Related papers: Constructing processes with prescribed mixing coef…
This paper proves a Berry--Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be $O(n^{-1/2})$ as $n\to\infty$, where $n$ denotes the sample…
We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some…
Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the…
Our ability to calculate rates of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant…
We perform a thorough analysis of the $\eta-\eta'$ mixing effects on the $\Lambda_b\rightarrow \Lambda \eta^{(')}$ decays based on the perturbative QCD (PQCD) factorization approach. Branching ratios, up-down and direct $CP$ asymmetries are…
We model voting behaviour in the multi-group setting of a two-tier voting system using sequences of de Finetti measures. Our model is defined by using the de Finetti representation of a probability measure (i.e. as a mixture 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…
A bound uniform over various loss-classes is given for data generated by stationary and phi-mixing processes, where the mixing time (the time needed to obtain approximate independence) enters the sample complexity only in an additive way.…
Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in…
The degree of entanglement is determined for an arbitrary state of a broad class of PT-symmetric bipartite composite systems. Subsequently we quantify the rate with which entangled states are generated and show that this rate can be…
We introduce conditions of lower decoupling to the study of waiting-time estimations of the cross entropy between two mutually independent stationary stochastic processes. Although similar decoupling conditions have been used in the…
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting…
In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…
Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, internal workings of the code and the number of iterations to convergence, the latter…
We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…