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The objective of this work is to provide a Bayesian re-interpretation to model falsification. We show that model falsification can be viewed as an approximate Bayesian computation (ABC) approach when hypotheses (models) are sampled from a prior. To achieve this, we recast model falsifiers as discrepancy metrics and density kernels such that they may be adopted within ABC and generalized ABC (GABC) methods. We call the resulting frameworks model falsified ABC and GABC, respectively. Moreover, as a result of our reinterpretation, the set of unfalsified models can be shown to be realizations of an approximate posterior. We consider both error and likelihood domain model falsification in our exposition. Model falsified (G)ABC is used to tackle two practical inverse problems albeit with synthetic measurements. The first type of problem concerns parameter estimation and includes applications of ABC to the inference of a statistical model where the likelihood can be difficult to compute, and the identification of a cubic-quintic dynamical system. The second type of example involves model selection for the base isolation system of a four degree-of-freedom base isolated structure. The performance of model falsified ABC and GABC are compared with Bayesian inference. The results show that model falsified (G)ABC can be used to solve inverse problems in a computationally efficient manner. The results are also used to compare the various falsifiers in their capability of approximating the posterior and some of its important statistics. Further, we show that model falsifier based density kernels can be used in kernel regression to infer unknown model parameters and compute structural responses under epistemic uncertainty.
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Salvaging Falsified Instrumental Variable Models
What should researchers do when their baseline model is falsified? We recommend reporting the set of parameters that are consistent with minimally nonfalsified models. We call this the falsification adaptive set (FAS). This set generalizes the standard baseline estimand to account for possible falsification. Importantly, it does not require the researcher to select or calibrate sensitivity parameters. In the classical linear IV model with multiple instruments, we show that the FAS has a simple closed‐form expression that only depends on a few 2SLS coefficients. We apply our results to an empirical study of roads and trade. We show how the FAS complements traditional overidentification tests by summarizing the variation in estimates obtained from alternative nonfalsified models.
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- Award ID(s):
- 1943138
- PAR ID:
- 10253726
- Date Published:
- Journal Name:
- Econometrica
- Volume:
- 89
- Issue:
- 3
- ISSN:
- 0012-9682
- Page Range / eLocation ID:
- 1449 to 1469
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3982/ECTA17969
