Related papers: Nested Compound Random Measures
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…
Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides…
When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…
Any nested Archimedean copula is defined starting from a rooted phylogenetic tree, for which a new class of nonparametric estimators is presented. An estimator from this new class relies on a two-step procedure where first a binary tree is…
This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recent posterior characterizations for the class of…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Gene-gene and gene-environment interactions are widely believed to play significant roles in explaining the variability of complex traits. While substantial research exists in this area, a comprehensive statistical framework that addresses…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…
We study the Gaussian sequence compound decision problem and analyze a Bayesian nonparametric estimator from an empirical Bayes, regret-based perspective. Motivated by sharp results for the classical nonparametric maximum likelihood…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The alternative models are based on the principles of embedding…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…
A Bayesian nonparametric method for unimodal densities on the real line is provided by considering a class of species sampling mixture models containing random densities that are unimodal and not necessarily symmetric. This class of…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…
We introduce a new class of sequential Monte Carlo methods which reformulates the essence of the nested sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. Two new algorithms are proposed, nested sampling via…
We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…