Related papers: Bayesian inference for Stable Levy driven Stochast…
In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the…
We propose a multilevel Monte Carlo-FEM algorithm to solve elliptic Bayesian inverse problems with "Besov random tree prior". These priors are given by a wavelet series with stochastic coefficients, and certain terms in the expansion…
Approximate Bayesian inference for models with computationally expensive, black-box likelihoods poses a significant challenge, especially when the posterior distribution is complex. Many inference methods struggle to explore the parameter…
Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has…
A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular alternative to the classical Markov chain…
We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…
Switching state-space models (SSSM) are a very popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
Stochastic gradient MCMC (SG-MCMC) has played an important role in large-scale Bayesian learning, with well-developed theoretical convergence properties. In such applications of SG-MCMC, it is becoming increasingly popular to employ…
We address the problem of static OD matrix estimation from a formal statistical viewpoint. We adopt a novel Bayesian framework to develop a class of models that explicitly cast trip configurations in the study region as random variables. As…
We present a scalable approach to performing approximate fully Bayesian inference in generic state space models. The proposed method is an alternative to particle MCMC that provides fully Bayesian inference of both the dynamic latent states…
We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…
Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using…
Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…
In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to…
In this paper, we first derive Milstein schemes for an interacting particle system associated with point delay McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs), possibly with a drift term exhibiting super-linear growth…
In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…