Related papers: Bayesian interpretation of periodograms
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…
Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying…
Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
In contrast to previous analyses, we demonstrate a Bayesian approach to the estimation of the CKM phase $\alpha$ that is invariant to parameterization. We also show that in addition to {\em computing} the marginal posterior in a Bayesian…
Unbiased estimators are introduced for averaged Bregman divergences which generalize Stein's Unbiased (Predictive) Risk Estimator, and the minimization of these estimators is proposed as a regularization parameter selection method for…
Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…
We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…