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We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…
Doubly intractable models are encountered in a number of fields, e.g. social networks, ecology and epidemiology. Inference for such models requires the evaluation of a likelihood function, whose normalising factor depends on the model…
Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…
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…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
Inference for continuous-time Markov chains (CTMCs) becomes challenging when the process is only observed at discrete time points. The exact likelihood is intractable, and existing methods often struggle even in medium-dimensional…
Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can…
Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these forward models do not admit tractable densities forcing…
Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…
Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…
Bayesian inference for Continuous-Time Markov Chains (CTMCs) on countably infinite spaces is notoriously difficult because evaluating the likelihood exactly is intractable. One way to address this challenge is to first build a non-negative…
In recent times empirical likelihood has been widely applied under Bayesian framework. Markov chain Monte Carlo (MCMC) methods are frequently employed to sample from the posterior distribution of the parameters of interest. However,…
In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…
Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and…
Bernoulli factory MCMC algorithms implement accept-reject Markov chains without explicit computation of acceptance probabilities, and are used to target posterior distributions associated with intractable likelihood models. Intractable…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…
We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…
We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…