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Customary modeling for continuous point-referenced data assumes a Gaussian process which is often taken to be stationary. When such models are fitted within a Bayesian framework, the unknown parameters of the process are assumed to be random so a random Gaussian process results. Here, we propose a novel spatial Dirichlet process mixture model to produce a… (More)

Bayesian nonparametric methods have been applied to survival analysis problems since the emergence of the area of Bayesian nonparametrics. However, the use of the flexible class of Dirichlet process mixture models has been rather limited in this context. This is, arguably, to a large extent, due to the standard way of fitting such models that precludes full… (More)

We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial non-homogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a… (More)

With survival data there is often interest not only in the survival time distribution but also in the residual survival time distribution. In fact, regression models to explain residual survival time might be desired. Building upon recent work of Kottas and Gelfand (2001) we formulate a semiparametric median residual life regression model induced by a… (More)

We develop a Bayesian method for nonparametric model–based quantile regression. The approach involves flexible Dirichlet process mixture models for the joint distribution of the response and the covariates, with posterior inference for different quantile curves emerging from the conditional response distribution given the covariates. An extension to allow… (More)

We propose an approach to modeling and risk assessment for extremes of environmental processes evolving over time and recorded at a number of spatial locations. We follow an extension of the point process approach to analysis of extremes under which the times of exceedances over a given threshold are assumed to arise from a non-homogeneous Poisson process.… (More)

The evaluation of the performance of a continuous diagnostic measure is a commonly encountered task in medical research.We develop Bayesian non-parametric models that use Dirichlet process mixtures and mixtures of Polya trees for the analysis of continuous serologic data.The modelling approach differs from traditional approaches to the analysis of receiver… (More)

- Milovan Krnjajic, Athanasios Kottas, David Draper
- Computational Statistics & Data Analysis
- 2008

In this paper we present the results of a simulation study to explore the ability of Bayesian parametric and nonparametric models to provide an adequate fit to count data, of the type that would routinely be analyzed parametrically either through fixed-effects or random-effects Poisson models. The context of the study is a randomized controlled trial with… (More)

- Athanasios Kottas, Márcia D. Branco, Alan E. Gelfand
- Biometrics
- 2002

In cytogenetic dosimetry, samples of cell cultures are exposed to a range of doses of a given agent. In each sample at each dose level, some measure of cell disability is recorded. The objective is to develop models that explain cell response to dose. Such models can be used to predict response at unobserved doses. More important, such models can provide… (More)

We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet process mixtures for this density, combined with nonparametric or semiparametric modeling for the mark distribution,… (More)