Related papers: Markov bases and subbases for bounded contingency …
Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite…
We consider Markov basis arising from fractional factorial designs with three-level factors. Once we have a Markov basis, $p$ values for various conditional tests are estimated by the Markov chain Monte Carlo procedure. For designed…
We present a method to generate contingency tables that follow loglinear models with prescribed marginal probabilities and dependence structures. We make use of (loglinear) Poisson regression, where the dependence structures, described…
Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
We revisit surplus on general life insurance contracts, represented by Markov models. We classify technical bases in terms of boundary conditions in Thiele's equation(s), allowing more general regulations than Scandinavian-style…
A binary contingency table is an m x n array of binary entries with prescribed row sums r=(r_1,...,r_m) and column sums c=(c_1,...,c_n). The configuration model for uniformly sampling binary contingency tables proceeds as follows. First,…
In a probabilistic graphical model on a set of variables $V$, the Markov blanket of a random vector $B$ is the minimal set of variables conditioned to which $B$ is independent from the remaining of the variables $V \backslash B$. We…
In the field of algebraic systems biology, the number of minimal polynomial models constructed using discretized data from an underlying system is related to the number of distinct reduced Gr\"obner bases for the ideal of the data points.…
Understanding causal relationships between variables is a fundamental problem with broad impact in numerous scientific fields. While extensive research has been dedicated to learning causal graphs from data, its complementary concept of…
Predicting the effect of unseen interventions is a fundamental research question across the data sciences. It is well established that in general such questions cannot be answered definitively from observational data. This realization has…
We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such…
The perceived advantage of machine learning (ML) models is that they are flexible and can incorporate a large number of features. However, many of these are typically correlated or dependent, and incorporating all of them can hinder model…
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…
Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the table. While classical results show that…
In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The…
Assuming sufficiently many terms of a n-dimensional table defined over a field are given, we aim at guessing the linear recurrence relations with either constant or polynomial coefficients they satisfy. In many applications, the table terms…
The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium…
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the…
Several interesting models for contingency tables are defined by a system of equality and inequality constraints on a suitable set of marginal log-linear parameters. After reviewing the most common difficulties which are intrinsic to order…