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A typical approach to estimate an unknown quantity is to design an experiment that produces a random variable Z distributed in 0; 1] with EZ] = , run this experiment independently a number of times and use the average of the outcomes as the estimate. In this paper, we consider the case when no a priori information about Z is known except that is distributed… (More)
Realistic statistical models often give rise to probability distributions that are then one should first attempt to use classical Monte Carlo methods that are based on iid Journal of the Royal Statistical Society, Series B 54, 657–699. MRI data, in Handbook of Markov Chain Monte Carlo, S. Brooks, A. Gelman. and output, VBA development environment and… (More)
By using the probabilistic method, we show that the maximum number of directed Hamiltonian paths in a complete directed graph with n vertices is at least (e − o(1)) n! 2 n−1 .
We consider a coalescing particle model where particles move in discrete time. At each time period, each remaining ball is independently put in one of n bins according to a probability distribution p ϭ (p 1 ,. .. , p n), and all balls put into the same bin merge into a single ball. Starting with k balls, we are interested in the properties of E[N(p, k)],… (More)
A random walk that is skip-free to the left can only move down one level at a time but can skip up several levels. Such random walk features prominently in many places in applied probability including queuing theory and the theory of branching processes. This article exploits the special structure in this class of random walk to obtain a number of… (More)
When a new computer software package is developed and all obvious erros removed, a testing procedure is often put into effect to eliminate the remaining errors in the package. One common procedure is to try the package on a set of randomly chosen problems. We suppose that whenever a program encounters an error, a system failure results. At this point the… (More)