Estimation of a regression spline sample selection model

It is often the case that an outcome of interest is observed for a restricted non-randomly selected sample of the population. In such a situation, standard statistical analysis yields biased results. This issue can be addressed using sample selection models which are based on the estimation of two regressions: a binary selection equation determining whether a particular statistical unit will be available in the outcome equation. Classic sample selection models assume a priori that continuous regressors have a pre-specified linear or non-linear relationship to the outcome, which can lead to erroneous conclusions. In the case of continuous response, methods in which covariate effects are modeled flexibly have been previously proposed, the most recent being based on a Bayesian Markov chain Monte Carlo approach. A frequentist counterpart which has the advantage of being computationally fast is introduced. The proposed algorithm is based on the penalized likelihood estimation framework. The construction of confidence intervals is also discussed. The empirical properties of the existing and proposed methods are studied through a simulation study. The approaches are finally illustrated by analyzing data from the RAND Health Insurance Experiment on annual health expenditures

Applications of Bayesian Nonparametrics to Reliability and Survival Data

Reliability and survival data are widely encountered across many common settings. Subjects under investigation often include machines, bioassays, patients, etc.; their reliability or survival distribution, and its association with covariate processes, are commonly of interest. Within this dissertation, the first two chapters focus on reliability data where repairable systems fail and get interventions, e.g. repairs in the event process. It begins with a nonparametric test for the commonly assumed \u27\u27good as old\u27\u27 assumption for minimal repair models and then a semi-parametric regression model is introduced for reliability data using Kijima\u27s effective age. The third chapter focuses on survival data observed with potential spatial correlation. We first develop a Bayesian semi-parametric approach to the extended hazard model and then extend this framework to allow for spatial correlation among survival times. In contrast to widely used frailty models, our approach preserves marginal interpretations. Flexible modeling approaches in the Bayesian context are used for baseline failure rate or hazard and Markov chain Monte Carlo techniques to obtain the posterior inferences. The proposed tests and models are examined in several simulation studies and applications

pexm: A JAGS Module for Applications Involving the Piecewise Exponential Distribution

In this study, we present a new module built for users interested in a programming language similar to BUGS to fit a Bayesian model based on the piecewise exponential (PE) distribution. The module is an extension to the open-source program JAGS by which a Gibbs sampler can be applied without requiring the derivation of complete conditionals and the subsequent implementation of strategies to draw samples from unknown distributions. The PE distribution is widely used in the fields of survival analysis and reliability. Currently, it can only be implemented in JAGS through methods to indirectly specify the likelihood based on the Poisson or Bernoulli probabilities. Our module provides a more straightforward implementation and is thus more attractive to the researchers aiming to spend more time exploring the results from the Bayesian inference rather than implementing the Markov Chain Monte Carlo algorithm. For those interested in extending JAGS, this work can be seen as a tutorial including important information not well investigated or organized in other materials. Here, we describe how to use the module taking advantage of the interface between R and JAGS. A short simulation study is developed to ensure that the module behaves well and a real illustration, involving two PE models, exhibits a context where the module can be used in practice

Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models

Structured additive regression provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large flexibility of structured additive regression makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor and (3) determining the required interactions. We propose a spike-and-slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In simulation studies and with (real) benchmark classification data, we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with time-varying effects for right-censored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive appendix

Dynamic Modeling and Statistical Analysis of Event Times

This review article provides an overview of recent work in the modeling and analysis of recurrent events arising in engineering, reliability, public health, biomedicine and other areas. Recurrent event modeling possesses unique facets making it different and more difficult to handle than single event settings. For instance, the impact of an increasing number of event occurrences needs to be taken into account, the effects of covariates should be considered, potential association among the interevent times within a unit cannot be ignored, and the effects of performed interventions after each event occurrence need to be factored in. A recent general class of models for recurrent events which simultaneously accommodates these aspects is described. Statistical inference methods for this class of models are presented and illustrated through applications to real data sets. Some existing open research problems are described.Comment: Published at http://dx.doi.org/10.1214/088342306000000349 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Semiparametric Generalized Exponential Regression Model with a Principled Distance-based Prior for Analyzing Trends in Rainfall

The Western Ghats mountain range holds critical importance in regulating monsoon rainfall across Southern India, with a profound impact on regional agriculture. Here, we analyze daily wet-day rainfall data for the monsoon months between 1901-2022 for the Northern, Middle, and Southern Western Ghats regions. Motivated by an exploratory data analysis, we introduce a semiparametric Bayesian generalized exponential (GE) regression model; despite the underlying GE distribution assumption being well-known in the literature, including in the context of rainfall analysis, no research explored it in a regression setting, as of our knowledge. Our proposed approach involves modeling the GE rate parameter within a generalized additive model framework. An important feature is the integration of a principled distance-based prior for the GE shape parameter; this allows the model to shrink to an exponential regression model that retains the advantages of the exponential family. We draw inferences using the Markov chain Monte Carlo algorithm. Extensive simulations demonstrate that the proposed model outperforms simpler alternatives. Applying the model to analyze the rainfall data over 122 years provides insights into model parameters, temporal patterns, and the impact of climate change. We observe a significant decreasing trend in wet-day rainfall for the Southern Western Ghats region.Comment: 24 pages, 8 figure

Bayesian analysis for the intraclass model and for the quantile semiparametric mixed-effects double regression models

This dissertation consists of three distinct but related research projects. The first two projects focus on objective Bayesian hypothesis testing and estimation for the intraclass correlation coefficient in linear models. The third project deals with Bayesian quantile inference for the semiparametric mixed-effects double regression models. In the first project, we derive the Bayes factors based on the divergence-based priors for testing the intraclass correlation coefficient (ICC). The hypothesis testing of the ICC is used to test the uncorrelatedness in multilevel modeling, and it has not well been studied from an objective Bayesian perspective. Simulation results show that the two sorts of Bayes factors have good performance in the hypothesis testing. Moreover, the Bayes factors can be easily implemented due to their unidimensional integral expressions. In the second project, we consider objective Bayesian analysis for the ICC in the context of normal linear regression model. We first derive two objective priors for the unknown parameters and show that both result in proper posterior distributions. Within a Bayesian decision-theoretic framework, we then propose an objective Bayesian solution to the problems of hypothesis testing and point estimation of the ICC based on a combined use of the intrinsic discrepancy loss function and objective priors. The proposed solution has an appealing invariance property under one-to-one reparameterization of the quantity of interest. Simulation studies are conducted to investigate the performance the proposed solution. Finally, a real data application is provided for illustrative purposes. In the third project, we study Bayesian quantile regression for semiparametric mixed effects model, which includes both linear and nonlinear parts. We adopt the popular cubic spline functions for the nonlinear part and model the variance of the random effect as a function of the explanatory variables. An efficient Gibbs sampler with the Metropolis-Hastings algorithm is proposed to generate posterior samples of the unknown parameters from their posterior distributions. Simulation studies and a real data example are used to illustrate the performance of the proposed methodology