fipp: Moments of symmetric additive functional computed over the...
In fipp: Induced Priors in Bayesian Mixture Models

Description Usage Arguments Value References Examples

View source: R/fipp.R

fipp is a closure which returns a function that computes moments of a user-specified functional over the induced prior partitions. Required arguments are: prior distribution of the number of mixture components and its parameters (see examples for details). Optional arguments are: the number of moments to be evaluated (currently only up to 2 are implemented) and whether the mean/variance or 1st/2nd moments should be printed out as a result of computing the first two moments (default is set to print out mean/variance).

fipp(
  lfunc,
  Kplus,
  N,
  type = c("DPM", "static", "dynamic"),
  alpha = NULL,
  gamma = NULL,
  maxK = NULL,
  log = FALSE
)

`lfunc`	a logged version of the additive symmetric functional intended to compute over the prior partition. The function should only accept one argument N_j (= number of observations in each partition).
`Kplus`	a numeric value that represents the number of filled clusters in data
`N`	the number of observation in data
`type`	the type of model considered. Three models (static/dynamic MFMs and DPM) are supported.
`alpha, gamma`	hyperparameters for the Dirichlet prior. For static MFM, gamma should be specified, while alpha should be specified for all other models (that is, for dynamic MFM and DPM).
`maxK`	the maximum number of K (= the number of mixture components) considered. Only needed for static/dynamic MFMs.
`log`	logical, indicating whether the probability should be logged or not

fipp returns a function which takes two required arguments (required only for static/dynamic MFMs) and 2 optional arguments:

priorK: a function with support on the positive integers. The function serves as a prior of K (default = NULL which is for DPM).
priorKparams: a named list of prior parameters for the function supplied in argument priorK (default = NULL which is for DPM).
order: maximum number of moments to be evaluated by the function (default = 2)
replace2ndwvar: replace 2nd moment with variance (default = TRUE)

Greve, J., Grün, B., Malsiner-Walli, G., and Frühwirth-Schnatter, S. (2020) Spying on the Prior of the Number of Data Clusters and the Partition Distribution in Bayesian Cluster Analysis. https://arxiv.org/abs/2012.12337

Escobar, M. D., and West, M. (1995) Bayesian Density Estimation and Inference Using Mixtures. Journal of the American Statistical Association 90 (430), Taylor & Francis: 577-–88. https://www.tandfonline.com/doi/abs/10.1080/01621459.1995.10476550

Miller, J. W., and Harrison, M. T. (2018) Mixture Models with a Prior on the Number of Components. Journal of the American Statistical Association 113 (521), Taylor & Francis: 340-–56. https://www.tandfonline.com/doi/full/10.1080/01621459.2016.1255636

Frühwirth-Schnatter, S., Malsiner-Walli, G., and Grün, B. (2020) Generalized mixtures of finite mixtures and telescoping sampling https://arxiv.org/abs/2005.09918

## Determine mean/variance of the number of singleton clusters for dynamic 
## MFM model conditional on K+ = 5, alpha = 1 with a sample size N = 100.
## We assume that K will be smaller than 30 by setting maxK = 30, please
## increase this value for more realistic analysis.
## 
## First create the function singletons():
singletons <- fipp(lfunc = function(n) log(n==1), Kplus = 5, N = 100,
  type = "dynamic", alpha = 1, maxK = 30)

## Then evaluate it using a Geom(0.1) prior:
singletons(dgeom, list(prob = 0.1))

## Try a different prior, the Poisson prior Pois(1):
singletons(dpois, list(lambda = 1))

## If mean is the only thing you are interested in, try the following:
singletons(dpois, list(lambda = 1), order = 1)

## Also, if you want 1st/2nd moments instead of mean/variance, try:
singletons(dpois, list(lambda = 1), replace2ndwvar = FALSE)