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The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap…
We introduce a differential complex of local observables given a decomposition of a global set of random variables into subsets. Its boundary operator allows us to define a transport equation equivalent to Belief Propagation. This…
Bayesian hierarchical clustering (BHC) is an agglomerative clustering method, where a probabilistic model is defined and its marginal likelihoods are evaluated to decide which clusters to merge. While BHC provides a few advantages over…
Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…
Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution…
We propose PROPAGATE, a fast approximation framework to estimate distance-based metrics on very large graphs such as the (effective) diameter, the (effective) radius, or the average distance within a small error. The framework assigns seeds…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on $[0,1]$. We consider a parametrization of Beta distributions in terms of mean and scale parameters and…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The Gibbs posterior formulation is a generalization of standard…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
A Bayesian Belief Network (BN) is a model of a joint distribution over a setof n variables, with a DAG structure to represent the immediate dependenciesbetween the variables, and a set of parameters (aka CPTables) to represent thelocal…
Approximate Bayesian computation (ABC) is an approach for sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model,…
We propose an application-tailored data-driven fully automated method for functional approximation of combinational circuits. We demonstrate how an application-level error metric such as the classification accuracy can be translated to a…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
Many models of interest in the natural and social sciences have no closed-form likelihood function, which means that they cannot be treated using the usual techniques of statistical inference. In the case where such models can be…
A major benefit of graphical models is that most knowledge is captured in the model structure. Many models, however, produce inference problems with a lot of symmetries not reflected in the graphical structure and hence not exploitable by…
This is a review of asymptotic and non-asymptotic behaviour of Bayesian methods under model specification. In particular we focus on consistency, i.e. convergence of the posterior distribution to the point mass at the best parametric…
For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to…