dirichletChain: Markov chain from a Dirichlet process
In markovchain: Easy Handling Discrete Time Markov Chains

dirichletChain

R Documentation

Markov chain from a Dirichlet process

Description

Generates a Markov chain whose rows are drawn from a truncated Dirichlet process with the stick-breaking (GEM) construction, as MarkovChain.dirichlet_process() of PyDTMC does.

Usage

dirichletChain(
  n,
  diffusion,
  states = NULL,
  diagonalBias = NULL,
  shiftConcentration = FALSE,
  byrow = TRUE,
  seed = NULL,
  name = "Dirichlet process chain"
)

Arguments

`n`	The number of states, at least 2. It can be omitted when `states` is given.
`diffusion`	The concentration parameter `\alpha > 0` of the Dirichlet process. Small values concentrate the probability of each row on its first states; large values spread it more evenly.
`states`	An optional character vector of `n` state names. Defaults to `as.character(1:n)`.
`diagonalBias`	An optional positive number `\beta`. When given, a draw from `\mathrm{Beta}(\beta, 1)` is added to each diagonal entry before the row is renormalised, which makes the chain more likely to stay where it is; larger values give a stronger bias.
`shiftConcentration`	If `TRUE`, the columns are reversed, so that the probability concentrates on the last states instead of the first ones.
`byrow`	Whether the transition matrix of the result is stored by rows (the default) or by columns.
`seed`	An optional whole number, as in `randomMarkovChain`.
`name`	The `name` slot of the result.

Details

For each row, b_1, \ldots, b_n are independent \mathrm{Beta}(1, \alpha) draws and the weights are

w_j = b_j \prod_{k < j} (1 - b_k),

normalised to sum to one (the truncation at n states leaves out the mass \prod_k (1 - b_k)). PyDTMC only accepts whole values of \alpha between 1 and n; any positive value is accepted here, since the construction is defined for every \alpha > 0.

Value

A markovchain object with n states.

References

Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica, 4(2), 639-650.

Examples

dirichletChain(5, diffusion = 2, seed = 1)
# a chain that tends to stay in its current state
dirichletChain(5, diffusion = 2, diagonalBias = 5, seed = 1)

markovchain documentation built on Oct. 10, 2026, 9:07 a.m.