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

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createSequenceMatrix(stringchar, toRowProbs = FALSE, sanitize = FALSE,
  possibleStates = character())

markovchainFit(data, method = "mle", byrow = TRUE, nboot = 10L,
  laplacian = 0, name = "", parallel = FALSE, confidencelevel = 0.95,
  hyperparam = matrix(), sanitize = FALSE, possibleStates = character())

Arguments

stringchar

Equivalent to data. Either a nx2 matrix or a character vector.

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

A character 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

α

level for conficence intervals width. Used only when method equal to "mle".

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 kxk where k is the number of states in the chain and the values should typically be non-negative integers.

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 "euristically". 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

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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")

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