The Markov-Bernoulli geometric distribution is obtained when a generalization, as a Markov process, of the independent Bernoulli sequence of random variables is introduced by considering the success probability changes with respect to the Markov chain. The resulting model is called the MarkovBernoulli model and it has a wide variety of application fields. In this study, some characterizations a...

A finite-state stationary process is called (one or twosided) super-K if its (one or two-sided) super-tail field—generated by keeping track of (initial or central) symbol counts as well as of arbitrarily remote names—is trivial. We prove that for every process (α, T ) which has a direct Bernoulli factor there is a generating partition β whose one-sided super-tail equals the usual one-sided tail...

This paper proposed a new regression model called l1regularized outlier isolation and regression (LOIRE) and a fast algorithm based on block coordinate descent to solve this model. Besides, assuming outliers are gross errors following a Bernoulli process, this paper also presented a Bernoulli estimate model which, in theory, should be very accurate and robust due to its complete elimination of ...

In this paper we consider a (possibly continuous) space of Bernoulli experiments. We assume that the Bernoulli distributions are correlated. All evidence data comes in the form of successful or failed experiments at different points. Current state-ofthe-art methods for expressing a distribution over a continuum of Bernoulli distributions use logistic Gaussian processes or Gaussian copula proces...

In classification, Bayes' rule is used to calculate the probabilities of the classes. The main aim is related about how we can make rational decisions to minimize expected risk. Bayes' theorem provides a way to calculate the probability of a hypothesis based on its prior probability, the probabilities of observing various data given the hypothesis, and the observed data itself. Probability and ...

It has equilibrium (and in fact reversible) measure μ the product Bernoulli measure of density p on {0, 1}Z. It can also be constructed by attaching a Poisson process clock to every site in Z. Every time a clock rings, the site is refreshed to a Bernoulli variable of parameter p, but only if its right neighbour is empty. This constraint creates the ”bubbles” one can see on the picture. A natura...

By a symbolic method, we introduce multivariate Bernoulli and Euler polynomials as powers of polynomials whose coefficients involve multivariate Lévy processes. Many properties of these polynomials are stated straightforwardly thanks to this representation, which could be easily implemented in any symbolic manipulation system. A very simple relation between these two families of multivariate po...