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We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for computationally expensive models. Although previous research has shown that BQ offers sample efficiency superior to Monte Carlo in computing the evidence of an individual model, applying BQ directly to model comparison may waste computation producing an overly-accurate estimate for the evidence of a clearly poor model. We propose an automated and efficient algorithm for computing the most-relevant quantity for model selection: the posterior model probability. Our technique maximizes the mutual information between this quantity and observations of the models’ likelihoods, yielding efficient sample acquisition across disparate model spaces when likelihood observations are limited. Our method produces more-accurate posterior estimates using fewer likelihood evaluations than standard Bayesian quadrature and Monte Carlo estimators, as we demonstrate on synthetic and real-world examples.
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Study of Jupiter’s Interior with Quadratic Monte Carlo Simulations
Abstract We construct models for Jupiter’s interior that match the gravity data obtained by the Juno and Galileo spacecraft. To generate ensembles of models, we introduce a novelquadraticMonte Carlo technique, which is more efficient in confining fitness landscapes than the affine invariant method that relies on linear stretch moves. We compare how long it takes the ensembles of walkers in both methods to travel to the most relevant parameter region. Once there, we compare the autocorrelation time and error bars of the two methods. For a ring potential and the 2d Rosenbrock function, we find that our quadratic Monte Carlo technique is significantly more efficient. Furthermore, we modified thewalkmoves by adding a scaling factor. We provide the source code and examples so that this method can be applied elsewhere. Here we employ our method to generate five-layer models for Jupiter’s interior that include winds and a prominent dilute core, which allows us to match the planet’s even and odd gravity harmonics. We compare predictions from the different model ensembles and analyze how much an increase in the temperature at 1 bar and ad hoc change to the equation of state affect the inferred amount of heavy elements in the atmosphere and in the planet overall.
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- Award ID(s):
- 2020249
- PAR ID:
- 10439977
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 953
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 111
- Size(s):
- Article No. 111
- Sponsoring Org:
- National Science Foundation
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