A Bayesian Motivated Laplace Inversion for Multivariate Probability Distributions |
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Authors: | Lorenzo Cappello Stephen G Walker |
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Institution: | 1.Department of Decision Sciences,Universita Commerciale Luigi Bocconi Via Roentgen 1,Milan,Italy;2.Department of Mathematics,University of Texas at Austin,Austin,USA |
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Abstract: | The paper introduces a recursive procedure to invert the multivariate Laplace transform of probability distributions. The procedure involves taking independent samples from the Laplace transform; these samples are then used to update recursively an initial starting distribution. The update is Bayesian driven. The final estimate can be written as a mixture of independent gamma distributions, making it the only methodology which guarantees to numerically recover a probability distribution with positive support. Proof of convergence is given by a fixed point argument. The estimator is fast, accurate and can be run in parallel since the target distribution is evaluated on a grid of points. The method is illustrated on several examples and compared to the bivariate Gaver–Stehfest method. |
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