probs: Estimated transition probabilities

In hdMTD: Inference for High-Dimensional Mixture Transition Distribution Models

Estimated transition probabilities

Description

Computes the Maximum Likelihood estimators (MLE) for an MTD Markov chain with relevant lag set S.

Usage

probs(X, S, matrixform = FALSE, A = NULL, warning = FALSE)

Arguments

X	A vector or single-column data frame containing a sample of a Markov chain (X[1] is the most recent).
S	A numeric vector of unique positive integers. Typically, S represents a set of relevant lags.
matrixform	Logical. If TRUE, the output is formatted as a stochastic transition matrix.
A	A numeric vector of distinct integers representing the state space. If not provided, this function will set A <- sort(unique(X)).
warning	Logical. If TRUE, the function warns the user when the state space is automatically set as A <- sort(unique(X)).

Details

The probabilities are estimated as:

\hat{p}(a | x_S) = \frac{N(x_S a)}{N(x_S)}

where N(x_S a) is the number of times the sequence x_S appeared in the sample followed by a, and N(x_S) is the number of times x_S appeared (followed by any state). If N(x_S) = 0, the probability is set to 1 / |A| (assuming a uniform distribution over A).

Value

A data frame or a matrix containing estimated transition probabilities:

• If matrixform = FALSE, the function returns a data frame with three columns:

  • The past sequence x_S (a concatenation of past states).

  • The current state a.

  • The estimated probability \hat{p}(a | x_S).

• If matrixform = TRUE, the function returns a stochastic transition matrix, where rows correspond to past sequences x_S and columns correspond to states in A.

Examples

X <- testChains[, 3]
probs(X, S = c(1, 30))
probs(X, S = c(1, 15, 30))

hdMTD documentation built on June 8, 2025, 10:30 a.m.