposed model to the National Basketball Association (NBA), for learning players' shooting habits and heterogeneity among different players over the 2017--2018 regular season. This illustrates our model as a way of providing insights from different aspects.

stat.AP↗

arXiv2021

Fast Bayesian inference of Block Nearest Neighbor Gaussian process for large data

This paper presents the development of a spatial block-Nearest Neighbor Gaussian process (block-NNGP) for location-referenced large spatial data. The key idea behind this approach is to divide the spatial domain into several blocks which are dependent under some constraints. The cross-blocks capture the large-scale spatial dependence, while each block captures the small-scale spatial dependence. The resulting block-NNGP enjoys Markov properties reflected on its sparse precision matrix. It is embedded as a prior within the class of latent Gaussian models, thus Bayesian inference is obtained using the integrated nested Laplace approximation (INLA). The performance of the block-NNGP is illustrated on simulated examples and massive real data for locations in the order of $10^4$.

stat.ME↗

arXiv2020

Generalized Co-sparse Factor Regression

Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements, binary indicators, and counts, and the observations may also be incomplete. Building upon the recent advances in mixed-outcome modeling and sparse matrix factorization, generalized co-sparse factor regression (GOFAR) is proposed, which utilizes the flexible vector generalized linear model framework and encodes the outcome dependency through a sparse singular value decomposition (SSVD) of the integrated natural parameter matrix. To avoid the estimation of the notoriously difficult joint SSVD, GOFAR proposes both sequential and parallel unit-rank estimation procedures. By combining the ideas of alternating convex search and majorization-minimization, an efficient algorithm with guaranteed convergence is developed to solve the sparse unit-rank problem and implemented in the R package gofar. Extensive simulation studies and two real-world applications demonstrate the effectiveness of the proposed approach.

stat.ME↗

arXiv2020

On moments of folded and doubly truncated multivariate extended skew-normal distributions

This paper develops recurrence relations for integrals that relate the density of multivariate extended skew-normal (ESN) distribution, including the well-known skew-normal (SN) distribution introduced by Azzalini and Dalla-Valle (1996) and the popular multivariate normal distribution. These recursions offer a fast computation of arbitrary order product moments of the multivariate truncated extended skew-normal and multivariate folded extended skew-normal distributions with the product moments as a byproduct. In addition to the recurrence approach, we realized that any arbitrary moment of the truncated multivariate extended skew-normal distribution can be computed using a corresponding moment of a truncated multivariate normal distribution, pointing the way to a faster algorithm since a less number of integrals is required for its computation which result much simpler to evaluate. Since there are several methods available to calculate the first two moments of a multivariate truncated normal distribution, we propose an optimized method that offers a better performance in terms of time and accuracy, in addition to consider extreme cases in which other methods fail. The R MomTrunc package provides these new efficient methods for practitioners.

math.ST↗

arXiv2020

Flexible Modeling of Hurdle Conway-Maxwell-Poisson Distributions with Application to Mining Injuries

While the hurdle Poisson regression is a popular class of models for count data with excessive zeros, the link function in the binary component may be unsuitable for highly imbalanced cases. Ordinary Poisson regression is unable to handle the presence of dispersion. In this paper, we introduce Conway-Maxwell-Poisson (CMP) distribution and integrate use of flexible skewed Weibull link functions as better alternative. We take a fully Bayesian approach to draw inference from the underlying models to better explain skewness and quantify dispersion, with Deviance Information Criteria (DIC) used for model selection. For empirical investigation, we analyze mining injury data for period 2013-2016 from the U.S. Mine Safety and Health Administration (MSHA). The risk factors describing proportions of employee hours spent in each type of mining work are compositional data; the probabilistic principal components analysis (PPCA) is deployed to deal with such covariates. The hurdle CMP regression is additionally adjusted for exposure, measured by the total employee working hours, to make inference on rate of mining injuries; we tested its competitiveness against other models. This can be used as predictive model in the mining workplace to identify features that increase the risk of injuries so that prevention can be implemented.

stat.AP↗

arXiv2020

Skewed link regression models for imbalanced binary response with applications to life insurance

For a portfolio of life insurance policies observed for a stated period of time, e.g., one year, mortality is typically a rare event. When we examine the outcome of dying or not from such portfolios, we have an imbalanced binary response. The popular logistic and probit regression models can be inappropriate for imbalanced binary response as model estimates may be biased, and if not addressed properly, it can lead to serious adverse predictions. In this paper, we propose the use of skewed link regression models (Generalized Extreme Value, Weibull, and Frechet link models) as more superior models to handle imbalanced binary response. We adopt a fully Bayesian approach for the generalized linear models (GLMs) under the proposed link functions to help better explain the high skewness. To calibrate our proposed Bayesian models, we use a real dataset of death claims experience drawn from a life insurance company's portfolio. Bayesian estimates of parameters were obtained using the Metropolis-Hastings algorithm and for Bayesian model selection and comparison, the Deviance Information Criterion (DIC) statistic has been used. For our mortality dataset, we find that these skewed link models are more superior than the widely used binary models with standard link functions. We evaluate the predictive power of the different underlying models by measuring and comparing aggregated death counts and death benefits.

stat.AP↗

arXiv2020

Approximate inferences for nonlinear mixed effects models with scale mixtures of skew-normal distributions

Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics, pharmacokinetic analyses, and studies of growth and decay. A standard assumption in nonlinear mixed effects models for continuous responses is that the random effects and the within-subject errors are normally distributed, making the model sensitive to outliers. We present a novel class of asymmetric nonlinear mixed effects models that provides efficient parameters estimation in the analysis of longitudinal data. We assume that, marginally, the random effects follow a multivariate scale mixtures of skew--normal distribution and that the random errors follow a symmetric scale mixtures of normal distribution, providing an appealing robust alternative to the usual normal distribution. We propose an approximate method for maximum likelihood estimation based on an EM-type algorithm that produces approximate maximum likelihood estimates and significantly reduces the numerical difficulties associated with the exact maximum likelihood estimation. Techniques for prediction of future responses under this class of distributions are also briefly discussed. The methodology is illustrated through an application to Theophylline kinetics data and through some simulating studies.

stat.ME↗

arXiv2020

Heckman selection-t model: parameter estimation via the EM-algorithm

Heckman selection model is perhaps the most popular econometric model in the analysis of data with sample selection. The analyses of this model are based on the normality assumption for the error terms, however, in some applications, the distribution of the error term departs significantly from normality, for instance, in the presence of heavy tails and/or atypical observation. In this paper, we explore the Heckman selection-t model where the random errors follow a bivariate Student's-t distribution. We develop an analytically tractable and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated Student's-t distributions. Simulations studies show the vulnerability of the Heckman selection-normal model, as well as the robustness aspects of the Heckman selection-t model. Two real examples are analyzed, illustrating the usefulness of the proposed methods. The proposed algorithms and methods are implemented in the new R package HeckmanEM.

stat.ME↗