Related papers: Random Transpositions on Contingency Tables

The number of ``carries'' when $n$ random integers are added forms a Markov chain [23]. We show that this Markov chain has the same transition matrix as the descent process when a deck of $n$ cards is repeatedly riffle shuffled. This gives…

The McNemar test evaluates the hypothesis that two correlated proportion is common in $2 \times 2$ contingency tables with the same categories. This study discusses a test for symmetry in $2 \times 2$ contingency tables with nonignorable…

There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…

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…

Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions are considered. Under these conditions, a concentration of…

This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…

A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments is determined by the sign of the current position. We explicitly identify an invariant…

Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…

In two-way contingency tables we sometimes find that frequencies along the diagonal cells are relatively larger(or smaller) compared to off-diagonal cells, particularly in square tables with the common categories for the rows and the…

This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…

We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…

Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of…

This note presents conjectures on polynomial/algebraic/sub-exponential convergence of transition probabilities for $\lambda$-null recurrent and $\lambda$-transient Markov chains in continuous time. The only known positive examples are in…

For Markov jump processes on irreducible networks with finite number of sites, we derive a general and explicit expression of the squared coefficient of variation for the net number of transitions from one site to a connected site in a…

In this work we define log-linear models to compare several square contingency tables under the quasi-independence or the quasi-symmetry model, and the relevant Markov bases are theoretically characterized. Through Markov bases, an exact…

The "carries" when n random numbers are added base b form a Markov chain with an "amazing" transition matrix determined by Holte. This same Markov chain occurs in following the number of descents or rising sequences when n cards are…

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…

Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…

Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…