Markov stability of the states of a transition network

Per-state persistence (self-transition probability), stationary probability, return time, sojourn time and mean first-passage times to and from the other states of a first-order Markov chain.

Usage

hg_markov_stability(
  data,
  normalize = TRUE,
  action = NULL,
  actor = NULL,
  time = NULL,
  session = NULL,
  time_threshold = 900,
  timezone = "UTC"
)

Arguments

data

A row-stochastic transition matrix, a network object (netobject, tna, cograph_network, netobject_group) whose weights are the transition matrix, or sequences in any form described in sequence-input, from which the first-order transition probabilities are estimated.

normalize

Logical. Normalise the rows to sum to one. Default TRUE.

action, actor, time, session, time_threshold, timezone

Long-format arguments (see sequence-input); leave the column names NULL for wide, list or model input.

Value

A net_markov_stability object. Read it with hg_get(): one row per state (what = "states", the default), the mean first-passage times ("passage_time") or the stationary distribution ("stationary").

Conditions

The quantities are defined only for an irreducible chain, one in which every state can reach every other. A chain that is not irreducible (a transient or absorbing state, or several closed classes, as a pruned higher-order network can have) raises hypernets_not_ergodic, a hypernets_bad_input, naming those states.

References

Kemeny, J. G., & Snell, J. L. (1976). Finite Markov Chains. Springer.

See also

markov_order()

Examples

P <- matrix(c(0.5, 0.3, 0.2,
              0.2, 0.5, 0.3,
              0.1, 0.4, 0.5), 3, 3, byrow = TRUE,
            dimnames = list(c("A", "B", "C"), c("A", "B", "C")))
ms <- hg_markov_stability(P)
hg_get(ms, sort_by = "stationary")
#>   state persistence stationary return_time sojourn_time avg_time_to_others
#> 1     B         0.5     0.4182        2.39            2               4.92
#> 2     C         0.5     0.3455        2.89            2               4.77
#> 3     A         0.5     0.2364        4.23            2               3.63
#>   avg_time_from_others
#> 1                 2.83
#> 2                 3.95
#> 3                 6.54
hg_get(ms, what = "passage_time", from = "A")
#>   from to    steps
#> 1    A  A 4.230769
#> 2    A  B 3.043478
#> 3    A  C 4.210526