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Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…

Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…

Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…

Stochastic inference on Lie groups plays a key role in state estimation problems such as; inertial navigation, visual inertial odometry, pose estimation in virtual reality, etc. A key problem is fusing independent concentrated Gaussian…

We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Estimating the parameters of compact binaries which coalesce and produce gravitational waves is a challenging Bayesian inverse problem. Gravitational-wave parameter estimation lies within the class of multifidelity problems, where a variety…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from…

In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…

Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI…

Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman…

Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…