A Bayesian Motivated Laplace Inversion for Multivariate Probability Distributions

Lorenzo Cappello () and Stephen G. Walker ()
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Lorenzo Cappello: Universita Commerciale Luigi Bocconi Via Roentgen 1
Stephen G. Walker: University of Texas at Austin

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 2, 777-797

Abstract: 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.

Keywords: Fixed-point; Inverse method; Recursive estimation; Stochastic approximation; 44A10; 62L20; 65WP1 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-017-9587-y

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