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Markov-chain Monte Carlo sampling has become a standard technique for exploring the posterior distribution of cosmological parameters constrained by observations of CMB anisotropies. Given an infinite amount of time, any MCMC sampler will…

Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large…

Decision trees have found widespread application within the machine learning community due to their flexibility and interpretability. This paper is directed towards learning decision trees from data using a Bayesian approach, which is…

Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. In this work,…

Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent deep learning methods have been used to enhance autoencoders, the need to provide…

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high…

To evaluate the cyclic behavior under different loading conditions using the kinematic and isotropic hardening theory of steel, a Chaboche viscoplastic material model is employed. The parameters of a constitutive model are usually…

Inference for continuous-time Markov chains (CTMCs) becomes challenging when the process is only observed at discrete time points. The exact likelihood is intractable, and existing methods often struggle even in medium-dimensional…

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior…

The advantages of sequential Monte Carlo (SMC) are exploited to develop parameter estimation and model selection methods for GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) style models. It provides an alternative method…

Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

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…