We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on nearest-neighbor mixture processes (NNMP), referred to as NNMP. To define the joint probability mass function (pmf) over set spatial locations, we build from local mixtures conditional pmfs using directed graphical model, with acyclic graph that summarizes nearest neighbor structure. The app...

We review inference under models with nonparametric Bayesian (BNP) priors. The discussion follows a set of examples for some common inference problems. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions. While we fo...

[1] This study presents monthly CO2 fluxes from 1997 to 2001 at a 3.75 latitude 5 longitude resolution, inferred using a geostatistical inverse modeling approach. The approach focuses on quantifying the information content of measurements from the NOAA-ESRL cooperative air sampling network with regard to the global CO2 budget at different spatial and temporal scales. The geostatistical approach...

When evaluating cognitive models based on fits to observed data (or, really, any model that has free parameters), parameter estimation is critically important. Traditional techniques like hill climbing by minimizing or maximizing a fit statistic often result in point estimates. Bayesian approaches instead estimate parameters as posterior probability distributions, and thus naturally account for...

Conditional copula models are flexible tools for modelling complex dependence structures in regression settings. We construct Bayesian inference for the conditional copula model adapted to regression settings in which the bivariate outcome is continuous or mixed. The dependence between the copula parameter and the covariate is modelled using cubic splines. The proposed joint Bayesian inference ...

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation based procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibbs sampling and Metropo...

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a ran...

Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general non-decomposable setting. Penalized likelihood inference on the other hand has made tremendous gains in the past few years in terms of scalability and tractability. Ba...

This paper presents two Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference of probabilistic context free grammars (PCFGs) from terminal strings, providing an alternative to maximum-likelihood estimation using the Inside-Outside algorithm. We illustrate these methods by estimating a sparse grammar describing the morphology of the Bantu language Sesotho, demonstrating that with sui...