16,369 research outputs found

    Driving Markov chain Monte Carlo with a dependent random stream

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    Markov chain Monte Carlo is a widely-used technique for generating a dependent sequence of samples from complex distributions. Conventionally, these methods require a source of independent random variates. Most implementations use pseudo-random numbers instead because generating true independent variates with a physical system is not straightforward. In this paper we show how to modify some commonly used Markov chains to use a dependent stream of random numbers in place of independent uniform variates. The resulting Markov chains have the correct invariant distribution without requiring detailed knowledge of the stream's dependencies or even its marginal distribution. As a side-effect, sometimes far fewer random numbers are required to obtain accurate results.Comment: 16 pages, 4 figure

    RAGE: A Java-implemented Visual Random Generator

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    Carefully designed Java applications turn out to be efficient and platform independent tools that can compete well with classical implementations of statistical software. The project presented here is an example underlining this statement for random variate generation. An end-user application called RAGE (Random Variate Generator) is developed to generate random variates from probability distributions. A Java class library called JDiscreteLib has been designed and implemented for the simulation of random variables from the most usual discrete distributions inside RAGE. For each distribution, specific and general algorithms are available for this purpose. RAGE can also be used as an interactive simulation tool for data and data summary visualization.

    Automatic Markov Chain Monte Carlo Procedures for Sampling from Multivariate Distributions

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    Generating samples from multivariate distributions efficiently is an important task in Monte Carlo integration and many other stochastic simulation problems. Markov chain Monte Carlo has been shown to be very efficient compared to "conventional methods", especially when many dimensions are involved. In this article we propose a Hit-and-Run sampler in combination with the Ratio-of-Uniforms method. We show that it is well suited for an algorithm to generate points from quite arbitrary distributions, which include all log-concave distributions. The algorithm works automatically in the sense that only the mode (or an approximation of it) and an oracle is required, i.e., a subroutine that returns the value of the density function at any point x. We show that the number of evaluations of the density increases slowly with dimension. (author's abstract)Series: Preprint Series / Department of Applied Statistics and Data Processin

    Building Loss Models

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    This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.Insurance risk model; Loss distribution; Claim arrival process; Poisson process; Renewal process; Random variable generation; Goodness-of-fit testing
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