Related papers: Foundations for Bayesian inference with engineered…
In this paper, we develop statistical inference techniques for the unknown coefficient functions and single-index parameters in single-index varying-coefficient models. We first estimate the nonparametric component via the local linear…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and…
Bayesian learning provides a unified skeleton to solve the electrophysiological source imaging task. From this perspective, existing source imaging algorithms utilize the Gaussian assumption for the observation noise to build the likelihood…
We demonstrate and explicate Bayesian methods for fitting the parameters that encode the impact of short-distance physics on observables in effective field theories (EFTs). We use Bayes' theorem together with the principle of maximum…
Over the past years, the interpretation of measurements in the context of effective field theories has attracted much attention in the field of particle physics. We present a tool for interpreting sets of measurements in such models using a…
In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
The task of quantifying the inherent uncertainty associated with neural network predictions is a key challenge in artificial intelligence. Bayesian neural networks (BNNs) and deep ensembles are among the most prominent approaches to tackle…
This paper discusses the amplitude estimation using data originating from a sine-like function as probability density function. If a simple least squares fit is used, a significant bias is observed for small amplitudes. It is shown that a…
We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
Quantum parameter estimation plays a key role in many fields like quantum computation, communication and metrology. Optimal estimation allows one to achieve the most precise parameter estimates, but requires accurate knowledge of the model.…
Obtaining heteroscedastic predictive uncertainties from a Bayesian Neural Network (BNN) is vital to many applications. Often, heteroscedastic aleatoric uncertainties are learned as outputs of the BNN in addition to the predictive means,…
Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradigm of active…
We develop Probabilistic Targeted Factor Analysis (PTFA), a likelihood-based framework for constructing latent factors that are explicitly targeted to variables of economic interest. PTFA provides a probabilistic foundation for Partial…