Generates the suite of functions related to the one sample binomial experiment
with a two-sided alternative hypothesis of interest.
Usage
binom1.2sided(p0, prob, a, b)
Arguments
p0
Scalar. The value of p under null hypothesis Ho: p==p0. Must be a value
between 0 and 1.
prob
Scalar. The prior probability that the null hypothesis is true. Must be a
value between 0 and 1.
a
Scalar. Shape1 parameter for prior Beta distribution. See documentation for
dbeta.
b
Scalar. Shape2 parameter for prior Beta distribution. See documentation for
dbeta.
Details
binom1.2sided is used to generate a suite of functions for a one-sample
binomial experiment with a two-sided alternative hypothesis. That is, when
X ~ Binomial(n,p)
H0: p == p0 vs. H1: p != p0
using the following prior on p
pi(p) = u*(p==p0) + (1-u)*(p!=p0)Beta(a,b),
where Beta(a,b) is Beta density with parameters a and b and
u is the prior probability of the null hypothesis (prob).
The functions that are generated are useful in examining the prior and
posterior densities of the parameter p, as well as constructing the
Bayes Factor and determining the sample size via an average error based
approach.
The arguments of binom1.2sided are passed to each of the additional
functions upon their creation as default values. That is, if p0 is
set to 0.5 in the call to binom1.2sided, each of the functions returned
will have the defaualt value of 0.5 for p0. If an argument is not
specified in the call to binom1.2sided, then it remains a required
parameter in all functions created.
Value
binom1.2sided returns a list of 4 functions:
logm
Returns a list of three vectors: the log marginal density under
the null hypothesis (logm0), the log marginal density under the
alternative hypothesis (logm1), the log marginal density
(logm). Each are evaluated at the observed data provided. This
function is passed to ssd.binom to calculate required sample
sizes. The function has the following usage:
logm(x, n, p0, prob, a, b)
x: Vector. Number of successes observed, out of n
independent Bernoulli trials.
n: Scalar. Sample size, the number of independent
Bernoulli trials.
Remaining parameters specified above for binom1.1sided.
logbf
Returns a vector: the value of the log Bayes Factor given the observed
data provided and the prior parameters specified. The function has the
following usage:
logbf(x, n, p0, prob, a, b)
For details on the parameters, see above function logm
prior
Returns a vector: the value of the prior density. The function has the
following usage:
prior(p, p0, prob, a, b)
p: Scalar. Quantiles for the prior distribution.
Remaining parameters specified above for binom1.1sided.
post
Returns a vector: the value of the posterior density. The function has the
following usage:
post(p, x, n, p0, prob, a, b)
p: Scalar. Quantiles for the posterior distribution.
x: Scalar. Number of successes observed, out of n
independent Bernoulli trials.
Remaining parameters specified above for binom1.1sided.
############################################################
# Generate the suite of functions for a one-sample binomial
# with a two-sided test. Consider the hypothesis
# H0: p==0.5 vs. H1: p!=0.5
#
# with a uniform prior on p under the alternative and a
# prior probability of the null hypothesis equal to 0.5.
# generate suite
f2 <- binom1.2sided(p0=0.5,prob=0.5,a=1,b=1)
# attach suite
attach(f2)
# plot prior and posterior given x = 25, n = 30
# - don't forget that point mass is not shown on plot
ps <- seq(0.01,0.99,0.01)
p1 <- prior(ps)
p2 <- post(ps,x=25,n=30)
plot(c(p1,p2)~rep(ps,2),type="n",ylab="Density",xlab="p",main="")
lines(p1~ps,lty=1,lwd=2)
lines(p2~ps,lty=2,lwd=2)
# perform sample size calculation with TE bound of 0.25 and weight 0.5
ssd.binom(alpha=0.25,w=0.5,logm=logm)
# detain suite
detach(f2)
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(BAEssd)
Loading required package: mvtnorm
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/BAEssd/binom1.2sided.Rd_%03d_medium.png", width=480, height=480)
> ### Name: binom1.2sided
> ### Title: Binomial Suite: One Sample, Two Sided
> ### Aliases: binom1.2sided
>
> ### ** Examples
>
> ############################################################
> # Generate the suite of functions for a one-sample binomial
> # with a two-sided test. Consider the hypothesis
> # H0: p==0.5 vs. H1: p!=0.5
> #
> # with a uniform prior on p under the alternative and a
> # prior probability of the null hypothesis equal to 0.5.
>
> # generate suite
> f2 <- binom1.2sided(p0=0.5,prob=0.5,a=1,b=1)
Loading the 'binom1.2sided' suite...
This suite contains functions pertaining to a one sample experiment
with a binary outcome. The hypothesis of interest has a two-sided
alternative.
>
> # attach suite
> attach(f2)
>
> # plot prior and posterior given x = 25, n = 30
> # - don't forget that point mass is not shown on plot
> ps <- seq(0.01,0.99,0.01)
> p1 <- prior(ps)
> p2 <- post(ps,x=25,n=30)
>
> plot(c(p1,p2)~rep(ps,2),type="n",ylab="Density",xlab="p",main="")
> lines(p1~ps,lty=1,lwd=2)
> lines(p2~ps,lty=2,lwd=2)
>
> # perform sample size calculation with TE bound of 0.25 and weight 0.5
> ssd.binom(alpha=0.25,w=0.5,logm=logm)
Bayesian Average Error Sample Size Determination
Call: ssd.binom(alpha = 0.25, w = 0.5, logm = logm)
Sample Size: 94
Total Average Error: 0.2494501
Acceptable sample size determined!
>
> # detain suite
> detach(f2)
>
>
>
>
>
> dev.off()
null device
1
>