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Composition of low-dimensional distributions, whose foundations were laid in the papaer published in the Proceeding of UAI'97 (Jirousek 1997), appeared to be an alternative apparatus to describe multidimensional probabilistic models. In…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…
Power spectrum estimation and evaluation of associated errors in the presence of incomplete sky coverage; non-homogeneous, correlated instrumental noise; and foreground emission is a problem of central importance for the extraction of…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…
Model selection aims to determine which theoretical models are most plausible given some data, without necessarily asking about the preferred values of the model parameters. A common model selection question is to ask when new data require…
This work introduces a Bayesian methodology for fitting large discrete graphical models with spike-and-slab priors to encode sparsity. We consider a quasi-likelihood approach that enables node-wise parallel computation resulting in reduced…
Computer vision tasks are difficult because of the large variability in the data that is induced by changes in light, background, partial occlusion as well as the varying pose, texture, and shape of objects. Generative approaches to…
We consider the specification of prior distributions for Bayesian model comparison, focusing on regression-type models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior…
Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…
We investigate Bayes posterior distributions in high-dimensional generalized linear models (GLMs) under the proportional asymptotics regime, where the number of features and samples diverge at a comparable rate. Specifically, we…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
Pseudo-marginal Metropolis-Hastings (pmMH) is a powerful method for Bayesian inference in models where the posterior distribution is analytical intractable or computationally costly to evaluate directly. It operates by introducing…
Model selection is an important activity in modern data analysis and the conventional Bayesian approach to this problem involves calculation of marginal likelihoods for different models, together with diagnostics which examine specific…