Multivariate density of observed values along a tree given an OU process of evolution and root-value

Calculates the conditional probability density of observed values at the tips and internal nodes of a tree, given that tree, the value at the root, z[N+1], where N is the number of tips in the tree, known measurement error e for each value in z, and a POUMM model of evolution. This function is mostly used to calculate the likelihood of simulated data under known model parameters.

dVNodesGivenTreePOUMM(
  z,
  tree,
  alpha,
  theta,
  sigma,
  sigmae = 0,
  e = rep(0, length(z)),
  log = TRUE
)

Arguments

z	A numeric vector of size length(tree$tip.label)+tree$Nnode representing the observed values at the tips, root and internal nodes.
tree	An object of class phylo.
alpha, theta, sigma	Numeric values, parameters of the OU model.
sigmae	Numeric non-negative value or vector of length(z) elements (default 0). Specifies the standard deviation of random environmental contribution (and eventually measurement error) to be added to the values. Note that if measurement standard error, se, is known and needs to be added to the environmental contribution, the right way to specify the parameter would be sqrt(sigmae^2+se^2), not sigmae+se.
e	Numeric vector of size length(z) representing exactly known error (sum of environmental contribution and measurement error). Defaults to a vector of zeroes.
log	Logical indicating whether a log-likelihood should be returned instead of a likelihood. Default is TRUE.

Value

A numeric value, the multivariate probability density of z under the given parameters.