相关论文: Closed form expressions for Bayesian sample size

The practical implementation of Bayesian inference requires numerical approximation when closed-form expressions are not available. What types of accuracy (convergence) of the numerical approximations guarantee robustness and what types do…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…

We present a growing dimension asymptotic formalism. The perspective in this paper is classification theory and we show that it can accommodate probabilistic networks classifiers, including naive Bayes model and its augmented version. When…

Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…

New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…

This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…

We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…

Under mild conditions, it is shown the strong consistency of the Bayes estimator of the density. Moreover, the Bayes risk (for some common loss functions) of the Bayes estimator of the density (i.e. the posterior predictive density) reaches…

The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…

Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…

Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical…

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…

The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…

For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…

How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…

Randomized controlled clinical trials provide the gold standard for evidence generation in relation to the efficacy of a new treatment in medical research. Relevant information from previous studies may be desirable to incorporate in the…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…