Related papers: A note on a Bayesian nonparametric estimator of th…
Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a non-parametric Bayesian approach to estimate the intensity…
This paper presents a novel approach to Bayesian nonparametric spectral analysis of stationary multivariate time series. Starting with a parametric vector-autoregressive model, the parametric likelihood is nonparametrically adjusted in the…
This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-\beta^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha^{'}. We show that this definition…
We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti…
Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…
We introduce and study a unified Bayesian framework for extended feature allocations which flexibly captures interactions -- such as repulsion or attraction -- among features and their associated weights. We provide a complete Bayesian…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…
In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the…
We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is…
We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…
Statistical inference on biodiversity has a rich history going back to RA Fisher. An influential ecological theory suggests the existence of a fundamental biodiversity number, denoted $\alpha$, which coincides with the precision parameter…