priorDistribution

Function to evaluate the prior probability of a transition matrix. It is based on conjugate priors and therefore a Dirichlet distribution is used to model the transitions of each state.

priorDistribution(transMatr, hyperparam = matrix())

Arguments

transMatr: The transition matrix whose probability is the parameter of interest.
hyperparam: The hyperparam matrix (optional). If not provided, a default value of 1 is assumed for each and therefore the resulting probability distribution is uniform.

Value

The log of the probabilities for each state is returned in a numeric vector. Each number in the vector represents the probability (log) of having a probability transition vector as specified in corresponding the row of the transition matrix.

Details

The states (dimnames) of the transition matrix and the hyperparam may be in any order.

Note

This function can be used in conjunction with inferHyperparam. For example, if the user has a prior data set and a prior transition matrix, he can infer the hyperparameters using inferHyperparam and then compute the probability of their prior matrix using the inferred hyperparameters with priorDistribution.

References

Yalamanchi SB, Spedicato GA (2015). Bayesian Inference of First Order Markov Chains. R package version 0.2.5

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