stationary_mle {MCMCprecision}

MLE for stationary distribution of discrete MCMC variables

Description

Maximum-likelihood estimation of stationary distribution \pi based on (a) a sampled trajectory z of a model-indicator variable or (b) a sampled transition count matrix N.

Usage

stationary_mle(z, N, labels, method = "rev", abstol = 1e-05, maxit = 1e+05)

Arguments

z

MCMC output for the discrete indicator variable with numerical, character, or factor labels (can also be a mcmc.list or a matrix with one MCMC chain per column).

N

the observed transitions matrix (if supplied, z is ignored). A quadratic matrix with sampled transition frequencies (N[i,j] = number of switches from z[t]=i to z[t+1]=j).

labels

optional: vector of labels for complete set of models (e.g., models not sampled in the chain z). If epsilon=0, this does not affect inferences due to the improper Dirichlet(0,..,0) prior.

method

Different types of MLEs:

• "iid": Assumes i.i.d. sampling of the model indicator variable z and estimates \pi as the relative frequencies each model was sampled.

• "rev": Estimate stationary distribution under the constraint that the transition matrix is reversible (i.e., fulfills detailed balance) based on the iterative fixed-point algorithm proposed by Trendelkamp-Schroer et al. (2015)

• "eigen": Computes the first left-eigenvector (normalized to sum to 1) of the sampled transition matrix

abstol

absolute convergence tolerance (only for method = "rev")

maxit

maximum number of iterations (only for method = "rev")

Details

The estimates are implemented mainly for comparison with the Bayesian sampling approach implemented in stationary, which quantify estimation uncertainty (i.e., posterior SD) of the posterior model probability estimates.

Value

a vector with posterior model probability estimates

References

Trendelkamp-Schroer, B., Wu, H., Paul, F., & Noé, F. (2015). Estimation and uncertainty of reversible Markov models. The Journal of Chemical Physics, 143(17), 174101. https://doi.org/10.1063/1.4934536

See Also

stationary

Examples

P <- matrix(c(.1,.5,.4,
              0,.5,.5,
              .9,.1,0), ncol = 3, byrow=TRUE)
z <- rmarkov(1000, P)
stationary_mle(z)

# input: transition frequency
tab <- transitions(z)
stationary_mle(N = tab)