Transition Matrix for non-homogeneous Hidden Markov Model

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Description

This function returns the transition matrix for a given distance between genes.

Usage

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QNH(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.

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.

Value

~Describe the value returned A matrix with the transition probabilities for that distance.

Author(s)

Oscar M. Rueda and Ramon Diaz-Uriarte

References

Rueda OM, Diaz-Uriarte R. Flexible and Accurate Detection of Genomic Copy-Number Changes from aCGH. PLoS Comput Biol. 2007;3(6):e122

See Also

plotQNH

Examples

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## Model with two hidden states
## Note that RJaCGH normalizes distances to be between 0 and 1
beta <- matrix(c(0, 1, 3, 0), 2, 2)
QNH(beta=beta, x=0.4)