Related papers: Bayesian model selection: Application to adjustmen…
We study model selection by the Bayesian information criterion (BIC) in fixed-dimensional exploratory factor analysis over a fixed finite family of compact covariance classes. Our main result shows that the BIC is strongly consistent for…
We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…
This paper considers the problem of model selection within the context of finite element model updating. Given that a number of FEM updating models, with different updating parameters, can be designed, this paper proposes using the Bayesian…
Time variation of Newtonian gravitational constant, $G$, is studied in the model universe with variable space dimension proposed recently. Using the Lagrangian formulation of these models, we find the effective gravitational constant as a…
High-quality nanomechanical oscillators can sensitively probe force, mass, or displacement in experiments bridging the gap between the classical and quantum domain. Dynamics of these stochastic systems is inherently determined by the…
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…
The Bayesian learning rule is a natural-gradient variational inference method, which not only contains many existing learning algorithms as special cases but also enables the design of new algorithms. Unfortunately, when variational…
A systematic procedure is proposed for deriving all the gauge symmetries of the general, not necessarily variational, equations of motion. For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the…
Occam's razor is a guiding principle that models should be simple enough to describe observed data. While Bayesian model selection (BMS) embodies it by the intrinsic regularization effect (IRE), how observed data scale the IRE has not been…
In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$. The general idea was obviously outlined…
With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
Methods utilizing instrumental variables have been a fundamental statistical approach to estimation in the presence of unmeasured confounding, usually occurring in non-randomized observational data common to fields such as economics and…
We propose a model-independent framework for fitting hadronic form-factor data, which is often only available at discrete kinematical points, using parameterisations based on to unitarity and analyticity. In this novel approach the latter…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
We study properties of the ground state of the Nelson model through functional integration. We obtain bounds on the average and the variance of the Bose field both in position and momentum space, on the distribution of the number of bosons,…
We consider the Bayesian detection statistic for a targeted search for continuous gravitational waves, known as the $\mathcal{B}$-statistic. This is a Bayes factor between signal and noise hypotheses, produced by marginalizing over the four…
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…
For a dynamical system, we study the set of points $\cal W$ whose orbit approximates any chosen point at certain specified rates. Our basic setting is that of left shift acting on topological Markov chains endowed with a local weak Gibbs…
Bayesian Poisson Non-Negative Matrix Factorization (NMF) is widely used to model count data, including in cancer mutational signature analysis. However, standard Gibbs samplers rely on computationally expensive Poisson augmentation, and…