Related papers: Nested Compound Random Measures
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…
Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…
Computer experiments can emulate the physical systems, help computational investigations, and yield analytic solutions. They have been widely employed with many engineering applications (e.g., aerospace, automotive, energy systems.…
In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies.…
A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…
Analysis of observational studies increasingly confronts the challenge of determining which of a possibly high-dimensional set of available covariates are required to satisfy the assumption of ignorable treatment assignment for estimation…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
We present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density $f_0$ of its jump sizes, as well as of its intensity $\lambda_0.$ We take a Bayesian approach to the problem and…
We present a systematic study of the nested sampling algorithm based on the example of the Potts model. This model, which exhibits a first order phase transition for $q>4$, exemplifies a generic numerical challenge in statistical physics:…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison. MultiNest is one of the most popular nested sampling implementations, and has…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based…
Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…
Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The…
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…