Changes of Period in Variable Stars of Long Period

Sterne, T. E.; Campbell, Leon

doi:10.1073/pnas.23.2.115

Cited by 6 publications

(2 citation statements)

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“…Sterne [13], [14], [15] reprenait peu apres le travail d'Eddington et Plakidis, en affinant la m6thode de recherche des variations de la p6riode vraie de l'6toile. 11 pr6cisait les conditions d'utilisation des diagrammes O-C (&carts entre periodes observ6es et calcul6es dans I'hypothese d'une periode vraie constante) couramment utilises pour la recherche des variations cycliques de la periode, et appliquait la theorie ainsi 6laboree i l'6tude de quelques 6toiles a courte et longue periode, et ' une binaire a 6clipse.…”

Section: Types De Maximaunclassified

Etude statistique dela courbe de lumiere de l'etoile variable SS Cygni

Martel¹

1964

Revue de l'Institut International de Statistique / Review of th

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Section: Types De Maximaunclassified

Etude statistique dela courbe de lumiere de l'etoile variable SS Cygni

Martel¹

1964

Revue de l'Institut International de Statistique / Review of th

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“…In this context, the autoregressive part of the model corresponds to random variation intrinsic to times between successive maximum (or minimum) brightnesses of a star, and the noninvertible moving average arises from differences between errors made in recording times of maximum (or minimum) brightness. The application of statistical methods to testing for period changes in variable stars has a long history in the astronomy literature; see, for example, Sterne and Campbell [24], Isles and Saw [4], Lombard [14], Percy and Colivas [18], Koen and Lombard [11,12] and Hart et al [3]. To our knowledge, only frequentist-type tests have been used to detect period changes in variable stars.…”

Section: Introductionmentioning

confidence: 99%

Approximating posterior probabilities in a linear model with possibly noninvertible moving average errors

Pokta¹,

Hart²

2008

Journal of Multivariate Analysis

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The method of Laplace is used to approximate posterior probabilities for a collection of polynomial regression models when the errors follow a process with a noninvertible moving average component. These results are useful in the problem of period-change analysis of variable stars and in assessing the posterior probability that a time series with trend has been overdifferenced. The nonstandard covariance structure induced by a noninvertible moving average process can invalidate the standard Laplace method. A number of analytical tools is used to produce corrected Laplace approximations. These tools include viewing the covariance matrix of the observations as tending to a differential operator. The use of such an operator and its Green's function provides a convenient and systematic method of asymptotically inverting the covariance matrix.In certain cases there are two different Laplace approximations, and the appropriate one to use depends upon unknown parameters. This problem is dealt with by using a weighted geometric mean of the candidate approximations, where the weights are completely data-based and such that, asymptotically, the correct approximation is used. The new methodology is applied to an analysis of the prototypical long-period variable star known as Mira.

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2015

Pulsating Stars

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Changes of Period in Variable Stars of Long Period

Cited by 6 publications

References 0 publications

Etude statistique dela courbe de lumiere de l'etoile variable SS Cygni

Etude statistique dela courbe de lumiere de l'etoile variable SS Cygni

Approximating posterior probabilities in a linear model with possibly noninvertible moving average errors

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