相关论文: On a Seminal Paper by Karlin and McGregor

This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of…

Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…

The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach.…

A major challenge in the analysis of population genomics data consists of isolating signatures of natural selection from background noise caused by random drift and gene flow. Analyses of massive amounts of data from many related…

In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the…

We discuss semiempirical approaches and parametric methods developed for modeling molecular vibronic spectra. These methods, together with databases of molecular fragments, have proved efficient and flexible for solving various problems…

Using a technique introduced by Sergei Naboko, we analyze a generalization of the parameter-controlled model of spectral transition, originally proposed by Smilansky and Solomyak, to the situation where the singular interaction responsible…

Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…

We derive the conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results…

In the context of survival analysis, Marshall and Olkin (1997) introduced families of distributions by adding a scalar parameter to a given survival function, parameterized or not. In that paper, we generalize their approach. We show how it…

The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…

Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly…

This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…

The simple (linear) birth-and-death process is a widely used stochastic model for describing the dynamics of a population. When the process is observed discretely over time, despite the large amount of literature on the subject, little is…

Since the famous paper written by Kaplan and Meier in 1958, survival analysis has become one of the most important fields in statistics. Nowadays it is one of the most important statistical tools in analyzing epidemiological and clinical…

We investigate the simulation methods for a large family of stable random fields that appeared in the recent literature, known as the Karlin stable set-indexed processes. We exploit a new representation and implement the procedure…

A new stochastic method for describing mortality is proposed and explored. It is based on differences of observed times series of the transform $\log(-\log x)$ of survival probabilities which seem to follow simple patterns over the years.…

This proceeding is intended to be a first introduction to spectral methods. It is written around some simple problems that are solved explicitly and in details and that aim at demonstrating the power of those methods. The mathematical…

We introduce the concept of an academic genealogy, or AG, and illustrate how AG charts may be constructed and then demonstrate how this methodology can be used by applying it to create the partial or full AG charts to two scientists, Paul…