Abstract. This chapter provides a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.

Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model’s validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a wellknown result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the sup-

The purpose of this paper is to describe a method for simulation of recently introduced fluid stochastic Petri nets. Since such nets result in rather complex set of partial differential equations, numerical solution becomes a formidable task. Because of a mixed, discrete and continuous state space, simulative solution also poses some interesting challenges, which are addressed in the paper. 1

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Neurons in which the level of excitation and inhibition are roughly balanced are shown to be very sensitive to the coherence of their synaptic input. The behavior of such balanced neurons with reversal potentials is analyzed both analytically and numerically using the leaky integrate-and-fire neural model. The investigation uses the Gaussian approximation with synaptic inputs modeled as inhomogeneous Poisson processes. The results indicate that for balanced neurons with N synaptic inputs, it is only necessary for O( # N) of the synaptic inputs to have a periodicity in order that their spike outputs become phase-locked to this periodic signal.

this paper, we review some of the importance-sampling techniques that have been developed in recent years to e#ciently estimate dependability measures in Markovian and non-Markovian models of highly dependable systems. 1 Acronyms MTTF Mean time to failure. MTBF Mean time between failures. CTMC Continuous-time Markov chain. DTMC Discrete-time Markov chain. GSMP Generalized semi-Markov process. SAVE System AVailability Estimator. CLT Central limit theorem. VRR Variance reduction ratio. TRR Total e#ort reduction ratio. MSDIS Measure-specific dynamic importance sampling. BLBLR Balance over links balanced likelihood ratio. BLBLRC Balance over links balanced likelihood ratio with cuts. 1 INTRODUCTION High dependability requirements of today's critical and/or commercial systems often lead to complicated and costly designs. The ability to predict relevant dependability measures for such complex systems is essential, not only to guarantee hig

This paper describes methods for simulating continuous time Markov chain models, using parallel architectures. The basis of our method is the technique of uniformization; within this framework there are a number of options concerning optimism and aggregation. We describe four different variations, paying particular attention to an adaptive method that optimistically assumes upper bounds on the rate at which one processor affects another in simulation time, and which recovers from violations of this assumption using global checkpoints. We describe our experiences with these methods on a variety of Intel multiprocessor architectures, including the Touchstone Delta, where excellent speedups of up to 220 using 256 processors are observed. Portions of this paper are reprinted with permission from "Parallel Algorithms for Simulating Continuous Time Markov Chains" in Proceedings of the 1993 Workshop on Parallel and Distributed Simulation, and from "Parallel Simulation of Markovian Que...

Simulation to obtain reliability and availability estimates has been widely used by system designers to evaluate and compare alternative choices before making design decisions. However, traditionally that approach worked only if significant computer resources were available or designers accepted a significant time delay between design iterations. In this paper, we present an alternative approach to compute measures of interest for a family of models that represent alternative design choices that is significantly more efficient than the traditional approach. The new approach combines the existing single-clock multiple-system simulation with adaptive uniformization. We achieve the speedup by simulating all the alternative configurations of the discrete-event model simultaneously while amortizing the cost of enabled event set management. That allows us to explore and evaluate multiple configuration settings of a discrete-event model at the same time, significantly increasing the number of alternative versions of the model that are explored in a given amount of time.

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Bayesian inference for the superposition of nonhomogeneous Poisson processes is studied. A Markov chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For each observed failure epoch, a latent variable is introduced that indicates which component of the superposition model gives rise to the failure. This data augmentation approach facilitates specification of the transitional kernel in the Markov chain. Moreover, new Bayesian tests are developed for the full superposition model against simpler submodels. Model determination by a predictive likelihood approach is studied. A numerical example based on a real data set is given. Key words and phrases: Additive intensity function, Data augmentation, Gibbs sampling, Metropolis algorithm, Model selection, Predictive reliability function. AMS 1991 subject classifications: Primary 62F15, secondary 62M20. Abbreviated Title: Superposed Poisson Processes 1 1.