Prior density of a transition matrix

Log-density of each row of a transition matrix under independent Dirichlet priors, the conjugate priors used by the Bayesian estimation of the package.

Usage

priorDistribution(transMatr, hyperparam = matrix())

Arguments

transMatr: The transition matrix, with the states as dimnames.
hyperparam: Matrix of Dirichlet hyperparameters, with the states as dimnames (in any order). The default, an empty matrix, sets all of them to 1, the uniform prior.

Value

A named numeric vector with, for each state, the logarithm of the Dirichlet density of its row of transMatr.

Note

With a prior data set and a prior transition matrix, the hyperparameters can be inferred with inferHyperparam() and the prior density of the matrix then evaluated with these hyperparameters.

References

Yalamanchi, S. B. and Spedicato, G. A. (2015). Bayesian inference of first order Markov chains. Vignette of the markovchain package.

Author

Sai Bhargav Yalamanchi, Giorgio Spedicato

Examples

priorDistribution(matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2,
                         dimnames = list(c("a", "b"), c("a", "b"))),
                  matrix(c(2, 2, 2, 2), nrow = 2,
                         dimnames = list(c("a", "b"), c("a", "b"))))
#>         a         b 
#> 0.4054651 0.4054651