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Consider a probit regression problem in which Y 1 , ..., Y n are independent Bernoulli random variables such that Pr.Y i D 1/ D Φ.x T i β/ where x i is a p-dimensional vector of known covariates that are associated with Y i , β is a p-dimensional vector of unknown regression coefficients and Φ./ denotes the standard normal distribution function. We study… (More)

- Vivekananda Roy, James P. Hobert
- J. Multivariate Analysis
- 2010

We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavy-tailed. Let π denote the intractable posterior density that results when this regression model is combined with the… (More)

The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the target distribution has uncountable support, as is nearly always the case in practice, it is generally quite difficult to get a handle on these spectra. We show… (More)

- Vivekananda Roy, Evangelos Evangelou, Zhengyuan Zhu
- Biometrics
- 2016

Spatial generalized linear mixed models (SGLMMs) are popular models for spatial data with a non-Gaussian response. Binomial SGLMMs with logit or probit link functions are often used to model spatially dependent binomial random variables. It is known that for independent binomial data, the robit regression model provides a more robust (against extreme… (More)

We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavy-tailed. Let π denote the intractable posterior density that results when this regression model is combined with the… (More)

A sequence of random variables {X n } n≥0 is called regenerative if it can be broken up into iid components. The problem addressed in this paper is to determine under what conditions is a Markov chain regenerative. It is shown that an irreducible Markov chain with a countable state space is regenerative for any initial distribution if and only if it is… (More)

- Michael B Robblee, Robert M. Dorazio, Joan A Browder, Vivekananda Roy, André Daniels
- 2008

Introduction The pink shrimp, familiar to most Floridians as either food or bait shrimp, is ubiquitous in both seagrass-and mangrove-dominated south Florida coastal waters. The pink shrimp, Farfantepenaeus duorarum, is a biological indicator in the Southern Estuaries Module of MAP, the Monitoring and Assessment Program of CERP. The South Florida Fish and… (More)

Estimating standard errors for importance sampling estimators with multiple Markov chains" (2015). Abstract The naive importance sampling estimator based on the samples from a single importance density can be extremely numerically unstable. We consider multiple distributions importance sampling es-timators where samples from more than one probability… (More)

In dynamic linear models (DLMs) with unknown fixed parameters, a standard Markov chain Monte Carlo (MCMC) sampling strategy is to alternate sampling of latent states conditional on fixed parameters and sampling of fixed parameters conditional on latent states. In some regions of the parameter space, this standard data augmentation (DA) algorithm can be… (More)

- Krishna B. Athreya, Vivekananda Roy
- J. Applied Probability
- 2015

Let f be an integrable function on an infinite measure space (S, S, π). We show that if a regenerative sequence {Xn} n≥0 with canonical measure π could be generated then a consistent estimator of λ ≡ S f dπ can be produced. We further show that under appropriate second moment conditions, a confidence interval for λ can also be derived. This is illustrated… (More)