Logarithm of the probabilities of state sequences
Compute the logarithm of the probability of each state sequence obtained from a state transition model. The probability of a sequence is equal to the product of each state probability of the sequence. There are several methods to compute a state probability.
The sequence to compute the probabilities.
either the name (
Model used to compute the probability of the first state. Either
The sequence likelihood P(s) is defined as the product of the probability with which each of its observed successive state is supposed to occur at its position. Let s=s_1s_2 ... s_l be a sequence of length l. Then
P(s)=P(s_1, 1) * P(s_2, 2) * ... * P(s_l, l)
with P(s_t,t) the probability to observe state s_t at position t.
The question is how to determinate the state probabilities P(s_t,t). Several methods are available and can be set using the
One commonly used method for computing them is to postulate a Markov model, which can be of various order. We can consider probabilities derived from the first order Markov model, that is, each P(s_t,t), t>1 is set as the transition rate p(s_t|s_(t-1)). This is available in
seqlogp by setting
The transition rates may be considered constant over time/positions (
time.varying=FALSE), that is estimated across sequences from the observations at positions t and t-1 for all t together. Time varying transition rates may also be considered (
time.varying=TRUE), in which case they are computed separately for each position, that is estimated across sequences from the observations at positions t and t-1 for each t, yielding an array of transition matrices. The user may also specify his own transition rates array or matrix.
Another method is to use the frequency of a state at each position to set P(s_t,t) (
prob="freq"). In the latter case, the probability of a sequence is independent of the probability of the transitions. Here again, the frequencies can be computed all together (
time.varying=FALSE) or separately for each position t (
For t=1, we set P(s_1,1) to the observed frequency of the state s_1 at position 1. Alternatively, the
begin argument allows to specify the probability of the first state.
The likelihood P(s) being generally very small,
seqlogp return -log(P(s)). The latter quantity is minimal when P(s) is equal to 1.
A vector containing the logarithm of each sequence probability.
Matthias Studer and Alexis Gabadinho (with Gilbert Ritschard for the help page)
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