Bayesian inference about small areas is of considerable current interest, and simultaneous intervals for the parameters for the areas are needed because these parameters are correlated. This is not usually pursued because with many areas the problem becomes difficult. We describe a method for finding simultaneous credible intervals for a relatively large number of parameters, each corresponding...

The prior distribution is an essential ingredient of any Bayesian analysis, and it plays a major role in determining the final results. As such, Bayesians attempt to use prior distributions that have certain properties. Perhaps the main property is a desire to accurately reflect prior information, i.e., information external to the experiment at hand. We would supplement this vague property with...

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model as running example we go through the steps of deriving the model as an infini...

Automatic clustering of utterances can be useful for the modeling of dialogue acts for dialogue applications. Previously, the Chinese restaurant process (CRP), a non-parametric Bayesian method, has been introduced and has shown promising results for the clustering of utterances in dialogue. This paper introduces the infinite HMM, which is also a non-parametric Bayesian method, and verifies its ...

Bayesian inference about small areas is of considerable current interest, and simultaneous intervals for the parameters for the areas are needed because these parameters are correlated. This is not usually pursued because with many areas the problem becomes difficult. We describe a method for finding simultaneous credible intervals for a relatively large number of parameters, each corresponding...

It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its rate adaptability to various smoothness classes of densities in arbitrary dimension is demonstrated. This sieve construction is expected to offer a substantia...

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the marginal likelihood of the data given a candidate structure. This term can be computed in closed-form for standard parametric families (e.g...

This paper develops a semi-parametric Bayesian regression model for estimating heterogeneous treatment effects from observational data. Standard nonlinear regression models, which may work quite well for prediction, can yield badly biased estimates of treatment effects when fit to data with strong confounding. Our Bayesian causal forests model avoids this problem by directly incorporating an es...

We present a Bayesian decision theoretic approach for developing replacament strategies. In so doing, we consider a semi-parametric model to describe the failure characteristics of systems by specifying a nonparametric form for cumulative intensity function and by taking into account effect of covariates by a parametric form. Use of a gamma process prior for the cumulative intensity function co...

A multiscale, non-parametric, Bayesian framework for identification of model parameters Motivation Bayesian Paradigm Nonparametric prior Inference Numerical Results Prediction Motivation T (0) = T 0 q(1) = q 0 l = 1 c(x) =?    d dx −c(x) dT dx = 0 T (0) = T 0 q(1) = −c(x) dT dx x=1 = q 0 (1) 2 / 56 A multiscale, non-parametric, Bayesian framework for identification of model parameters Motiva...