Related papers: Inferring the initial condition for the Balitsky-K…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
The small-$x$ evolution of protons is determined from numerical solutions of the JIMWLK equations, starting from an initial condition at moderate $x$ for a finite size proton. The resulting dipole amplitude is used to calculate the total…
We present a global analysis of available data on inclusive structure functions and reduced cross sections measured in electron-proton scattering at small values of Bjorken-x, x<0.01, including the latest data from HERA on reduced cross…
We use recently proposed method of ratios to assess the quality of geometrical scaling in deep inelastic scattering for different forms of the saturation scale. We consider original form of geometrical scaling (motivated by the…
We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $\theta \in \mathbb{R}^d$, and which include multivariate skew normal…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
Using the Balitsky-Kovchegov (BK) equation as an explicit example, we show that nonlinear QCD evolution leads to an instability in the propagation toward the infrared of the gluon transverse momentum distribution, if one starts with a state…
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior…
Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
The BFKL and the unified angular-ordered equations are solved to determine the gluon distribution at small $x$. The impact of kinematic constraints is investigated. Predictions are made for observables sensitive to the gluon at small $x$.…
Deep inelastic scattering (DIS) total cross section data at small-x as measured by the HERA experiments is well described by Balitsky-Kovchegov (BK) evolution in the leading order dipole picture. Recently the full Next-to-Leading Order…
Building on the newly available solution of the Balitsky-Kovchegov (BK) equation with the full impact-parameter dependence, we extend the study of parton evolution from proton to nuclear targets. Since a key part of the scientific programme…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…
Background and Objective: Wilson statistics describe well the power spectrum of proteins at high frequencies. Therefore, it has found several applications in structural biology, e.g., it is the basis for sharpening steps used in cryogenic…
This paper argues that the half-Cauchy distribution should replace the inverse-Gamma distribution as a default prior for a top-level scale parameter in Bayesian hierarchical models, at least for cases where a proper prior is necessary. Our…
In this work, we investigate the estimation of a parameter $f$ in PDEs using Bayesian procedures, and focus on posterior distributions constructed using Gaussian process priors, and its variational approximation. We establish contraction…
We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…