Good-Turing Frequency Estimation

Description

Non-parametric empirical Bayes estimates of the frequencies of observed (and unobserved) species.

Usage

goodTuring(x, conf=1.96)
goodTuringPlot(x)
goodTuringProportions(counts)

Arguments

Details

Observed counts are assumed to be Poisson distributed. Using an non-parametric empirical Bayes strategy, the algorithm evaluates the posterior expectation of each species mean given its observed count. The posterior means are then converted to proportions. In the empirical Bayes step, the counts are smoothed by assuming a log-linear relationship between frequencies and frequencies of frequencies. The fundamentals of the algorithm are from Good (1953). Gale and Sampson (1995) proposed a simplied algorithm with a rule for switching between the observed and smoothed frequencies, and it is Gale and Sampson's simplified algorithm that is implemented here. The number of zero values in x are not used in the algorithm, but is returned by this function.

Sampson gives a C code version on his webpage at http://www.grsampson.net/RGoodTur.html which gives identical results to this function.

goodTuringPlot plots log-probability (i.e., log frequencies of frequencies) versus log-frequency.

goodTuringProportions runs goodTuring on each column of data, then uses the results to predict the proportion of each gene in each library.

Value

goodTuring returns a list with components

goodTuringProportions returns a matrix of proportions of the same size as counts.

Author(s)

Aaron Lun and Gordon Smyth, adapted from Sampson's C code from http://www.grsampson.net/RGoodTur.html

References

Gale, WA, and Sampson, G (1995). Good-Turing frequency estimation without tears. Journal of Quantitative Linguistics 2, 217-237.

Examples

#  True means of observed species
lambda <- rnbinom(10000,mu=2,size=1/10)
lambda <- lambda[lambda>1]

#  Oberved frequencies
Ntrue <- length(lambda)
x <- rpois(Ntrue, lambda=lambda)
freq <- goodTuring(x)
goodTuringPlot(x)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(edgeR)
Loading required package: limma
> png(filename="/home/ddbj/snapshot/RGM3/R_BC/result/edgeR/goodTuring.Rd_%03d_medium.png", width=480, height=480)
> ### Name: goodTuring
> ### Title: Good-Turing Frequency Estimation
> ### Aliases: goodTuring goodTuringPlot goodTuringProportions
> ### Keywords: models
> 
> ### ** Examples
> 
> #  True means of observed species
> lambda <- rnbinom(10000,mu=2,size=1/10)
> lambda <- lambda[lambda>1]
> 
> #  Oberved frequencies
> Ntrue <- length(lambda)
> x <- rpois(Ntrue, lambda=lambda)
> freq <- goodTuring(x)
> goodTuringPlot(x)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>