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 columns. In this case the quasi-independence model with an additional parameter for each of the diagonal cells is usually fitted to the data. A simpler model than...

The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in the power sum polynomials. The Markov chain has stationary distribution a new two-parameter family of measures on partitions, the inverse of the Macdonald we...

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 columns. In this case the quasi-independence model with an additional parameter for each of the diagonal cells is usually fitted to the data. A simpler model than...

Several different models for predicting coverage in a fault-tolerant system are discussed, including models for permanent, intermittent, and transient errors. Markov, semi-Markov, nonhomogeneous Markov, and extended stochastic Petri net models for computing coverage are developed. Two types of events which interfere with recovery are examined; methods for modeling such events (applicable if the...

We propose a new collaborative filtering method that can predict the next purchase item by efficiently using the sequential information in purchase histories for recommendations. Markov models and maximum entropy models are both widely used techniques for such recommendations. In Markov models, parameters can be estimated and updated fast and efficiently, but predictions may not be accurate. On...

In this paper, we study large deviations of maximum likelihood and related estimators for hidden Markov models. A hidden Markov model consists of parameterized Markov chains in a Markovian random environment, with the underlying environmental Markov chain viewed as missing data. A difficulty with parameter estimation in this model is the non-additivity of the log-likelihood function. Based on a...

This paper proposes a modified quasi-likelihood test of Markov regime switching models. Despite its popularity in economics and finance, there are few papers that develop tests for regime switching models. Recently, Cho and White (2007) derive the asymptotic distribution of the quasi-likelihood ratio (QLR) statistic of Markov regime switching models with a scalar parameter. The asymptotic distr...

Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the best-fit parameters are insufficient when models are high dimensional and under-constrained. As a result, Bayesian methods, which treat model parameters as random ...

We consider families of smooth one-dimensional maps with several critical points and outline the main ideas of the construction in the parameter space that allows to get infinite Markov Partitions and SRB measures for a positive set of parameter values. The construction is based on the properties of uniformly scaled Markov partitions from [6]. The same approach works for families of Henon-like ...

Fig. 2. space by Patrick-Fisher's algorithm (solid line) and E (dotted line). Bayes error estimates for SONAR data transformed to IO-dimensional high-dimensional data these results might be more in favor of E.) This is a result of the fact that each iteration of simplex requires that the samples be transformed to the low-dimensional space, and then the Bayes error estimated in that space, which...