DirFactor: Gibbs sampler for Depedent Dirichlet factor model.

In boyuren158/DirFactor: Dependent Dirichlet processes factor model for nonparametric ordination fo microbiome data

Description

Gibbs sampler for Depedent Dirichlet factor model.

Usage

DirFactor(data, hyper, start = NA, save.path = NA, save.obj = c("sigma",
  "Q", "T.aug", "X", "Y", "er", "delta", "phi"), burnin = 0.2, thinning = 5,
  step = 1000, step.disp = 10)

Arguments

data	Required. A count matrix with species in rows and biological samples in column.
hyper	Required. A list of hyper-parameters in the priors.
start	A list of starting values of model parameters. Default is NA and the starting values will be generated automatically based on the input data. See Details for the required fields of the list.
save.path	A string contains the path to save the MCMC results. For example, save.path="~/sim" will save results of the ith iteration to ~/sim_i.rds. Default is NA and a temp directory will be assigned.
save.obj	A list of model parameters that will be saved, default is all parameters.
burnin	A number between 0 and 1. Fraction of burn-in samples. Default is 0.2.
thinning	A positive integer. The MCMC results will be saved every thinning iterations. Default is 5.
step	A positive integer. The total number of MCMC iterations. Default is 1000.
step.disp	A positive integer. A message will report the number of iterations finished every step.disp iterations. Default is 10.

Details

The Dependent Dirichlet process factor model assumes the observed data is distributed according to a multinomial distrition for each biological sample, conditioning on the probabilities of species, which is assumed to follow a Dependent Dirichlet processes a priori. The model has two major parts. sigma, Q directly specify the probabilities of species in each biological samples and X, Y, er, delta, phi specify the hyper-prior on Q. T.aug is an auxilary parameter and does not have direct interpretation. More details on model and prior specification can be found in Ren et. al. (2016).

Users are required to provide a list containing the values of the hyper-parameters. The list must contain fields as following.

• alpha and beta: hyper-parameters in the prior of sigma. sigma follows a Poisson process on (0,1) with intensity ασ^{-1-β}\cdot(1-σ)^{-1/2+β} a priori.

• a.er and b.er: hyper-parameters in the prior of er. er follows an inverse gamma distribution 1/Gamma(a.er,b.er) a priori.

• m: number of factors the model is assumed to have. Usually a value much smaller than the number of biological samples.

• nv: hyper-parameter of the prior of phi. phi follows Gamma(nv/2,nv/2) a priori.

• a1 and a2: hyper-parameters in the prior of delta. The prior of delta[1] is Gamma(a1,1) and the prior of delta[2:m] is independent Gamma(a2,1). a2 must not be smaller than 1 in order to achieve factor shrinkage Bhattacharya et al. (2011).

If the users want to specify the starting values for the model parameters, they can pass a list with fields sigma, Q, T.aug, X, Y, er, delta, phi to the function augment start. Assume there are n biological samples and p species in data. Each field is specified as following:

• sigma: a vector with p components and the starting values have to be in (0,1).

• Q: a matrix with p rows and n columns and the starting values of Q should be positive if the corresponding cell in data is positive.

• T.aug: a vector with n positive components.

• X: a m\times p matrix.

• Y: a m\times n matrix.

• er: a positive scalar.

• delta: a positive vector with m components.

• phi: a n\times m positive matrix.

Value

A list with two fields: running.time and save.path. running.time is the total amount of time for finishing the MCMC simulation. save.path is the path to the saved results.

Examples

my.hyper = list( nv = 3, a.er = 1, b.er = 0.3, a1 = 3, 
                 a2 = 4, m = 10, alpha = 10, beta = 0 )
my.sim = SimDirFactorBlock( 1e6, n = 22, p = 68, m = 3, my.hyper, K = 2 )
DirFactor( my.sim$data[[1]], my.hyper, save.obj = c("Y", "er"), step.disp = 100 )

boyuren158/DirFactor documentation built on May 13, 2019, 1:38 a.m.