Integration with an adaptive harmonic mean algorithm
| Autor: | Philipp Eller, Vasyl Hafych, Allen Caldwell, Oliver Schulz, Marco Szalay, Rafael C. Schick |
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| Rok vydání: | 2019 |
| Předmět: |
Physics
Nuclear and High Energy Physics Harmonic mean Astronomy and Astrophysics Markov chain Monte Carlo Probability and statistics 02 engineering and technology High dimensional 021001 nanoscience & nanotechnology Bayesian inference 01 natural sciences Atomic and Molecular Physics and Optics Marginal likelihood Task (project management) ddc 010104 statistics & probability symbols.namesake symbols 0101 mathematics 0210 nano-technology Algorithm |
| Popis: | Numerically estimating the integral of functions in high dimensional spaces is a nontrivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such as a Markov Chain Monte Carlo provides samples of the function. We present an Adaptive Harmonic Mean Integration (AHMI) algorithm. Given samples drawn according to a probability distribution proportional to the function, the algorithm will estimate the integral of the function and the uncertainty of the estimate by applying a harmonic mean estimator to adaptively chosen regions of the parameter space. We describe the algorithm and its mathematical properties, and report the results using it on multiple test cases. |
| Databáze: | OpenAIRE |
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