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Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

Metropolis-Hastings estimates intractable expectations - can differentiating the algorithm estimate their gradients? The challenge is that Metropolis-Hastings trajectories are not conventionally differentiable due to the discrete…

We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive…

This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…

In the last years there has been a growing interest in proposing methods for estimating covariance functions for geostatistical data. Among these, maximum likelihood estimators have nice features when we deal with a Gaussian model. However…

Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on…

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

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…

Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…

Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…

When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…

This work is driven by the ubiquitous dissent over the abilities and contributions of the Metropolis-Hastings and reversible jump algorithm within the context of trans dimensional sampling. We demystify this topic by taking a deeper look…

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from…

We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…

Estimating model parameters of a general family of cure models is always a challenging task mainly due to flatness and multimodality of the likelihood function. In this work, we propose a fully Bayesian approach in order to overcome these…

Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…