Related papers: The Nishimori line and Bayesian Statistics
We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian…
We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…
We derive a rigorous lower bound on the average local energy for the Ising model with quenched randomness. The result is that the lower bound is given by the average local energy calculated in the absence of all interactions other than the…
We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…
The main goal of the paper is to prove central limit theorems for the magnetization rescaled by $\sqrt{N}$ for the Ising model on random graphs with $N$ vertices. Both random quenched and averaged quenched measures are considered. We work…
At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…
We focus on a linear chain of $N$ first-neighbor-coupled logistic maps at their edge of chaos in the presence of a common noise. This model, characterised by the coupling strength $\epsilon$ and the noise width $\sigma_{max}$, was recently…
Bayesian error analysis paves the way to the construction of credible and plausible error regions for a point estimator obtained from a given dataset. We introduce the concept of region accuracy for error regions (a generalization of the…
We study the +/- J random-plaquette Z_2 gauge model (RPGM) in three spatial dimensions, a three-dimensional analog of the two-dimensional +/- J random-bond Ising model (RBIM). The model is a pure Z_2 gauge theory in which randomly chosen…
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…
Dyson [Commun. Math. Phys. 12, 91 (1969)] rigorously proved the existence of a phase transition in the one-dimensional Ising model with long-range interactions of the form $r^{-\alpha}$ for $1 < \alpha < 2$. In the present study, we extend…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
The two-dimensional q-state Potts model is subjected to a Z_q symmetric disorder that allows for the existence of a Nishimori line. At q=2, this model coincides with the +/- J random-bond Ising model. For q>2, apart from the usual pure and…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Many Bayesian inference problems involve high dimensional models for which only a subset of the model variables are of actual interest. All other variables are just nuisance parameters that one would ideally like to integrate out…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
Scientific fields such as insider-threat detection and highway-safety planning often lack sufficient amounts of time-series data to estimate statistical models for the purpose of scientific discovery. Moreover, the available limited data…