Precision {LaplacesDemon}  R Documentation 
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 inversegamma distribution
as a conjugate prior. Today, conjugacy is usually considered to be
merely a convenience, and in this example, a nonconjugate halfCauchy
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

Prec 
This is a precision matrix, usually represented as

prec 
This is a precision scalar or vector, usually represented as

sd 
This is a standard deviation scalar or vector, usually
represented as 
var 
This is a variance scalar or vector, usually
represented as 
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, 
Prec2Cov 
This returns a covariance matrix, 
prec2sd 
This returns a standard deviation, 
prec2var 
This returns a variance, 
sd2prec 
This returns a precision, 
sd2var 
This returns a variance, 
var2prec 
This returns a precision, 
var2sd 
This returns a standard deviation, 
Author(s)
Statisticat, LLC. software@bayesianinference.com
See Also
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)