markovchain (version 0.9.5)

createSequenceMatrix: 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()
)

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.

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.

Author

Giorgio Spedicato, Tae Seung Kang, Sai Bhargav Yalamanchi

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.

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")