radish_algorithm: Likelihood of parameterized conductance surface

In nspope/radish: Fast gradient-based optimization of resistance surfaces

Description

Calculates likelihood, gradient, hessian, and partial derivatives of a parameterized conductance surface, given a function mapping spatial data to conductance and a function mapping resistance distance (covariance) to genetic distance; using the algorithm in Pope (in prep).

Usage

radish_algorithm(
  f,
  g,
  s,
  S,
  theta,
  nu = NULL,
  objective = TRUE,
  gradient = TRUE,
  hessian = TRUE,
  partial = TRUE,
  nonnegative = TRUE,
  validate = FALSE
)

Arguments

f	A function of class 'conductance_model'
g	A function of class 'measurement_model'
s	An object of class 'radish_graph'
S	A matrix of observed genetic distances
theta	Parameters for conductance surface (e.g. inputs to 'f')
nu	Number of genetic markers (potentially used by 'g')
objective	Compute negative loglikelihood?
gradient	Compute gradient of negative loglikelihood wrt theta?
hessian	Compute Hessian matrix of negative loglikelihood wrt theta?
partial	Compute partial derivatives of negative loglikelihood wrt theta and spatial covariates/observed genetic distances
nonnegative	Force regression-like 'measurement_model' to have nonnegative slope?
validate	Numerical validation via 'numDeriv' (very slow, use for debugging small examples)

Value

A list containing at a minimum:

covariance

rows/columns of the generalized inverse of the graph Laplacian for a subset of target vertices

Additionally, if 'objective == TRUE':

objective	(if 'objective') the negative loglikelihood
phi	(if 'objective') fitted values of the nuisance parameters of 'g'
boundary	(if 'objective') is the solution on the boundary (e.g. no genetic structure)?
fitted	(if 'objective') matrix of expected genetic distances among target vertices
gradient	(if 'gradient') gradient of negative loglikelihood with respect to theta
hessian	(if 'hessian') Hessian matrix of the negative loglikelihood with respect to theta
partial_X	(if 'partial') Jacobian of the gradient with respect to the spatial covariates
partial_S	(if 'partial') Jacobian of the gradient with respect to the observed genetic distances

References

Pope NS. In prep. Fast gradient-based optimization of resistance surfaces.

Examples

library(raster)

data(melip)

covariates <- raster::stack(list(altitude=melip.altitude, forestcover=melip.forestcover))
surface <- radish_conductance_surface(covariates, melip.coords, directions = 8)

radish_algorithm(radish::loglinear_conductance, radish::leastsquares, surface, 
                 ifelse(melip.Fst < 0, 0, melip.Fst), nu = 1000, theta = c(-0.3, 0.3))

nspope/radish documentation built on July 12, 2020, 11:50 a.m.