Related papers: Probabilistic morphisms and Bayesian nonparametric…
One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive…
The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…
A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
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 probabilistic programming languages (BPPLs) let users denote statistical models as code while the interpreter infers the posterior distribution. The semantics of BPPLs are usually mathematically complex and unable to reason about…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
The recently developed semi-parametric generalized linear model (SPGLM) offers more flexibility as compared to the classical GLM by including the baseline or reference distribution of the response as an additional parameter in the model.…
Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
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…
In this paper, we describe a Bayesian nonparametric approach to make inference for a bivariate spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all bivariate spherically symmetric…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…