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This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…

Attention modules, as simple and effective tools, have not only enabled deep neural networks to achieve state-of-the-art results in many domains, but also enhanced their interpretability. Most current models use deterministic attention…

The brms package allows R users to easily specify a wide range of Bayesian single-level and multilevel models, which are fitted with the probabilistic programming language Stan behind the scenes. Several response distributions are…

We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior…

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…

We propose a fast inference method for Bayesian nonlinear support vector machines that leverages stochastic variational inference and inducing points. Our experiments show that the proposed method is faster than competing Bayesian…

Model-based diagnosis reasons backwards from a functional schematic of a system to isolate faults given observations of anomalous behavior. We develop a fully probabilistic approach to model based diagnosis and extend it to support…

A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…

We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we…

Spatial modelling often uses Gaussian random fields to capture the stochastic nature of studied phenomena. However, this approach incurs significant computational burdens (O(n3)), primarily due to covariance matrix computations. In this…

We introduce the first, general purpose, slice sampling inference engine for probabilistic programs. This engine is released as part of StocPy, a new Turing-Complete probabilistic programming language, available as a Python library. We…

Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…

High-dimensional data can be useful for causal inference by providing many confounders that may bolster the plausibility of the ignorability assumption. Propensity score methods are powerful tools for causal inference, are popular in health…

Clinical trials often seek to determine the superiority, equivalence, or non-inferiority of an experimental condition (e.g., a new drug) compared to a control condition (e.g., a placebo or an already existing drug). The use of frequentist…

Many domain experts do not have the time or expertise to write formal Bayesian models. This paper takes an informal problem description as input, and combines a large language model and a probabilistic programming language to define a joint…

There is increasing interest in flexible parametric models for the analysis of time-to-event data, yet Bayesian approaches that offer incorporation of prior knowledge remain underused. A flexible Bayesian parametric model has recently been…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

Bayesian optimization is proposed for automatic learning of optimal controller parameters from experimental data. A probabilistic description (a Gaussian process) is used to model the unknown function from controller parameters to a…

Mechanistic models are important tools to describe and understand biological processes. However, they typically rely on unknown parameters, the estimation of which can be challenging for large and complex systems. We present pyPESTO, a…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…