Run Probabilities in Sequences of Markov-Dependent Trials

Stationary Probabilities of Markov Chains

In this paper, based on probabilistic arguments, we obtain an explicit solution of the stationary distribution for a discrete time Markov chain with an upper Hessenberg time stationary transition probability matrix. Our solution then leads to a numerically stable and eecient algorithm for computing stationary probabilities. Two other expressions for the stationary distribution are also derived,...

The Run Probabilities of Tes Processes

The run statistics of a discrete-time, real-valued stochastic process are the statistics of process excursions above a given level. As such they are a special case of first passage times (hitting times) in discrete time. The study of run probabilities is motivated by applications such as compressed video, where a random and autocorrelated sequence of compressed frames arrives deterministically ...

Central and Local Limit Theories in Markov Dependent Random Variables

Randomized controlled trials: who fails run-in?

BACKGROUND Early identification of participants at risk of run-in failure (RIF) may present opportunities to improve trial efficiency and generalizability. METHODS We conducted a partial factorial-design, randomized, controlled trial of calcium and vitamin D to prevent colorectal adenoma recurrence at 11 centers in the United States. At baseline, participants completed two self-administered q...

Toward Markov Logic with Conditional Probabilities

Combining probability and first-order logic has been the subject of intensive research during the last ten years. The most well-known formalisms combining probability and some subset of first-order logic are probabilistic relational models (PRMs), Bayesian logic programs (BLPs) and Markov logic networks (MLNs). Of these three formalisms, MLN is the currently most actively researched. While the ...