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This paper is concerned with elucidating a relationship between two common coupling methods for the continuous time Markov chain models utilized in the cell biology literature. The couplings considered here are primarily used in a…
Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising…
We present a new method for simulating Markovian jump processes with time-dependent transitions rates, which avoids the transformation of random numbers by inverting time integrals over the rates. It relies on constructing a sequence of…
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…
Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks…
Flowgraph models provide an alternative approach in modeling a multi-state stochastic process. One of the most widely used stochastic processes that have many real-world applications especially in actuarial models is the Markov jump process…
We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we…
We consider prediction in multiple studies with potential differences in the relationships between predictors and outcomes. Our objective is to integrate data from multiple studies to develop prediction models for unseen studies. We propose…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
Statistical static timing analysis deals with the increasing variations in manufacturing processes to reduce the pessimism in the worst case timing analysis. Because of the correlation between delays of circuit components, timing model…
We introduce the concept of `discrete-time persistence', which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n \Delta T. For a Gaussian Markov process with relaxation rate \mu, we show…
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
Markov chain Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty.…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
Event sequences can be modeled by temporal point processes (TPPs) to capture their asynchronous and probabilistic nature. We propose an intensity-free framework that directly models the point process distribution by utilizing normalizing…
We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…
The waiting time distribution (WTD) is a common tool for analysing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete,…
Piecewise-deterministic Markov processes (PDMPs) offer a powerful stochastic modeling framework that combines deterministic trajectories with random perturbations at random times. Estimating their local characteristics (particularly the…
We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study…