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Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability…
We propose a Bayesian inference approach for a class of latent Markov models. These models are widely used for the analysis of longitudinal categorical data, when the interest is in studying the evolution of an individual unobservable…
Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a…
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…
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…
Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…
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 propose a new methodology for solving a discrete time stochastic Markovian control problem under model uncertainty. By utilizing the Dirichlet process, we model the unknown distribution of the underlying stochastic process…
Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…
Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it…
This article tackles the old problem of prediction via a nonparametric transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known challenging due to model unidentifiability though appealing because of its robust…
Conjugate pairs of distributions over infinite dimensional spaces are prominent in statistical learning theory, particularly due to the widespread adoption of Bayesian nonparametric methodologies for a host of models and applications. Much…
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…
Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis…
This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model.…
Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
This paper studies quasi Bayesian estimation and uncertainty quantification for an unknown function that is identified by a nonparametric conditional moment restriction. We derive contraction rates for a class of Gaussian process priors.…
It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…
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…