Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies
The Kullback-Leibler divergence, κ, is a widely used measure of the difference between an observed probability distribution and a reference one; κ=0 when the two distributions are equal, but it has no upper limit to help interpret the significance of any other κ value. Using as an example the proble...
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| Format: | Article |
| Language: | English |
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Universidad Nacional Autónoma de México, Instituto de Geofísica
2023-07-01
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| Series: | Geofísica Internacional |
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| Online Access: | http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/1578 |
| _version_ | 1797787528786345984 |
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| author | Fidencio Alejandro Nava Pichardo |
| author_facet | Fidencio Alejandro Nava Pichardo |
| author_sort | Fidencio Alejandro Nava Pichardo |
| collection | DOAJ |
| description | The Kullback-Leibler divergence, κ, is a widely used measure of the difference between an observed probability distribution and a reference one; κ=0 when the two distributions are equal, but it has no upper limit to help interpret the significance of any other κ value. Using as an example the problem of distinguishing clustering or gaps in the time occurrence of earthquakes from seismicity uniformly distributed in time, a Monte Carlo method for evaluating the significance of a particular κ value is presented, a method that takes into account the number of classes in the distributions and the length of the sample. Application of this method yields a probability according to which the hypothesis of the observed distribution being a realization of the reference one can be discarded or accepted with a quantitative degree of confidence. This method, and two possible reference values, are presented using the Poisson distribution as an example, but they can be used for other reference distributions. |
| first_indexed | 2024-03-13T01:23:13Z |
| format | Article |
| id | doaj.art-565391841e08447b85dafe2dff1bed01 |
| institution | Directory Open Access Journal |
| issn | 0016-7169 2954-436X |
| language | English |
| last_indexed | 2024-03-13T01:23:13Z |
| publishDate | 2023-07-01 |
| publisher | Universidad Nacional Autónoma de México, Instituto de Geofísica |
| record_format | Article |
| series | Geofísica Internacional |
| spelling | doaj.art-565391841e08447b85dafe2dff1bed012023-07-04T17:27:53ZengUniversidad Nacional Autónoma de México, Instituto de GeofísicaGeofísica Internacional0016-71692954-436X2023-07-0162351952310.22201/igeof.2954436xe.2023.62.3.15781578Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studiesFidencio Alejandro Nava Pichardo0https://orcid.org/0000-0001-6778-2017Centro de Investigación y de Educación Superior de Ensenada, B.C., Departamento de SismologíaThe Kullback-Leibler divergence, κ, is a widely used measure of the difference between an observed probability distribution and a reference one; κ=0 when the two distributions are equal, but it has no upper limit to help interpret the significance of any other κ value. Using as an example the problem of distinguishing clustering or gaps in the time occurrence of earthquakes from seismicity uniformly distributed in time, a Monte Carlo method for evaluating the significance of a particular κ value is presented, a method that takes into account the number of classes in the distributions and the length of the sample. Application of this method yields a probability according to which the hypothesis of the observed distribution being a realization of the reference one can be discarded or accepted with a quantitative degree of confidence. This method, and two possible reference values, are presented using the Poisson distribution as an example, but they can be used for other reference distributions.http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/1578divergencia kullback-leiblerdistribución de poissonsismología estadística |
| spellingShingle | Fidencio Alejandro Nava Pichardo Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies Geofísica Internacional divergencia kullback-leibler distribución de poisson sismología estadística |
| title | Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies |
| title_full | Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies |
| title_fullStr | Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies |
| title_full_unstemmed | Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies |
| title_short | Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies |
| title_sort | significance estimation for the kullback leibler divergence the poissonian case in seismological studies |
| topic | divergencia kullback-leibler distribución de poisson sismología estadística |
| url | http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/1578 |
| work_keys_str_mv | AT fidencioalejandronavapichardo significanceestimationforthekullbackleiblerdivergencethepoissoniancaseinseismologicalstudies |