Pt function

Transition Probability Function

This function calculates the transition probability function for a process during a period of time.

Pt(S, Pi, t)

Arguments

• S: a 4 x 4 symmetric matrix
• Pi: a diagonal matrix containing the stationary distribution for the process
• t: a period of time describing the length of the process

Details

This function needs the 4 x 4 symmetric matrix S, II and the process length t in order to find the transition probability over that process, where $P_{ij}(t)$ is the probability that the ith nucleotide changes to the j-th nucleotide during the period of t.

Returns

A 4 x 4 matrix containing the transition probabilities for a process.

References

Faisal Ababneh, Lars S Jermiin, Chunsheng Ma, John Robinson (2006). Matched-pairs tests of homogeneity with applications to homologous nucleotide sequences. Bioinformatics, 22(10), 1225-1231.

See Also

Smatrix

Examples

Pi<-diag(c(.1,.1,.1,.7)) 
S<-Smatrix(c(.3,.3,.3,.3,.3,.3),diag(Pi))
t<-1
p<-Pt(S, Pi, t)
p