Likelihood calculations for continuous-time Markov chain along a tree
This module implements several variants of the so-called pruning algorithm, as well as functions to sample substitution mappings conditionally on leaf values.
type matrix_decomposition =
[ `Mat of Linear_algebra.mat
| `Transpose of Linear_algebra.mat
| `Diag of Linear_algebra.vec ]
listThe type matrix_decomposition represents a product of matrices. In the case that the product is eventually applied to a vector, it is faster to perform a series of matrix-vector products than computing the product of matrices.
`Mat of mat represents a matrix without any decomposition.`Transpose of mat represents the transpose of a matrix.`Diag of vec represents a diagonal matrix.Example usage:
let decomposition = [
`Mat matrix1;
`Transpose matrix2;
`Diag vector1;
] in
let result = matrix_decomposition_reduce ~dim:3 decomposition in
(* process_result result ...*)val matrix_decomposition_reduce :
dim:int ->
matrix_decomposition ->
Linear_algebra.matmatrix_decomposition_reduce dim md computes the product of elements in md as a single matrix of dimension dim.
module SV : sig ... endval pruning :
('n, 'l, 'b) Tree.t ->
nstates:int ->
transition_probabilities:('b -> matrix_decomposition) ->
leaf_state:('l -> int) ->
root_frequencies:Linear_algebra.vec ->
floatpruning t ~nstates ~transition_probabilities ~leaf_state
~root_frequencies returns the probability of observing the states returned by leaf_state at the leaves of t given the CTMC specified by nstates, transition_probabilities and root_frequencies.
val pruning_with_missing_values :
('n, 'l, 'b) Tree.t ->
nstates:int ->
transition_probabilities:('b -> matrix_decomposition) ->
leaf_state:('l -> int option) ->
root_frequencies:Linear_algebra.vec ->
floatpruning t ~nstates ~transition_probabilities ~leaf_state
~root_frequencies returns the probability of observing the states returned by leaf_state at the leaves of t given the CTMC specified by nstates, transition_probabilities and root_frequencies. With this variant, one can specify that some leaves are unobserved.
val conditional_likelihoods :
('n, 'l, 'b) Tree.t ->
nstates:int ->
leaf_state:('l -> int) ->
transition_probabilities:('b -> Linear_algebra.mat) ->
(shifted_vector, int, 'b * Linear_algebra.mat) Tree.tconditional_likelihoods t ~nstates ~leaf_state
~transition_probabilities computes the conditional likelihoods of observing the states returned by leaf_state at the leaves of t given the CTMC specified by nstates and transition_probabilities.
val conditional_simulation :
Gsl.Rng.t ->
(shifted_vector, int, 'b * Linear_algebra.mat) Tree.t ->
root_frequencies:Linear_algebra.vec ->
(int, int, 'b * Linear_algebra.mat) Tree.tconditional_simulation rng tree ~root_frequencies performs a conditional simulation on the provided tree given the root_frequencies using the provided random number generator rng.
module Ambiguous : sig ... endIn this variant implementation, one can specify some uncertainty for a given leaf, by letting leaf_state return true for several states. In that case, it is understood that each state has equal probability. If leaf_state always returns false for a given leaf, it is interpreted as the leaf being unobserved.
module Uniformized_process : sig ... endmodule Path_sampler : sig ... endval substitution_mapping :
rng:Gsl.Rng.t ->
path_sampler:('b -> Path_sampler.t) ->
(int, int, 'b * Linear_algebra.mat) Tree.t ->
(int, int, 'b * (int * float) array) Tree.t