Sujit K. Ghosh

Generalized linear models : a Bayesian perspective

Part 1 Extending the GLMs. Part 2 Categorical and longitudinal data. Part 3 Semiparametric approaches. Part 4 Model diagnositics and value selection in GLMs. Part 5 Challenging problems in GLMs.

Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models

It is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed-effects (LME) model. Typical approaches perform selection separately on each of the fixed and random effect components. However, changing the structure of one set of effects can lead to different choices of variables for the other set of effects. We propose simultaneous selection of the fixed and random factors in an LME model using a modified Cholesky decomposition. Our method is based on a penalized joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects. It performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero. A constrained expectation-maximization algorithm is then used to obtain the final estimates. It is further shown that the proposed penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example.

Spatio-Temporal Modeling of Residential Sales Data

This article focuses on the location, time, and spatio-temporal components associated with suitably aggregated data to improve prediction of individual asset values. Such effects are introduced in the context of hierarchical models, which we find more natural than attempting to model covariance structure. Indeed, our cross-sectional database, a sample of 7,936 transactions for 49 subdivisions over a 10-year period in Baton Rouge, Louisiana, precludes covariance modeling. A wide range of models arises, each fitted using sampling-based methods because likelihood-based fitting may not be possible. Choosing among an array of nonnested models is carried out using a posterior predictive criterion. In addition, one year of data is held out for model validation. A thorough analysis of the data incorporating all of the aforementioned issues is presented.

Shape restricted nonparametric regression with Bernstein polynomials

The objective of this article is to develop a computationally efficient estimator of the regression function subject to various shape constraints. In particular, nonparametric estimators of monotone and/or convex (concave) regression functions are obtained by using a nested sequence of Bernstein polynomials. One of the key distinguishing features of the proposed estimator is that a given shape constraint (e.g., monotonicity and/or convexity) is maintained for any finite sample size and satisfied over the entire support of the predictor space. Moreover, it is shown that the Bernstein polynomial based regression estimator can be obtained as a solution of a constrained least squares method and hence the estimator can be computed efficiently using a quadratic programming algorithm. Finally, the asymptotic properties (e.g., strong uniform consistency) of the estimator are established under very mild conditions, and finite sample properties are explored using several simulation studies and real data analysis. The predictive performances are compared with some of the existing methods.

Spatio-Temporal Modeling of Agricultural Yield Data with an Application to Pricing Crop Insurance Contracts

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Paraná (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited.

Bayesian Analysis of Circular Data Using Wrapped Distributions

Circular data arise in a number of different areas such as geological, meteorological, biological and industrial sciences. Standard statistical techniques can not be used to model circular data due to the circular geometry of the sample space. One of the common methods to analyze circular data is known as the wrapping approach. This approach is based on a simple fact that a probability distribution on a circle can be obtained by wrapping a probability distribution defined on the real line. A large class of probability distributions that are flexible to account for different features of circular data can be obtained by the aforementioned approach. However, the likelihood-based inference for wrapped distributions can be very complicated and computationally intensive. The EM algorithm to compute the MLE is feasible, but is computationally unsatisfactory. A data augmentation method using slice sampling is proposed to overcome such computational difficulties. The proposed method turns out to be flexible and computationally efficient to fit a wide class of wrapped distributions. In addition, a new model selection criteria for circular data is developed. Results from an extensive simulation study are presented to validate the performance of the proposed estimation method and the model selection criteria. Application to a real data set is also presented and parameter estimates are compared to those that are available in the literature.

Impact of Source Reduction on the Spatial Distribution of Larvae and Pupae of Aedes albopictus (Diptera: Culicidae) in Suburban Neighborhoods of a Piedmont Community in North Carolina

Abstract Aedes albopictus (Skuse) is a principal nuisance mosquito species and a potential arbovirus vector throughout its geographic range in the United States. This species lays eggs, and progeny complete development in water-filled containers that are discarded in suburban landscapes. Source reduction of containers, achieved through environmental sanitation, was used to experimentally manipulate mosquito production to gain insight into the spatial structure of the population of immature Ae. albopictus. Our studies were conducted in suburban landscapes in Raleigh, NC, during the 2002 and 2003 mosquito seasons. Spatial analyses, using estimates of the mean and total standing crop of pupae and counts of the numbers of mosquito-positive containers, showed that the distribution of mosquito production was not spatially dependent on a neighborhood-wide basis. However, in all neighborhoods, mosquito production was clustered in at least one and often more than one adjacent residence. Point pattern analyses that considered only the presence or absence of pupae showed that pupae-positive residences were dispersed throughout neighborhoods receiving monthly source reduction treatments and clustered throughout control neighborhoods, indicating that source reduction affected the spatial distribution of pupae. Conversely, spatial analyses based on the presence or absence of larvae and pupae showed that mosquito production was randomly distributed among residences in both control and source reduction neighborhoods, showing that Ae. albopictus recolonized containers within several weeks after source reduction was implemented. Knowledge of the spatial distribution of production sites would allow management efforts for Ae. albopictus to be targeted to residences supporting high levels of mosquito production.

A variable selection approach to monotonic regression with Bernstein polynomials

One of the standard problems in statistics consists of determining the relationship between a response variable and a single predictor variable through a regression function. Background scientific knowledge is often available that suggests that the regression function should have a certain shape (e.g. monotonically increasing or concave) but not necessarily a specific parametric form. Bernstein polynomials have been used to impose certain shape restrictions on regression functions. The Bernstein polynomials are known to provide a smooth estimate over equidistant knots. Bernstein polynomials are used in this paper due to their ease of implementation, continuous differentiability, and theoretical properties. In this work, we demonstrate a connection between the monotonic regression problem and the variable selection problem in the linear model. We develop a Bayesian procedure for fitting the monotonic regression model by adapting currently available variable selection procedures. We demonstrate the effectiveness of our method through simulations and the analysis of real data.

Performance of Information Criteria for Spatial Models.

Model choice is one of the most crucial aspect in any statistical data analysis. It is well known that most models are just an approximation to the true data-generating process but among such model approximations, it is our goal to select the ‘best’ one. Researchers typically consider a finite number of plausible models in statistical applications, and the related statistical inference depends on the chosen model. Hence, model comparison is required to identify the ‘best’ model among several such candidate models. This article considers the problem of model selection for spatial data. The issue of model selection for spatial models has been addressed in the literature by the use of traditional information criteria-based methods, even though such criteria have been developed based on the assumption of independent observations. We evaluate the performance of some of the popular model selection critera via Monte Carlo simulation experiments using small to moderate samples. In particular, we compare the performance of some of the most popular information criteria such as Akaike information criterion (AIC), Bayesian information criterion, and corrected AIC in selecting the true model. The ability of these criteria to select the correct model is evaluated under several scenarios. This comparison is made using various spatial covariance models ranging from stationary isotropic to nonstationary models.

Proportional hazards models: a latent competing risk approach

We propose a novel semiparametric version of the widely used proportional hazards survival model. Features include an arbitrarily rich class of continuous base-line hazards, an attractive epidemiological interpretation of the hazard as a latent competing risk model and trivial handling of censoring. Models are fitted by using a data augmentation scheme. The methodology is applied to a data set recording times to first hospitalization following clinical diagnosis of acquired immune deficiency syndrome for a sample of 169 patients.