Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches
The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as a function of the orientation of two vectors; one representing the optimal signal-to-noise ratio, and the other representing the maximised likelihood ratio or <inline-formula><math xmlns="http://...
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| Format: | Article |
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MDPI AG
2021-06-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/7/6/174 |
| _version_ | 1797531709645783040 |
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| author | Karl Wette |
| author_facet | Karl Wette |
| author_sort | Karl Wette |
| collection | DOAJ |
| description | The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as a function of the orientation of two vectors; one representing the optimal signal-to-noise ratio, and the other representing the maximised likelihood ratio or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-statistic. Analytic marginalisation over the angle between the vectors yields a marginalised likelihood ratio, which is a function of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-statistic. Further analytic marginalisation over the optimal signal-to-noise ratio is explored using different choices of prior. Monte-Carlo simulations show that the marginalised likelihood ratios had identical detection power to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-statistic. This approach demonstrates a route to viewing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-statistic in a Bayesian context, while retaining the advantages of its efficient computation. |
| first_indexed | 2024-03-10T10:48:34Z |
| format | Article |
| id | doaj.art-2d266ec826794904bb4dd61c21e4ea81 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T10:48:34Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-2d266ec826794904bb4dd61c21e4ea812023-11-21T22:23:20ZengMDPI AGUniverse2218-19972021-06-017617410.3390/universe7060174Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave SearchesKarl Wette0ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav) and Centre for Gravitational Astrophysics, Australian National University, Canberra, ACT 2601, AustraliaThe likelihood ratio for a continuous gravitational wave signal is viewed geometrically as a function of the orientation of two vectors; one representing the optimal signal-to-noise ratio, and the other representing the maximised likelihood ratio or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-statistic. Analytic marginalisation over the angle between the vectors yields a marginalised likelihood ratio, which is a function of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-statistic. Further analytic marginalisation over the optimal signal-to-noise ratio is explored using different choices of prior. Monte-Carlo simulations show that the marginalised likelihood ratios had identical detection power to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-statistic. This approach demonstrates a route to viewing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-statistic in a Bayesian context, while retaining the advantages of its efficient computation.https://www.mdpi.com/2218-1997/7/6/174continuous gravitational wavesdata analysismatched filterBayesian inferencemarginal likelihoodanalytic marginalization |
| spellingShingle | Karl Wette Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches Universe continuous gravitational waves data analysis matched filter Bayesian inference marginal likelihood analytic marginalization |
| title | Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches |
| title_full | Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches |
| title_fullStr | Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches |
| title_full_unstemmed | Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches |
| title_short | Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches |
| title_sort | geometric approach to analytic marginalisation of the likelihood ratio for continuous gravitational wave searches |
| topic | continuous gravitational waves data analysis matched filter Bayesian inference marginal likelihood analytic marginalization |
| url | https://www.mdpi.com/2218-1997/7/6/174 |
| work_keys_str_mv | AT karlwette geometricapproachtoanalyticmarginalisationofthelikelihoodratioforcontinuousgravitationalwavesearches |