Bayesian Analysis

Estimating a bivariate linear relationship

David Leonard

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Abstract

Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and errors is unidentified without additional information. I propose a prior density that incorporates the fact that the slope and variance parameters together determine the covariance matrix of the unobserved true values but is otherwise diffuse. The marginal posterior density of the slope is invariant to interchange and scaling of the coordinates and depends on the data only through the sample correlation coefficient and ratio of standard deviations. It covers the interval between the two ordinary least squares estimates but diminishes rapidly outside of it. I introduce the R package leivfor computing the posterior density, and I apply it to examples in astronomy and method comparison.

Article information

Source
Bayesian Anal., Volume 6, Number 4 (2011), 727-754.

Dates
First available in Project Euclid: 13 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1339616542

Digital Object Identifier
doi:10.1214/11-BA627

Mathematical Reviews number (MathSciNet)
MR2869963

Zentralblatt MATH identifier
1330.62278

Keywords
Errors-in-variables Identifiability Measurement error Straight line fitting

Citation

Leonard, David. Estimating a bivariate linear relationship. Bayesian Anal. 6 (2011), no. 4, 727--754. doi:10.1214/11-BA627. https://projecteuclid.org/euclid.ba/1339616542


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