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High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
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 recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of…
In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…
Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte…
Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts,…
Variable clustering is important for explanatory analysis. However, only few dedicated methods for variable clustering with the Gaussian graphical model have been proposed. Even more severe, small insignificant partial correlations due to…
We consider the challenges that arise when fitting complex ecological models to 'large' data sets. In particular, we focus on random effect models which are commonly used to describe individual heterogeneity, often present in ecological…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme…
We develop a Bayesian variable selection method, called SVEN, based on a hierarchical Gaussian linear model with priors placed on the regression coefficients as well as on the model space. Sparsity is achieved by using degenerate spike…
We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…
Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…
Motivated by genetic association studies of pleiotropy, we propose here a Bayesian latent variable approach to jointly study multiple outcomes or phenotypes. The proposed method models both continuous and binary phenotypes, and it accounts…
In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…
The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…
High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…
When performing Bayesian computations in practice, one is often faced with the challenge that the constituent model components and/or the data are only available in a distributed fashion, e.g. due to privacy concerns or sheer volume. While…