Related papers: Multidimensional integration through Markovian sam…
Suppose that a mobile sensor describes a Markovian trajectory in the ambient space. At each time the sensor measures an attribute of interest, e.g., the temperature. Using only the location history of the sensor and the associated…
We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. Our method is based on expressing the Fisher metric in terms of the posterior distributions…
Evaluating expectations on an Ising model (or Boltzmann machine) is essential for various applications, including statistical machine learning. However, in general, the evaluation is computationally difficult because it involves intractable…
Stochastic Thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from anti-symmetric jump observables defined on the edges of the graph representing the…
Simulated annealing - moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions - has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers.…
Two identities in statistical mechanics involving entropy differences (or ratios of density of states) at constant energy are derived. The first provides a nontrivial extension of the Jarzynski equality to the microcanonical ensemble [C.…
Given an unnormalized probability density $\pi\propto\mathrm{e}^{-V}$, estimating its normalizing constant $Z=\int_{\mathbb{R}^d}\mathrm{e}^{-V(x)}\mathrm{d}x$ or free energy $F=-\log Z$ is a crucial problem in Bayesian statistics,…
Stochastic kriging is a popular technique for simulation metamodeling due to its exibility and analytical tractability. Its computational bottleneck is the inversion of a covariance matrix, which takes $O(n^3)$ time in general and becomes…
We present a new approach to a classical problem in statistical physics: estimating the partition function and other thermodynamic quantities of the ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem have been…
Multidimensional numerical integration is a central ingredient of theoretical predictions in high-energy physics, where multiloop Feynman diagrams and phase-space integrals are computationally demanding due to divergences and complex…
We introduce a linear-scaling stochastic method to compute real-space maps of any positive local spectral operator in a tight-binding model. By employing positive-definite estimators, the sampling error at each site can be rigorously…
The exact stochastic decomposition of non-Markovian dissipative quantum dynamics is combined with the time-dependent semiclassical initial value formalism. It is shown that even in the challenging regime of moderate friction and low…
The Jarzynski estimator is a powerful tool that uses nonequilibrium statistical physics to numerically obtain partition functions of probability distributions. The estimator reconstructs partition functions with trajectories of the…
Building on a variant of the Jarzynski equation we propose a new method to numerically determine the prior-predictive value in a Bayesian inference problem. The method generalizes thermodynamic integration and is not hampered by…
Smoothness has long been the dominant form of parsimony in functional data analysis, to the point of occasionally being conflated with the very notion of functional data. However, many core inferential tasks depend on the inverse…
Ratios of normalizing constants for two distributions are needed in both Bayesian statistics, where they are used to compare models, and in statistical physics, where they correspond to differences in free energy. Two approaches have long…
Hyperspectral images can be represented either as a set of images or as a set of spectra. Spectral classification and segmentation and data reduction are the main problems in hyperspectral image analysis. In this paper we propose a Bayesian…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
The evaluation of the free energy of a stochastic model is considered a significant issue in various fields of physics and machine learning. However, the exact free energy evaluation is computationally infeasible because the free energy…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…