Algorithm AS R80: A Remark on Algorithm AS 76: An Integral Useful in Calculating Noncentral t and Bivariate Normal Probabilities

Boys, Richard J.

doi:10.2307/2347755

Cited by 6 publications

(5 citation statements)

References 9 publications

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“…Since magnitude and redshift limits can be accounted for by selection probability function µ S V 1 max , we can say that there are no cut-off values for any component of ŷ except for m * and s, which means that the integral over all the other components will just be the marginalization of the 8D probability distribution function (PDF). In this case, the likelihood normalization factor f j in Equation (B10) can be expressed in terms of a bivariate normal PDF, We use the algorithm of Boys (1989) to evaluate BvN, also making use of STAN ʼs optimized built-in functions for Φ and f.…”

Section: B6 Likelihood Normalizationmentioning

confidence: 99%

Galaxy and Mass Assembly (GAMA): Stellar-to-dynamical Mass Relation. I. Constraining the Precision of Stellar Mass Estimates

Dogruel,

Taylor,

Cluver

et al. 2023

ApJ

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In this empirical work, we aim to quantify the systematic uncertainties in stellar-mass (M ⋆) estimates made from spectral energy distribution (SED) fitting through stellar population synthesis (SPS) for galaxies in the local Universe by using the dynamical mass (M dyn) estimator as an SED-independent check on stellar mass. We first construct a statistical model of the high-dimensional space of galaxy properties; including size (R e ), velocity dispersion (σ e ), surface brightness (I e ), mass-to-light ratio (M ⋆/L), rest-frame color, Sérsic index (n), and dynamical mass (M dyn), and accounting for selection effects and covariant errors. We disentangle the correlations among galaxy properties and find that the variation in M ⋆/M dyn is driven by σ e , Sérsic index and color. We use these parameters to calibrate an SED-independent M ⋆ estimator, M ˆ ⋆ . We find the random scatter of the relation M ⋆ − M ˆ ⋆ to be 0.108 dex and 0.147 dex for quiescent and star-forming galaxies, respectively. Finally, we inspect the residuals as a function of SPS parameters (dust, age, metallicity, and star formation rate) and spectral indices (Hα, Hδ, and D n 4000). For quiescent galaxies, ∼65% of the scatter can be explained by the uncertainty in SPS parameters, with dust and age being the largest sources of uncertainty. For star-forming galaxies, while age and metallicity are the leading factors, SPS parameters account for only ∼13% of the scatter. These results leave us with remaining unmodelled scatters of 0.055 dex and 0.122 dex for quiescent and star-forming galaxies, respectively. This can be interpreted as a conservative limit on the precision in M ⋆ that can be achieved via simple SPS modeling.

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Section: B6 Likelihood Normalizationmentioning

confidence: 99%

Galaxy and Mass Assembly (GAMA): Stellar-to-dynamical Mass Relation. I. Constraining the Precision of Stellar Mass Estimates

Dogruel,

Taylor,

Cluver

et al. 2023

ApJ

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“…model where a3 = ao/(1 + ar)112 and aT = al/(1 + ar)1/2. Simple algorithms for <I> and <1>2 are given by Hill (1973) and Young and Minder (1974), with updates given by Chou (1985) .and Boys (1989b).…”

Section: Screening Solutionmentioning

confidence: 99%

“…This screening methodology has received considerable attention in recent years; see, in addition, Owen ef al. (1975), Owen and Boddie (1976), Owen and Su (1977), Owen and Hass (1978), Li and Owen (1979), Odeh andOwen (1980), Wong et al (1985), Dunsmore and Boys (1987) and Boys (1989a). Most of this work develops global procedures in situations where possessing the attribute corresponds to a continuous variable Y belonging to a prescribed specification region C y • The procedures are derived by assuming certain parametric models, namely a normal model for (Y, X) or a binary response-normal covariate model for (T, X), some within a classical framework, others within a Bayesian framework.…”

Section: Introductionmentioning

confidence: 99%

“…In some circumstances a continuous feature variable can be used to screen future individuals (or items) for the presence or absence of a particular attribute. The screening methodology described by Owen et al (1981) and Boys andDunsmore (1986, 1987) extends the ideas of discrimination and classification by controlling the level of misclassification in the retained population. The screening mechanism is designed to retain individuals so that, of those retained, the probability of possessing the attribute takes some high prespecified value o.…”

Section: Introductionmentioning

confidence: 99%

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On a Kernel Approach to a Screening Problem

Boys

1992

Journal of the Royal Statistical Society Series B: Statistical Methodology

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SUMMARY Screening methods are developed which raise the proportion of individuals possessing an attribute in the retained population to a predetermined level. A specification region for the screening variable is derived by using a kernel smoothing approach. The sensitivity of the procedure is assessed within a range of parametric models. Comparisons are also made with empirical and estimative solutions. The kernel method is illustrated by an example of screening within a medical context.

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“…Hill (1978) and Thomas (1979) provide changes such that TFN can be used to compute T(h, a) for -00 < a< O. Chou (1985) extends the parameter range further to include -00 and 00 for both a and h. Boys (1989) reports inaccuracy of the modified version of TFN when h is small and a is large. He provides an approximation of order h S to T(h, a) for I h I < 0.3 and I a 1 > 7.…”

Section: Introductionmentioning

confidence: 99%

Remark AS R89: A Remark on Algorithm AS 76: An Integral Useful in Calculating Central t and Bivariate Normal Probabilities

Goedhart¹,

Jansen²

1992

Applied Statistics

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Algorithm AS R80: A Remark on Algorithm AS 76: An Integral Useful in Calculating Noncentral t and Bivariate Normal Probabilities

Cited by 6 publications

References 9 publications

Galaxy and Mass Assembly (GAMA): Stellar-to-dynamical Mass Relation. I. Constraining the Precision of Stellar Mass Estimates

Galaxy and Mass Assembly (GAMA): Stellar-to-dynamical Mass Relation. I. Constraining the Precision of Stellar Mass Estimates

On a Kernel Approach to a Screening Problem

Remark AS R89: A Remark on Algorithm AS 76: An Integral Useful in Calculating Central t and Bivariate Normal Probabilities

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