Publication: Goodness of fit for models with intractable likelihood
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2021-09-01
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Springer
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Abstract
Routine goodness-of-fit analyses of complex models with intractable likelihoods are
hampered by a lack of computationally tractable diagnostic measures with wellunderstood
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-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.
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Keywords
Approximate bayesian computation, Model adequacy, Model checking, Simulation-based modeling
Bibliographic citation
Cabras, S., Castellanos, M. E., & Ratmann, O. (2021). Goodness of fit for models with intractable likelihood.TEST,30 (3), pp. 713-736