Related papers: A flexible class of priors for orthonormal matrice…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
The interpretation of data in terms of multi-parameter models of new physics, using the Bayesian approach, requires the construction of multi-parameter priors. We propose a construction that uses elements of Bayesian reference analysis. Our…
Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a structured Bayesian group factor analysis model…
Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
Bayesian hierarchical models are frequently used in practical data analysis contexts. One interpretation of these models is that they provide an indirect way of assigning a prior for unknown parameters, through the introduction of…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
Foundation models, and in particular large language models, can generate highly informative responses, prompting growing interest in using these ''synthetic'' outputs as data in empirical research and decision-making. This paper introduces…
Most of existing results on regularized system identification focus on regularized impulse response estimation. Since the impulse response model is a special case of orthonormal basis functions, it is interesting to consider if it is…
Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
We analyze effective approximation of unitary matrices. In our formulation, a unitary matrix is represented as a product of rotations in two-dimensional subspaces, so-called Givens rotations. Instead of the quadratic dimension dependence…
Optimization models involving quaternion matrices are widely used in color image process and other engineering areas. These models optimize real functions of quaternion matrix variables. In particular, $\ell_0$-norms and rank functions of…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…
Variational inference approximates Bayesian posterior distributions by projecting onto a tractable family of distributions. While most theoretical analyses evaluate the quality of this approximation using global divergence measures, many…
Prior elicitation methods for Bayesian analyses transfigure prior information into quantifiable prior distributions. Recently, methods that leverage copulas have been proposed to accommodate more flexible dependence structures when…
The PARAFAC2 is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example because of differences in signal sampling or batch sizes. A fully probabilistic…
Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. A matrix Bingham-von Mises-Fisher distribution is a probability distribution on the set of orthonormal matrices that…