相关论文: On the first k moments of the random count of a pa…

This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…

The pattern $(k_1, k_2, \dots, k_\ell)$ is defined to have at least $k_1$ consecutive $1$'s followed by at least $k_2$ consecutive $2$'s, $\dots$, followed by at least $k_\ell$ consecutive $\ell$'s. By iteratively applying the method that…

We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…

We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of…

We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a…

This paper proposes an algorithm to generate random numbers from any member of the truncated multivariate elliptical family of distributions with a strictly decreasing density generating function. Based on Neal (2003) and Ho et al. (2012),…

These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…

Probability generating functions for first passage times of Markov chains are found using the method of collective marks. A system of equations is found which can be used to obtain moments of the first passage times.

We derive moment identities for the stochastic integrals of multiparameter processes in a random-connection model based on a point process admitting a Papangelou intensity. Those identities are written using sums over partitions, and they…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…

We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…

We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…

Methods used to infer nuclear parameters from neutron count statistics fall into two categories depending on whether they use moments or count number probabilities. As probabilities are in general more difficult to calculate, we are…

We obtain quantitative Four Moments Theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumption we make on the Pearson distribution is that it admits four moments. While…

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…

In recent work of Baik, Deift and Rains convergence of moments was established for the limiting joint distribution of the lengths of the first k rows in random Young tableaux. The main difficulty was obtaining a good estimate for the tail…

There are known expressions to calculate the moments of the first passage time in Markov chains. Nevertheless, it is commonly forgotten that in most applications the parameters of the Markov chain are constructed using estimates based upon…

Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…

We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…