Related papers: Scalable Approximations of Marginal Posteriors in …
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions for the…
We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates $p$ may be large relative to the samples size $n$, but at most a moderate number $q$ of covariates are active. Specifically, we…
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)…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…
This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent…
We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian…
We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…
The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable.…
Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
Predictive coding (PC) is an influential theory of information processing in the brain, providing a biologically plausible alternative to backpropagation. It is motivated in terms of Bayesian inference, as hidden states and parameters are…
We consider the problem of decoding a discrete signal of categorical variables from the observation of several histograms of pooled subsets of it. We present an Approximate Message Passing (AMP) algorithm for recovering the signal in the…
Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…
We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model. For the rejection sampling version of ABC, it is known that…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
We develop a method to carry out MAP estimation for a class of Bayesian regression models in which coefficients are assigned with Gaussian-based spike and slab priors. The objective function in the corresponding optimization problem has a…
The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete…