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Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

Efficient Bayesian inference remains a computational challenge in hierarchical models. Simulation-based approaches such as Markov Chain Monte Carlo methods are still popular but have a large computational cost. When dealing with the large…

Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and…

We present FlowSN, a statistical framework using simulation-based inference (SBI) with normalising flows to account for selection effects in observational astronomy. Failure to account for selection effects can lead to biased inference on…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

We introduce a new method for learning Bayesian neural networks, treating them as a stack of multivariate Bayesian linear regression models. The main idea is to infer the layerwise posterior exactly if we know the target outputs of each…

In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…

We introduce two synthetic likelihood methods for Simulation-Based Inference (SBI), to conduct either amortized or targeted inference from experimental observations when a high-fidelity simulator is available. Both methods learn a…

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…

Simulation-based inference (SBI) is the preferred framework for estimating parameters of intractable models in science and engineering. A significant challenge in this context is the large computational cost of simulating data from complex…

Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…

This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling,…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

Simulation-based inference (SBI) is a method to perform inference on a variety of complex scientific models with challenging inference (inverse) problems. Bayesian Optimal Experimental Design (BOED) aims to efficiently use experimental…

A learning-based posterior distribution estimation method, Probabilistic Dipole Inversion (PDI), is proposed to solve quantitative susceptibility mapping (QSM) inverse problem in MRI with uncertainty estimation. A deep convolutional neural…

Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data…

The Laser Interferometer Space Antenna (LISA) data stream will inevitably contain gaps due to maintenance and environmental disturbances, introducing nonstationarities and spectral leakage that compromise standard frequency-domain…