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Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…

This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple…

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…

Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates…

Multistage models based on relativistic viscous hydrodynamics have proven successful in describing hadron measurements from relativistic nuclear collisions. These measurements are sensitive to the shear and the bulk viscosities of QCD and…

While many areas of machine learning have benefited from the increasing availability of large and varied datasets, the benefit to causal inference has been limited given the strong assumptions needed to ensure identifiability of causal…

Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…

Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…

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…

We discuss the use of empirical Bayes for data integration, in the sense of transfer learning. Our main interest is in settings where one wishes to learn structure (e.g. feature selection) and one only has access to incomplete data from…

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…

Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data…

The aim of survey statistics is to produce estimates with a minimal bias and a corresponding acceptable variance given a specific budget, preferable with a minor response burden for the participants. In recent years, considerable efforts…

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…

This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…