Q.NH: Transition Matrix for non-homogeneous Hidden Markov Model
Description
This function returns the transition matrix for a given distance between genes.
Usage
Q.NH(beta, x, q=-beta)
Arguments
beta
beta parameter of transition matrix. Must be a square
matrix with dimension equal to the number of hidden states.
x
Distance between genes to compute the transition matrix. Must
be a scalar.
q
q parameter of transition matrix. Note that in RJaCGH q is
always -beta (details below). Must be a square matrix with dimension equal to the
number of hidden states.
Value
~Describe the value returned
A matrix with the transition probabilities for that distance.
Details
RJaCGH assumes a non-homogeneous transition matrix with this form:
Q[i,j] = exp(-beta[i,j] + beta[i,j]*x) / sum(i,.) exp(-beta[i,.] +
beta[i,.]*x
All beta[i,i] are constrained to be zero, for the model to be
identifiable.
All beta[i,j] are positive. This model is chosen for its simplicity
and because it agrees with
biological assumptions, for it makes the
probabilities of staying in the same state decreasing with the
distance to the next gene, and reaches a probability of 1/number of
hidden state when the distance to the next gene is the maximum.
To avoid overflow errors, RJaCGH normalizes distances to be between 0
and 1.
References
Rueda OM, Diaz-Uriarte R.
Flexible and Accurate Detection of Genomic Copy-Number Changes from
aCGH.
PLoS Comput Biol. 2007;3(6):e122
## Model with two hidden states## Note that RJaCGH normalizes distances to be between 0 and 1beta <- matrix(c(0, 1, 3, 0), 2, 2)
Q.NH(beta=beta, x=0.4)