markovchainFit: Function to fit a discrete Markov chain

In spedygiorgio/markovchain: Easy Handling Discrete Time Markov Chains

Function to fit a discrete Markov chain

Description

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.

Usage

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()
)

Arguments

stringchar	It can be a n x n matrix or a character vector or a list
toRowProbs	converts a sequence matrix into a probability matrix
sanitize	put 1 in all rows having rowSum equal to zero
possibleStates	Possible states which are not present in the given sequence
data	It can be a character vector or a n x n matrix or a n x n data frame or a list
method	Method used to estimate the Markov chain. Either "mle", "map", "bootstrap" or "laplace"
byrow	it tells whether the output Markov chain should show the transition probabilities by row.
nboot	Number of bootstrap replicates in case "bootstrap" is used.
laplacian	Laplacian smoothing parameter, default zero. It is only used when "laplace" method is chosen.
name	Optional character for name slot.
parallel	Use parallel processing when performing Boostrap estimates.
confidencelevel	\alpha level for conficence intervals width. Used only when method equal to "mle".
confint	a boolean to decide whether to compute Confidence Interval or not.
hyperparam	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.

Details

Disabling confint would lower the computation time on large datasets. If data or stringchar contain NAs, the related NA containing transitions will be ignored.

Value

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.

Note

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.

Author(s)

Giorgio Spedicato, Tae Seung Kang, Sai Bhargav Yalamanchi

References

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

See Also

markovchainSequence, markovchainListFit

Examples

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")

spedygiorgio/markovchain documentation built on Feb. 29, 2024, 3:01 p.m.