get_freeparametersvalue: Extract free parameter values from a migration structure.

In FlywayNet: Estimate Migration Birds Flyways Network with HSMM

Extract free parameter values from a migration structure.

Description

Get values of free parameters. Indeed taking into account sites order, known impossible sites links, sites dead probability, not all the sites transition probabilities have to be estimated. Others parameters values may be evaluated from free parameters.

Usage

get_freeparametersvalue(
  migr,
  update_transitions = TRUE,
  update_sojourns = NULL,
  use_adhoc_dirichlet = FALSE
)

Arguments

migr	A migration structure.
update_transitions	If TRUE, transitions are considered unknown and their values should be returned.
update_sojourns	Vector of boolean, that identifies which sojourn times should be returned.
use_adhoc_dirichlet	If TRUE, the transition probabilities are given in the ad hoc Dirichlet distribution (q_ij values). See details.

Details

Let N be number of sites, d_i the death probability at a given site i, p_ij the transition probability from site i to site j. Then we must have a multinomial probability distribution that respects : p_i1 + ... + p_iN + di = 1. Drawing p_i1, ..., p_iN so that this set of values forms a multinomial distribution can be done with the multivariate Dirichlet distribution which is difficult to handle in estimation processes (especially ABC). The adhoc dirichlet proposed here is a way to provide a bijection between a multinomial distribution and a a set of uniform distribution in [0:1]. This way, from N values q_ij drawn uniformely in [0:1], we can compute p_ij with the constraint of the multinomial distribution. And inversely, if we have the multinomial distribution then we can compute uniquely the q_ij values. A way to do it is to define recursively the p_ij values as

p_ij = q_ij * (1- d_i - p_i1 - ... - p_i(j-1))

Also, the d_i values are expected to be known and the last probability transition from one site i (eg. p_iN) can be computed from others p_ij and d_i. Finally, the 'link_knowledge' identifies the transitions that are not possible (with probability 0) which are also removed from the extraction.

Value

return named vector of default values of parameters to estimate.

Examples

 migr <- generate_toy_migration()
 get_freeparametersvalue(migr) 

FlywayNet documentation built on March 18, 2022, 7:21 p.m.