Function to infer the hyperparameters for Bayesian inference from an a priori matrix or a data set

Since the Bayesian inference approach implemented in the package is based on conjugate priors, hyperparameters must be provided to model the prior probability distribution of the chain parameters. The hyperparameters are inferred from a given a priori matrix under the assumption that the matrix provided corresponds to the mean (expected) values of the chain parameters. A scaling factor vector must be provided too. Alternatively, the hyperparameters can be inferred from a data set.

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

Arguments

transMatr: A valid transition matrix, with dimension names.
scale: A vector of scaling factors, each element corresponds to the row names of the provided transition matrix transMatr, in the same order.
data: A data set from which the hyperparameters are inferred.

Value

Returns the hyperparameter matrix in a list.

Details

transMatr and scale need not be provided if data is provided.

Note

The hyperparameter matrix returned is such that the row and column names are sorted alphanumerically, and the elements in the matrix are correspondingly permuted.

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

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(data = 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
#>