Precision: Precision

In LaplacesDemonR/LaplacesDemon: Complete Environment for Bayesian Inference

Precision

Description

Bayesians often use precision rather than variance. These are elementary utility functions to facilitate conversions between precision, standard deviation, and variance regarding scalars, vectors, and matrices, and these functions are designed for those who are new to Bayesian inference. The names of these functions consist of two different scale parameters, separated by a ‘2’, and capital letters refer to matrices while lower case letters refer to scalars and vectors. For example, the Prec2Cov function converts a precision matrix to a covariance matrix, while the prec2sd function converts a scalar or vector of precision parameters to standard deviation parameters.

The modern Bayesian use of precision developed because it was more straightforward in a normal distribution to estimate precision \tau with a gamma distribution as a conjugate prior, than to estimate \sigma^2 with an inverse-gamma distribution as a conjugate prior. Today, conjugacy is usually considered to be merely a convenience, and in this example, a non-conjugate half-Cauchy prior distribution is recommended as a weakly informative prior distribution for scale parameters.

Usage

Cov2Prec(Cov)
Prec2Cov(Prec)
prec2sd(prec=1)
prec2var(prec=1)
sd2prec(sd=1)
sd2var(sd=1)
var2prec(var=1)
var2sd(var=1)

Arguments

Cov	This is a covariance matrix, usually represented as \Sigma.
Prec	This is a precision matrix, usually represented as \Omega.
prec	This is a precision scalar or vector, usually represented as \tau.
sd	This is a standard deviation scalar or vector, usually represented as \sigma.
var	This is a variance scalar or vector, usually represented as \sigma^2.

Details

Bayesians often use precision rather than variance, where precision is the inverse of the variance. For example, a linear regression may be represented equivalently as \textbf{y} \sim \mathcal{N}(\mu, \sigma^2), or \textbf{y} \sim \mathcal{N}(\mu, \tau^{-1}), where \sigma^2 is the variance, and \tau is the precision, which is the inverse of the variance.

Value

Cov2Prec	This returns a precision matrix, \Omega, from a covariance matrix, \Sigma, where \Omega = \Sigma^{-1}.
Prec2Cov	This returns a covariance matrix, \Sigma, from a precision matrix, \Omega, where \Sigma = \Omega^{-1}.
prec2sd	This returns a standard deviation, \sigma, from a precision, \tau, where \sigma = \sqrt{\tau^{-1}}.
prec2var	This returns a variance, \sigma^2, from a precision, \tau, where \sigma^2 = \tau^{-1}.
sd2prec	This returns a precision, \tau, from a standard deviation, \sigma, where \tau = \sigma^{-2}.
sd2var	This returns a variance, \sigma^2, from a standard deviation, \sigma, where \sigma^2 = \sigma \sigma.
var2prec	This returns a precision, \tau, from a variance, \sigma^2, where \tau = \frac{1}{\sigma^2}.
var2sd	This returns a standard deviation, \sigma, from a variance, \sigma^2, where \sigma = \sqrt{\sigma^2}.

Author(s)

Statisticat, LLC. [e-mail]

See Also

Cov2Cor

Examples

library(LaplacesDemon)
Cov2Prec(matrix(c(1,0.1,0.1,1),2,2))
Prec2Cov(matrix(c(1,0.1,0.1,1),2,2))
prec2sd(0.5)
prec2var(0.5)
sd2prec(1.4142)
sd2var(01.4142)
var2prec(2)
var2sd(2)

LaplacesDemonR/LaplacesDemon documentation built on April 1, 2024, 7:22 a.m.