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Goodness of fit for models with intractable likelihood

Author

Listed:
  • Stefano Cabras

    (Universidad Carlos III de Madrid)

  • María Eugenia Castellanos

    (Universidad Rey Juan Carlos
    Università degli Studi di Cagliari)

  • Oliver Ratmann

    (Imperial College London)

Abstract

Routine goodness-of-fit analyses of complex models with intractable likelihoods are hampered by a lack of computationally tractable diagnostic measures with well-understood frequency properties, that is, with a known sampling distribution. This frustrates the ability to assess the extremity of the data relative to fitted simulation models in terms of pre-specified test statistics, an essential requirement for model improvement. Given an Approximate Bayesian Computation setting for a posited model with an intractable likelihood for which it is possible to simulate from them, we present a general and computationally inexpensive Monte Carlo framework for obtaining $$p$$ p -valuesthat are asymptotically uniformly distributed in [0, 1] under the posited model when assumptions about the asymptotic equivalence between the conditional statistic and the maximum likelihood estimator hold. The proposed framework follows almost directly from the conditional predictive p-value proposed in the Bayesian literature. Numerical investigations demonstrate favorable power properties in detecting actual model discrepancies relative to other diagnostic approaches. We illustrate the technique on analytically tractable examples and on a complex tuberculosis transmission model.

Suggested Citation

  • Stefano Cabras & María Eugenia Castellanos & Oliver Ratmann, 2021. "Goodness of fit for models with intractable likelihood," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 713-736, September.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:3:d:10.1007_s11749-020-00747-7
    DOI: 10.1007/s11749-020-00747-7
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    References listed on IDEAS

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