Integer variables estimation problems: the Bayesian approach
In geodesy as well as in geophysics there are a number of examples where the unknown parameters are partly constrained to be integer numbers, while other parameters have a continuous range of possible values. In all such situations the ordinary least square principle, with integer variates fixed to...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Istituto Nazionale di Geofisica e Vulcanologia (INGV)
1997-06-01
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| Series: | Annals of Geophysics |
| Subjects: | |
| Online Access: | http://www.annalsofgeophysics.eu/index.php/annals/article/view/3878 |
| _version_ | 1817994090015358976 |
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| author | G. Venuti F. Sansò |
| author_facet | G. Venuti F. Sansò |
| author_sort | G. Venuti |
| collection | DOAJ |
| description | In geodesy as well as in geophysics there are a number of examples where the unknown parameters are partly constrained to be integer numbers, while other parameters have a continuous range of possible values. In all such situations the ordinary least square principle, with integer variates fixed to the most probable integer value, can lead to paradoxical results, due to the strong non-linearity of the manifold of admissible values. On the contrary an overall estimation procedure assigning the posterior distribution to all variables, discrete and continuous, conditional to the observed quantities, like the so-called Bayesian approach, has the advantage of weighting correctly the possible errors in choosing different sets of integer values, thus providing a more realistic and stable estimate even of the continuous parameters. In this paper, after a short recall of the basics of Bayesian theory in section 2, we present the natural Bayesian solution to the problem of assessing the estimable signal from noisy observations in section 3 and the Bayesian solution to cycle slips detection and repair for a stream of GPS measurements in section 4. An elementary synthetic example is discussed in section 3 to illustrate the theory presented and more elaborate, though synthetic, examples are discussed in section 4 where realistic streams of GPS observations, with cycle slips, are simulated and then back processed. |
| first_indexed | 2024-04-14T01:47:22Z |
| format | Article |
| id | doaj.art-ffae8f14c2be49f4b955c2122a38b7e6 |
| institution | Directory Open Access Journal |
| issn | 1593-5213 2037-416X |
| language | English |
| last_indexed | 2024-04-14T01:47:22Z |
| publishDate | 1997-06-01 |
| publisher | Istituto Nazionale di Geofisica e Vulcanologia (INGV) |
| record_format | Article |
| series | Annals of Geophysics |
| spelling | doaj.art-ffae8f14c2be49f4b955c2122a38b7e62022-12-22T02:19:29ZengIstituto Nazionale di Geofisica e Vulcanologia (INGV)Annals of Geophysics1593-52132037-416X1997-06-0140510.4401/ag-3878Integer variables estimation problems: the Bayesian approachG. VenutiF. SansòIn geodesy as well as in geophysics there are a number of examples where the unknown parameters are partly constrained to be integer numbers, while other parameters have a continuous range of possible values. In all such situations the ordinary least square principle, with integer variates fixed to the most probable integer value, can lead to paradoxical results, due to the strong non-linearity of the manifold of admissible values. On the contrary an overall estimation procedure assigning the posterior distribution to all variables, discrete and continuous, conditional to the observed quantities, like the so-called Bayesian approach, has the advantage of weighting correctly the possible errors in choosing different sets of integer values, thus providing a more realistic and stable estimate even of the continuous parameters. In this paper, after a short recall of the basics of Bayesian theory in section 2, we present the natural Bayesian solution to the problem of assessing the estimable signal from noisy observations in section 3 and the Bayesian solution to cycle slips detection and repair for a stream of GPS measurements in section 4. An elementary synthetic example is discussed in section 3 to illustrate the theory presented and more elaborate, though synthetic, examples are discussed in section 4 where realistic streams of GPS observations, with cycle slips, are simulated and then back processed.http://www.annalsofgeophysics.eu/index.php/annals/article/view/3878Bayesian theoryprior and posterior probabilityinteger and continuous variables |
| spellingShingle | G. Venuti F. Sansò Integer variables estimation problems: the Bayesian approach Annals of Geophysics Bayesian theory prior and posterior probability integer and continuous variables |
| title | Integer variables estimation problems: the Bayesian approach |
| title_full | Integer variables estimation problems: the Bayesian approach |
| title_fullStr | Integer variables estimation problems: the Bayesian approach |
| title_full_unstemmed | Integer variables estimation problems: the Bayesian approach |
| title_short | Integer variables estimation problems: the Bayesian approach |
| title_sort | integer variables estimation problems the bayesian approach |
| topic | Bayesian theory prior and posterior probability integer and continuous variables |
| url | http://www.annalsofgeophysics.eu/index.php/annals/article/view/3878 |
| work_keys_str_mv | AT gvenuti integervariablesestimationproblemsthebayesianapproach AT fsanso integervariablesestimationproblemsthebayesianapproach |