R: MLE for stationary distribution of discrete MCMC variables

stationary_mle {MCMCprecision} | R Documentation

## MLE for stationary distribution of discrete MCMC variables

### Description

Maximum-likelihood estimation of stationary distribution π 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 π 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)

[Package MCMCprecision version 0.4.0 Index]