Creates an object containing the parameters of a Beta distribution. This is used for constructing the prior or storing the information of the posterior.
Value
Returns an object of class "inz_dbeta".
An object of class "inz_dbeta" is a list which contains the following:
- alpha
the shape parameter \(\alpha\).
- beta
the shape parameter \(\beta\).
If the function is used to construct the prior, the likelihood is stored
as an attribute.
Details
Parameter 1: shape \(\alpha > 0\)
Parameter 2: shape \(\beta > 0\)
The Beta distribution is the conjugate prior for (but is not limited to) the Binomial likelihood.
For prior use only:
If no alpha or beta parameter values are provided, a default
value of \(\alpha = 1\) and \(\beta = 1\) will be used respectively.
Hence, a default prior of Beta(1,1) will be used if alpha and beta
are both NULL, which is equivalent to a uninformative, Uniform(0,1) prior.
Examples
# Constructing the prior with the likelihood (default prior is used)
if (FALSE) { # \dontrun{
lik <- inz_lbinom(surf_data, Gender)
inz_dbeta(likelihood = lik)
# Using a subjective prior
inz_dbeta(likelihood = lik, alpha = 8, beta = 2)
} # }
# Grouped data example
if (FALSE) { # \dontrun{
grouped_lik <- inz_lbinom(surf_data, Gender, Qualification)
inz_dbeta(likelihood = grouped_lik)
} # }
# Example of inz_dbeta usage in the calculate_posterior function
inz_dbeta(alpha = 108, beta = 94)
#> $alpha
#> [1] 108
#>
#> $beta
#> [1] 94
#>
#> attr(,"class")
#> [1] "inz_dbeta"