Transition Matrix for non-homogeneous Hidden Markov Model
This function returns the transition matrix for a given distance between genes.
beta parameter of transition matrix. Must be a square matrix with dimension equal to the number of hidden states.
Distance between genes to compute the transition matrix. Must be a scalar.
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.
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.
~Describe the value returned A matrix with the transition probabilities for that distance.
Oscar M. Rueda and Ramon Diaz-Uriarte
Rueda OM, Diaz-Uriarte R. Flexible and Accurate Detection of Genomic Copy-Number Changes from aCGH. PLoS Comput Biol. 2007;3(6):e122
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