Approximate Bayesian computation with the Wasserstein distance

A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these d...

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Vydáno v:Journal of the Royal Statistical Society. Series B, Statistical methodology Ročník 81; číslo 2; s. 235 - 269
Hlavní autoři: Bernton, Espen, Jacob, Pierre E., Gerber, Mathieu, Robert, Christian P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Wiley 01.04.2019
Oxford University Press
Témata:
Approximate Bayesian computation
Bayesian analysis
Bayesian theory
Biology
Computation
Computer simulation
Data
data collection
Datasets
equations
Generative models
Hilbert curve
Hilbert space
Likelihood‐free inference
Optimal transport
Property
Queueing
Queues
Regression analysis
Statistical methods
Statistical models
Statistics
Summaries
Time series
time series analysis
Volatility
Wasserstein distance
ISSN:1369-7412, 1467-9868
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Shrnutí:A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well-known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g-and-k distributions, a toggle switch model from systems biology, a queuing model and a Lévy-driven stochastic volatility model.
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ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12312