Probability that a Markov chain hits the set of states A
before the set B (the committor function), from every initial state or
from one.
Arguments
- object
A
markovchainobject.- A, B
Disjoint sets of states, given as indices (positions in
states(object)).- p
Optional index of the initial state. If omitted, the probabilities for all initial states are returned.
Value
A numeric vector with the probability for each initial state, or
a single number if p is given.
Details
The committor \(q\) solves the linear system
\(q_i = \sum_j P_{ij} q_j\) for the states outside \(A \cup B\),
with \(q = 1\) on A and \(q = 0\) on B. The system has a unique
solution when A or B can be reached from every state.
See also
Other first passage and hitting:
absorptionProbabilities(),
firstPassage(),
firstPassageMultiple(),
hittingProbabilities(),
meanAbsorptionTime(),
meanFirstPassageTime(),
meanNumVisits(),
meanRecurrenceTime(),
noofVisitsDist()
Examples
transMatr <- matrix(c(0, 0, 0, 1, 0.5,
0.5, 0, 0, 0, 0,
0.5, 0, 0, 0, 0,
0, 0.2, 0.4, 0, 0,
0, 0.8, 0.6, 0, 0.5), nrow = 5)
object <- new("markovchain", states = c("a", "b", "c", "d", "e"),
transitionMatrix = transMatr)
# probability of reaching "e" before "c", from each state
committorAB(object, 5, 3)
#> a b c d e
#> 0.4444444 0.8888889 0.0000000 0.4444444 1.0000000
committorAB(object, 5, 3, p = 1)
#> a
#> 0.4444444