admixturegraph (version 1.0.2)

log_likelihood: Calculate (essentially) the log likelihood of a graph with parameters, given the observation.

Description

Or the log likelihood of the observation, given graph with parameters, depending how things are modeled. Basically this is just cost_function that doesn't optimize the edge variables but has them as an argument instead.

Usage

log_likelihood(f, concentration, matrix, graph, parameters = extract_graph_parameters(graph))

Arguments

f

The observed $f$ statistics (the column D from data).

concentration

The Cholesky decomposition of the inverted covariance matrix. So if $S$ is the covariance matrix, this is $C = chol(S^(-1))$ satisfying $S^(-1) = C^t*C$.

matrix

A column reduced edge optimisation matrix (typically given by the function build_edge_optimisation_matrix).

graph

The admixture graph. Here to give default value for:

parameters

Just because we need to know variable names.

Value

The output is a function. Given admixture proportions x and edge lengths e, the graph topology $T$ implies an estimate $F$ for the statistics $f$. This output function calculates $$l = (F-f)^t S^{-1}(F-f)$$ from x and e. Up to a constant error and multiplier that is a log likelihood function, as $$\det(2 \pi S)^{-1/2} e^{-l/2}$$ can be seen as a likelihood of a graph with parameters, given the observation, or the other way around (possibly up to a normalization constant).

See Also

cost_function

edge_optimisation_function

calculate_concentration