Related papers: Likelihood approximations via Gaussian approximate…
Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…
Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
In classification tasks, softmax functions are ubiquitously used as output activations to produce predictive probabilities. Such outputs only capture aleatoric uncertainty. To capture epistemic uncertainty, approximate Gaussian inference…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that…
In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…
Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
We present exact non-Gaussian joint likelihoods for auto- and cross-correlation functions on arbitrarily masked spherical Gaussian random fields. Our considerations apply to spin-0 as well as spin-2 fields but are demonstrated here for the…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…
We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…
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…
Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…