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Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
Quantum state tomography (QST) is typically performed from a frequentist viewpoint using maximum likelihood estimation (MLE) which seeks to find the best plausible state consistent with the data by maximizing a likelihood function /…
A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC…
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
In observational studies, the propensity score plays a central role in estimating causal effects of interest. The inverse probability weighting (IPW) estimator is commonly used for this purpose. However, if the propensity score model is…
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from…
There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…
In this paper we develop a likelihood-free approach for population calibration, which involves finding distributions of model parameters when fed through the model produces a set of outputs that matches available population data. Unlike…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…
In statistical practice, a realistic Bayesian model for a given data set can be defined by a likelihood function that is analytically or computationally intractable, due to large data sample size, high parameter dimensionality, or complex…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
Bayesian inference with stochastic models is often difficult because their likelihood functions involve high-dimensional integrals. Approximate Bayesian Computation (ABC) avoids evaluating the likelihood function and instead infers model…
$\alpha$-stable distributions are utilised as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate $\alpha$-stable models admit closed…
This paper proposes a simple, novel, and fully-Bayesian approach for causal inference in partially linear models with high-dimensional control variables. Off-the-shelf machine learning methods can introduce biases in the causal parameter…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…