Supplies a list of arguments for use in mcmc_IMIFA pertaining to the use of the multiplicative gamma process (MGP) shrinkage prior and adaptive Gibbs sampler (AGS) for use with the infinite factor models "IFA", "MIFA", "OMIFA", and "IMIFA".
mgpControl(alpha.d1 = 2.1,
alpha.d2 = 3.1,
phi.hyper = c(3, 2),
sigma.hyper = c(3, 2),
prop = 0.7,
eps = 0.1,
adapt = TRUE,
forceQg = FALSE,
cluster.shrink = TRUE,
b0 = 0.1,
b1 = 5e-05,
beta.d1 = 1,
beta.d2 = 1,
start.AGS = 0L,
stop.AGS = Inf,
delta0g = FALSE,
...)Shape hyperparameter of the column shrinkage on the first column of the loadings according to the MGP shrinkage prior. Passed to MGP_check to ensure validity. Defaults to 2.1.
Shape hyperparameter of the column shrinkage on the subsequent columns of the loadings according to the MGP shrinkage prior. Passed to MGP_check to ensure validity. Defaults to 3.1.
A vector of length 2 giving the shape and rate hyperparameters for the gamma prior on the local shrinkage parameters. Passed to MGP_check to ensure validity. Defaults to c(3, 2). It is suggested that the rate be <= shape minus 1 to induce local shrinkage, though the cumulative shrinkage property is unaffected by these hyperparameters. Excessively small values may lead to critical numerical issues and should thus be avoided; indeed it is suggested that the shape be >=1.
A vector of length 2 giving the shape and rate hyperparameters for the gamma prior on the cluster shrinkage parameters. Passed to MGP_check to ensure validity. Defaults to c(3, 2). Again, it is suggested that the shape be >= 1. Only relevant for the "IMIFA", "OMIFA", and "MIFA" methods when isTRUE(cluster.shrink).
Proportion of loadings elements within the neighbourhood eps of zero necessary to consider a loadings column redundant. Defaults to floor(0.7 * P)/P, where P is the number of variables in the data set. However, if the data set is univariate or bivariate, the default is 0.5 (see Note).
Neighbourhood epsilon of zero within which a loadings entry is considered negligible according to prop. Defaults to 0.1. Must be positive.
A logical value indicating whether adaptation of the number of cluster-specific factors is to take place when the MGP prior is employed. Defaults to TRUE. Specifying FALSE and supplying range.Q within mcmc_IMIFA provides a means to either approximate the infinite factor model with a fixed high truncation level, or to use the MGP prior in a finite factor context, however this is NOT recommended for the "OMIFA" and "IMIFA" methods.
A logical indicating whether the upper limit on the number of cluster-specific factors Q is also cluster-specific. Defaults to FALSE: when TRUE, the number of factors in each cluster is kept below the number of observations in each cluster, in addition to the bound defined by range.Q. Only relevant for the "IMIFA", "OMIFA", and "MIFA" methods, and only invoked when adapt is TRUE. May be useful for low-dimensional data sets for which identifiable solutions are desired.
A logical value indicating whether to place the prior specified by sigma.hyper on the cluster shrinkage parameters. Defaults to TRUE. Specifying FALSE is equivalent to fixing all cluster shrinkage parameters to 1. Only relevant for the "IMIFA", "OMIFA", and "MIFA" methods. If invoked, the posterior mean cluster shrinkage factors will be reported.
Intercept & slope parameters for the exponentially decaying adaptation probability:
p(iter) = 1/exp(b0 + b1 * (iter - start.AGS)).
Defaults to 0.1 & 0.00005, respectively. Must be non-negative and strictly positive, respectively, to ensure diminishing adaptation.
Rate hyperparameter of the column shrinkage on the first column of the loadings according to the MGP shrinkage prior. Passed to MGP_check to ensure validity. Defaults to 1.
Rate hyperparameter of the column shrinkage on the subsequent columns of the loadings according to the MGP shrinkage prior. Passed to MGP_check to ensure validity. Defaults to 1.
The iteration at which adaptation under the AGS is to begin. Defaults to burnin for the "IFA" and "MIFA" methods, defaults to 0 for the "OMIFA" and "IMIFA" methods, and defaults to 0 for all methods if the data set is univariate or bivariate. Cannot exceed burnin.
The iteration at which adaptation under the AGS is to stop completely. Defaults to Inf, such that the AGS is never explicitly forced to stop (thereby overriding the diminishing adaptation probability after stop.AGS). Must be greater than start.AGS. The diminishing adaptation probability prior to stop.AGS is still governed by the arguments b0 and b1.
Logical indicating whether the alpha.d1 and alpha.d2 hyperparameters can be cluster-specific. Defaults to FALSE. Only relevant for the "MIFA" method and only allowed when z.list is supplied within mcmc_IMIFA.
Catches unused arguments.
A named list in which the names are the names of the arguments related to the MGP and AGS and the values are the values supplied to the arguments.
Murphy, K., Viroli, C., and Gormley, I. C. (2020) Infinite mixtures of infinite factor analysers, Bayesian Analysis, 15(3): 937-963. <doi:10.1214/19-BA1179>.
Durante, D. (2017). A note on the multiplicative gamma process, Statistics & Probability Letters, 122: 198-204.
Bhattacharya, A. and Dunson, D. B. (2011) Sparse Bayesian infinite factor models, Biometrika, 98(2): 291-306.
mcmc_IMIFA, MGP_check, mixfaControl, bnpControl, storeControl
# NOT RUN {
mgpctrl <- mgpControl(phi.hyper=c(2.5, 1), eps=1e-02)
# data(olive)
# sim <- mcmc_IMIFA(olive, "IMIFA", n.iters=5000, MGP=mgpctrl)
# Alternatively specify these arguments directly
# sim <- mcmc_IMIFA(olive, "IMIFA", n.iters=5000, phi.hyper=c(2.5, 1), eps=1e-02)
# }
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