Various multiplicative multinomial probability utilities

Description

Various multiplicative multinomial probability utilities for different types of observation

Usage

MM(y,n=NULL,paras)
MM_allsamesum(y, n=NULL, paras)
MM_differsums(y, n=NULL, paras)
MM_allsamesum_A(y, paras)
MM_differsums_A(y, paras)
MM_single(yrow, paras, givelog=FALSE)
MM_support(paras, ss)

Arguments

Details

Consider non-negative integers y_1,...,y_k with y_1+...+y_k=y. Then suppose the frequency function of the distribution Y_1,...,Y_k is

Ccdot{ychoose y_1,…,y_k} ∏_{i=1}^k p_i^{y_i} ∏_{1≤q i<j≤q k}{θ_{ij}}^{y_iy_j}

where p_i,...,p_k >= 0, p_1+...+p+k=1 correspond to probabilities; and theta_{ij}>0 for 1 <= i < j <= k are additional parameters.

Here C stands for a normalization constant:

C=C(p,θ,Y)= ∑_{y_1 + cdots + y_k=y} ∏_{i=1}^k p_i^{y_i} ∏_{1≤q i<j≤q k}{θ_{ij}}^{y_iy_j}

which is evaluated numerically. This is expensive.

The usual case is to use function MM().

• Function MM() returns the log of the probability of a matrix of rows of independent multinomial observations. It is a wrapper for MM_allsamesum() and MM_differsums(). Recall that optional argument n specifies the number of times that each row is observed. Calls NormC().

• Function MM_allsamesum() gives the log of the probability of observing a matrix where the rowsums are identical. Calls NormC().

• Function MM_differsums() gives the log of the probability of observing a matrix where the rowsums are not necessarily identical. Warning: This function takes a long time to run. Calls NormC(), possibly many times.

• Functions MM_allsamesum_A() and MM_differsums_A() are analogous to functions MM_allsamesum() and MM_differsums() but interpret the matrix y as having rows corresponding to observations; each row is observed once, as in data(pollen). Both call NormC().

• Function MM_single() gives a likelihood function for a paras object with a single multinomial observation (that is, a single line of matrix y). Does not call NormC().

• Function MM_support() gives the support (that is, the log-likelihood) of a paras object; argument ss is the sufficient statistic, as returned by suffstats(). Does not call NormC().

• Function dMM() [documented more fully at rMM.Rd] gives the probability of a single multivariate observation (ie a single row of the matrix argument y). Calls NormC().

Author(s)

Robin K. S. Hankin

Examples

data(voting)

data(voting)
p <- Lindsey(voting, voting_tally)

MM(voting,voting_tally,p)   #No other value of 'p' gives a bigger value

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.

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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(MM)
Loading required package: magic
Loading required package: abind
Loading required package: partitions
Loading required package: emulator
Loading required package: mvtnorm
Loading required package: Oarray
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/MM/MM.Rd_%03d_medium.png", width=480, height=480)
> ### Name: MM
> ### Title: Various multiplicative multinomial probability utilities
> ### Aliases: MM MM_allsamesum MM_differsums MM_allsamesum_A MM_differsums_A
> ###   MM_single MM_support
> 
> ### ** Examples
> 
> data(voting)
> 
> data(voting)
> p <- Lindsey(voting, voting_tally)
> 
> MM(voting,voting_tally,p)   #No other value of 'p' gives a bigger value
[1] -254.0724
> 
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>