Hyperparameters for Bayesian estimation of a Markov chain

The Bayesian estimation of the package uses independent Dirichlet priors for the rows of the transition matrix. This function infers their hyperparameters either from a prior transition matrix, taken as the prior mean, and a scale for each row (its total hyperparameter), or from a data set, as the transition counts plus one.

Usage

inferHyperparam(transMatr = matrix(), scale = numeric(), data = character())

Arguments

transMatr

A prior transition matrix, with the states as dimnames.

scale

A numeric vector with the scale (sum of the hyperparameters) of each row of transMatr, in the same order.

data

A sequence of states (or a data set accepted by markovchainFit()) from which the hyperparameters are inferred.

Value

A list with element scaledInference (from transMatr and scale) or dataInference (from data), the matrix of hyperparameters. Its rows and columns are sorted alphanumerically by state name.

Details

Either data, or transMatr and scale, must be given.

References

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

See also

markovchainFit() (method = "map"), which uses them.

Other Bayesian inference: predictiveDistribution(), priorDistribution()

Author

Sai Bhargav Yalamanchi, Giorgio Spedicato

Examples

data(rain, package = "markovchain")
inferHyperparam(data = rain$rain)
#> $dataInference
#>       0 1-5  6+
#> 0   363 127  61
#> 1-5 137  91  69
#> 6+   51  80 125
#> 

weatherStates <- c("sunny", "cloudy", "rain")
weatherMatrix <- matrix(c(0.7, 0.2, 0.1,
                          0.3, 0.4, 0.3,
                          0.2, 0.4, 0.4),
                        byrow = TRUE, nrow = 3,
                        dimnames = list(weatherStates, weatherStates))
inferHyperparam(transMatr = weatherMatrix, scale = c(10, 10, 10))
#> $scaledInference
#>        cloudy rain sunny
#> cloudy      4    3     3
#> rain        4    4     2
#> sunny       2    1     7
#>