Related papers: Ensemble Kalman Inversion for General Likelihoods
Let $f(y|\theta), \; \theta \in \Omega$ be a parametric family, $\eta(\theta)$ a given function, and $G$ an unknown mixing distribution. It is desired to estimate $E_G (\eta(\theta))\equiv \eta_G$ based on independent observations…
We revisit the classical credibility results of Jewell and B\"uhlmann to obtain credibility premiums for a GLM using a modern Bayesian approach. Here the prior distributions can be chosen without restrictions to be conjugate to the response…
A recent trend in Bayesian research has been revisiting generalizations of the likelihood that enable Bayesian inference without requiring the specification of a model for the data generating mechanism. This paper focuses on a Bayesian…
In recent years, several ensemble-based filtering methods have been proposed and studied. The main challenge in such procedures is the updating of a prior ensemble to a posterior ensemble at every step of the filtering recursions. In the…
Generalized linear models (GLMs) arguably represent the standard approach for statistical regression beyond the Gaussian likelihood scenario. When Bayesian formulations are employed, the general absence of a tractable posterior distribution…
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…
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…
Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not…
Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…
This paper provides a unified perspective of iterative ensemble Kalman methods, a family of derivative-free algorithms for parameter reconstruction and other related tasks. We identify, compare and develop three subfamilies of ensemble…
We describe a generalization of the large sieve to situations where the underlying groups are nonabelian, and give several applications to the arithmetic of abelian varieties. In our applications, we sieve the set of primes via the system…
Regression classes modeling more than the mean of the response have found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this family of models. Expectiles offer a quantile-like…
We obtain the tail probability of generalized sub-Gaussian canonical processes. It can be viewed as a variant of the Bernstein-type inequality in the i.i.d case, and we further get a tighter bound of concentration inequality through…
Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
Motivated by big data and the vast parameter spaces in modern machine learning models, optimisation approaches to Bayesian inference have seen a surge in popularity in recent years. In this paper, we address the connection between the…
Recently, combinations of generative and Bayesian machine learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…