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Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among…
Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically…
A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…
We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several…
Likelihood-free methods such as approximate Bayesian computation (ABC) have extended the reach of statistical inference to problems with computationally intractable likelihoods. Such approaches perform well for small-to-moderate dimensional…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
Methods for Bayesian simulation in the presence of computationally intractable likelihood functions are of growing interest. Termed likelihood-free samplers, standard simulation algorithms such as Markov chain Monte Carlo have been adapted…
Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a…
This paper presents a comprehensive algorithm for fitting generative models whose likelihood, moments, and other quantities typically used for inference are not analytically or numerically tractable. The proposed method aims to provide a…
Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been…
The is no other model or hypothesis verification tool in Bayesian statistics that is as widely used as the Bayes factor. We focus on generative models that are likelihood-free and, therefore, render the computation of Bayes factors…
In Bayesian classification, it is important to establish a probabilistic model for each class for likelihood estimation. Most of the previous methods modeled the probability distribution in the whole sample space. However, real-world…
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…
Propensity score methods are widely used for estimating treatment effects from observational studies. A popular approach is to estimate propensity scores by maximum likelihood based on logistic regression, and then apply inverse probability…
The design of optimal test statistics is a key task in frequentist statistics and for a number of scenarios optimal test statistics such as the profile-likelihood ratio are known. By turning this argument around we can find the profile…
Large Language Models (LLMs) are widely used to evaluate natural language generation tasks as automated metrics. However, the likelihood, a measure of LLM's plausibility for a sentence, can vary due to superficial differences in sentences,…