Probabilistic and least-squares inference of the parameters of a straight-line model

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dc.contributor.authorLira, Ignacio
dc.contributor.authorElster, Clemens
dc.contributor.authorWoeger, Wolfgang
dc.date.accessioned2025-01-21T01:05:23Z
dc.date.available2025-01-21T01:05:23Z
dc.date.issued2007
dc.description.abstractTwo methods are presented by which a straight line is to be fitted to a cloud of points in Cartesian coordinates. It is assumed that data are available in the form of a series of measurements in each coordinate, together with an assessment of their covariance matrices. In the first (probabilistic) method, the joint probability density function (PDF) for the two parameters of the straight line is considered. An explicit expression for this PDF is derived; it allows one to compute numerically the expectations, the variances and the covariance between the two parameters of the straight line. The second method is that of least-squares; it renders a non-linear system of equations for the point estimates of the parameters, as well as an approximation to their covariance matrix. In contrast to least-squares, the probabilistic method allows for the exact calculation of the probability that the true values of the parameters lie within specified intervals.
dc.fuente.origenWOS
dc.identifier.doi10.1088/0026-1394/44/5/014
dc.identifier.issn0026-1394
dc.identifier.urihttps://doi.org/10.1088/0026-1394/44/5/014
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/95906
dc.identifier.wosidWOS:000250140500017
dc.issue.numero5
dc.language.isoen
dc.pagina.final384
dc.pagina.inicio379
dc.revistaMetrologia
dc.rightsacceso restringido
dc.subject.ods04 Quality Education
dc.subject.odspa04 Educación de calidad
dc.titleProbabilistic and least-squares inference of the parameters of a straight-line model
dc.typeartículo
dc.volumen44
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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