R: Normal Suite: One Sample, Two Sided, Unknown Variance
norm1UV.2sided
R Documentation
Normal Suite: One Sample, Two Sided, Unknown Variance
Description
Generates the suite of functions related to the one sample normal experiment
with a two-sided alternative hypothesis of interest when the variance is
unknown.
Scalar. The critical value of the mean under the null hypothesis:
theta==theta0.
prob
Scalar. The prior probability of the null hypothesis. Must be a value
between 0 and 1.
mu
Scalar. The mean of the normal prior density on theta under the alternative
hypothesis. See documentation for dnorm.
scale
Scalar. Used to determine the standard deviation for the normal prior
density on theta under the alternative hypothesis. The standard deviation
is equal to scale*sigma. See documentation for dnorm.
shape
Scalar. The shape parameter for the gamma prior on the inverse of the
unknown standard deviation sigma2. See documenation for
dgamma.
rate
Scalar. The rate parameter for the gamma prior on the inverse of the
unknown standard deviation sigma2. See documentation for
dgamma.
Details
norm1UV.2sided is used to generate a suite of functions for a
one-sample normal experiment with a two-sided alternative hypothesis when the
variance is unknown. That is, when
where Normal(mu,tau2) is Normal density with mean mu and variance
tau2 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 parameters theta and sigma2, as well
as constructing the Bayes Factor and determining the sample size via an
average error based approach.
The arguments of norm1UV.2sided are passed to each of the additional
functions upon their creation as default values. That is, if mu is
set to 1 in the call to norm1UV.2sided, each of the functions returned
will have the defaualt value of 1 for mu. If an argument is not
specified in the call to norm1UV.2sided, then it remains a required
parameter in all functions created.
Value
norm1UV.2sided returns a list of 5 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. The
function takes the following usage:
logm(xbar, s2, n, theta0, prob, mu, scale, shape, rate)
xbar: Vector. Observed sample mean from the experiment.
s2: Vector. Observed sample standard deviation from the
experiment.
n: Scalar. Sample size.
Remaining parameters described above for norm1UV.2sided.
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(xbar, s2, n, theta0, prob, mu, scale, shape, rate)
For details on the arguments, see logm above.
prior
Returns a vector. The value of the prior density. The function has the
following usage:
############################################################
# Generate the suite of functions for a one-sample normal
# with a two-sided test. Consider the hypothesis
# H0: theta==0 vs. H1: theta!=0
#
# with a normal prior for theta with prior mean 2 and
# scale of 1/3 for the standard deviation. The prior proability
# of the null hypothesis is set to 0.5. The prior density
# on sigma2 is taken to be InverseGamma with parameters
# 11 and 30 for the shape and rate.
# generate suite
f8 <- norm1UV.2sided(theta0=0,prob=0.5,mu=2,scale=(1/3),shape=11,rate=30)
# attach suite
attach(f8)
# calculate the Bayes Factor for the following observed data
# n = 30, xbar = 1, s2 = 2
logbf(xbar=1,s2=2,n=30)
# perform sample size calculation with TE bound of 0.25 and weight 0.5
ssd.norm1UV.2sided(alpha=0.25,w=0.5)
# detain suite
detach(f8)
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/norm1UV.2sided.Rd_%03d_medium.png", width=480, height=480)
> ### Name: norm1UV.2sided
> ### Title: Normal Suite: One Sample, Two Sided, Unknown Variance
> ### Aliases: norm1UV.2sided
>
> ### ** Examples
>
> ############################################################
> # Generate the suite of functions for a one-sample normal
> # with a two-sided test. Consider the hypothesis
> # H0: theta==0 vs. H1: theta!=0
> #
> # with a normal prior for theta with prior mean 2 and
> # scale of 1/3 for the standard deviation. The prior proability
> # of the null hypothesis is set to 0.5. The prior density
> # on sigma2 is taken to be InverseGamma with parameters
> # 11 and 30 for the shape and rate.
>
> # generate suite
> f8 <- norm1UV.2sided(theta0=0,prob=0.5,mu=2,scale=(1/3),shape=11,rate=30)
Loading the 'norm1UV.2sided' suite...
This suite contains functions pertaining to one-sample experiment
involving a normally distributed response with unknown variance.
The hypothesis of interest has a two-sided alternative.
>
> # attach suite
> attach(f8)
>
> # calculate the Bayes Factor for the following observed data
> # n = 30, xbar = 1, s2 = 2
> logbf(xbar=1,s2=2,n=30)
[1] 6.775567
>
> # perform sample size calculation with TE bound of 0.25 and weight 0.5
> ssd.norm1UV.2sided(alpha=0.25,w=0.5)
Bayesian Average Error Sample Size Determination
Call: ssd.norm1UV.2sided(alpha = 0.25, w = 0.5)
Sample Size: 5
Total Average Error: 0.2316
Acceptable sample size determined!
>
> # detain suite
> detach(f8)
>
>
>
>
>
> dev.off()
null device
1
>