Xsampler: Z-polytope sampler for linear inverse problems

In MartinLHazelton/DynamicLatticeBasis: Dynamic Lattice Bases for Z-Polytope Sampling

Z-polytope sampler for linear inverse problems

Description

For the linear inverse problem y=Ax where y and x are counts, the y-fibre (solution set) is a Z-polytope (i.e. the points on the integer lattice within a convex polytope). This function implements samplers for the Z-polytope, with using a dynamic lattice basis or a full Markov basis. The underyling model for x can be Poisson, uniform or negative binomial.

Usage

Xsampler(
  y,
  A,
  lambda,
  U = NULL,
  Method = "MH",
  Reorder = TRUE,
  tune.par = 0.5,
  combine = FALSE,
  x.order = NULL,
  x.ini = NULL,
  Model = "Poisson",
  Proposal = "Unif",
  NB.alpha = 1,
  ndraws = 10000,
  burnin = 2000,
  verbose = 0,
  THIN = 1
)

Arguments

y	Vector of observed count data.
A	Model configuration matrix, assumed to be binary.
lambda	Mean vector for x.
U	Optional matrix the columns of which should be a Markov (sub)-basis.
Method	"MH" for Metropolis-Hastings sampler, "Gibbs" for Gibbs sampler.
Reorder	Should the columns of A be reordered? Defaults to TRUE.
tune.par	Tuning parameter (alpha) controlling variation in fitness values for lattice bases. Defaults to 0.5.
combine	Should extra moves be included combining lattice basis vectors? Defaults to FALSE, but should usually be set to TRUE if A is not unimodular.
x.order	If Reorder=FALSE, x.order can be used to reorder columns of A to match ordering of entries of x. Defaults to NULL when no such reordering is performed.
x.ini	Vector of initial values for x. Default is NULL, when initial values derived through integer programming.
Model	"Poisson", "Uniform", "NegBin" or "Normal" (the last being a discrete approximation).
Proposal	"NonUnif" or "Unif" (default).
NB.alpha	Dispersion parameter for negaqtive-binomial distribution. Defaults to 1.
ndraws	Number of iterations to run sampler after burn-in. One iteration comprises cycling through the full basis (possibly augmented by a combined move). Defaults to 10^4.
burnin	Number of iteractions for burn in period. Defaults to 2000, which is usually more than adequate.
verbose	Controls level of detail in recording lattice bases used.
THIN	Thinning parameter for output. Defaults to 1 (no thinning).

Value

A list with components X (a matrix, each row corresponding to samplers for an entry of x) and x.order (a vector describing dynamic selection of lattice bases, if verbose=1).

Examples

data(LondonRoad)
Xsampler(A=LondonRoad$A,y=LondonRoad$y,lambda=LondonRoad$lambda,Model="Poisson",Method="Gibbs",tune.par=0.5,combine=FALSE)

MartinLHazelton/DynamicLatticeBasis documentation built on March 1, 2024, 3:14 a.m.