Given a sequence of states arising from a stationary state, it fits the underlying Markov chain distribution using either MLE (also using a Laplacian smoother), bootstrap or by MAP (Bayesian) inference.
createSequenceMatrix(
stringchar,
toRowProbs = FALSE,
sanitize = FALSE,
possibleStates = character()
)
markovchainFit(
data,
method = "mle",
byrow = TRUE,
nboot = 10L,
laplacian = 0,
name = "",
parallel = FALSE,
confidencelevel = 0.95,
confint = TRUE,
hyperparam = matrix(),
sanitize = FALSE,
possibleStates = character()
)It can be a $$n x n$$ matrix or a character vector or a list
converts a sequence matrix into a probability matrix
put 1 in all rows having rowSum equal to zero
Possible states which are not present in the given sequence
It can be a character vector or a $$n x n$$ matrix or a $$n x n$$ data frame or a list
Method used to estimate the Markov chain. Either "mle", "map", "bootstrap" or "laplace"
it tells whether the output Markov chain should show the transition probabilities by row.
Number of bootstrap replicates in case "bootstrap" is used.
Laplacian smoothing parameter, default zero. It is only used when "laplace" method is chosen.
Optional character for name slot.
Use parallel processing when performing Boostrap estimates.
$$\alpha$$ level for conficence intervals width.
Used only when method equal to "mle".
a boolean to decide whether to compute Confidence Interval or not.
Hyperparameter matrix for the a priori distribution. If none is provided, default value of 1 is assigned to each parameter. This must be of size $$k x k$$ where k is the number of states in the chain and the values should typically be non-negative integers.
A list containing an estimate, log-likelihood, and, when "bootstrap" method is used, a matrix of standards deviations and the bootstrap samples. When the "mle", "bootstrap" or "map" method is used, the lower and upper confidence bounds are returned along with the standard error. The "map" method also returns the expected value of the parameters with respect to the posterior distribution.
Disabling confint would lower the computation time on large datasets. If data or stringchar
contain NAs, the related NA containing transitions will be ignored.
This function has been rewritten in Rcpp. Bootstrap algorithm has been defined "heuristically".
In addition, parallel facility is not complete, involving only a part of the bootstrap process.
When data is either a data.frame or a matrix object, only MLE fit is
currently available.
A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
Inferring Markov Chains: Bayesian Estimation, Model Comparison, Entropy Rate, and Out-of-Class Modeling, Christopher C. Strelioff, James P. Crutchfield, Alfred Hubler, Santa Fe Institute
Yalamanchi SB, Spedicato GA (2015). Bayesian Inference of First Order Markov Chains. R package version 0.2.5
sequence <- c("a", "b", "a", "a", "a", "a", "b", "a", "b", "a", "b", "a", "a",
"b", "b", "b", "a")
sequenceMatr <- createSequenceMatrix(sequence, sanitize = FALSE)
mcFitMLE <- markovchainFit(data = sequence)
mcFitBSP <- markovchainFit(data = sequence, method = "bootstrap", nboot = 5, name = "Bootstrap Mc")
na.sequence <- c("a", NA, "a", "b")
# There will be only a (a,b) transition
na.sequenceMatr <- createSequenceMatrix(na.sequence, sanitize = FALSE)
mcFitMLE <- markovchainFit(data = na.sequence)
# data can be a list of character vectors
sequences <- list(x = c("a", "b", "a"), y = c("b", "a", "b", "a", "c"))
mcFitMap <- markovchainFit(sequences, method = "map")
mcFitMle <- markovchainFit(sequences, method = "mle")