Related papers: Bayesian spectral density estimation using P-splin…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
Bayesian neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network…
The idea of replacing hardware by software to compensate for scattered radiation in flat-panel X-ray imaging is well established in the literature. Recently, deep-learningbased image translation approaches, most notably the U-Net, have…
This paper proposes a novel framework for the approximation and analysis of circular density data using compositional periodic splines within Bayes spaces with the Hilbert space structure. By applying the centered log-ratio transformation,…
Accurate reconstruction of probability density functions (PDFs) from data is essential in engineering applications. Classical global moment-based polynomial approximations often suffer from oscillations, instability in the tails, and…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the classical spectral-based adjacency/Laplacian spectral embedding,…
Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. Prior specification is, however, relatively…
We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modeling uncertainty is one of the key features of Bayesian methods. Using Bernoulli dropout with…
Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over…
Our focus is on constructing a multiscale nonparametric prior for densities. The Bayes density estimation literature is dominated by single scale methods, with the exception of Polya trees, which favor overly-spiky densities even when the…
Let $\mathbf {X}=\{X_t, t=1,2,... \}$ be a stationary Gaussian random process, with mean $EX_t=\mu$ and covariance function $\gamma(\tau)=E(X_t-\mu)(X_{t+\tau}-\mu)$. Let $f(\lambda)$ be the corresponding spectral density; a stationary…
Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…
Sup-norm curve estimation is a fundamental statistical problem and, in principle, a premise for the construction of confidence bands for infinite-dimensional parameters. In a Bayesian framework, the issue of whether the…
This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…
Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. However, due to the flexibility of these models,…
The usual procedure for estimating the significance of a peak in a power spectrum is to calculate the probability of obtaining that value or a larger value by chance, on the assumption that the time series contains only noise (e.g. that the…
There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being…