norm2KV.2sided {BAEssd}  R Documentation 
Generates the suite of functions related to the two sample normal experiment with a twosided alternative hypothesis of interest when the variance is known.
norm2KV.2sided(sigma, prob, mu0, tau0, mu1, tau1, mu2, tau2)
sigma 
Scalar. The known standard deviation of the population. 
prob 
Scalar. The prior probability of the null hypothesis. Must be a value between 0 and 1. 
mu0 
Scalar. The mean of the normal prior density on theta under the null
hypothesis. See documentation for 
tau0 
Scalar. The standard deviation of the normal prior density on theta under
the null hypothesis. See documentation for 
mu1 
Scalar. The mean of the normal prior density on mean for sample 1 under the
alternative hypothesis. See documentation for 
tau1 
Scalar. The standard deviation of the normal prior density on mean for
sample 1 under the alternative hypothesis. See documentation for

mu2 
Scalar. The mean of the normal prior density on mean for sample 2 under the
alternative hypothesis. See documentation for 
tau2 
Scalar. The standard deviation of the normal prior density on mean for
sample 2 under the alternative hypothesis. See documentation for

norm2KV.2sided
is used to generate a suite of functions for a
twosample normal experiment with a twosided alternative hypothesis when the
variance is known and the samples are independent. That is, when
X[j] ~ Normal(theta[j],sigma2)
H0: theta[1] == theta[2] vs. H1: theta[1] != theta[2]
using the following prior on theta[1] and theta[2]
pi(theta) = u*I(theta[1]==theta[2])Normal(mu0,tau0^2) + (1u)*I(theta[1]!=theta[2])Normal(mu1,tau1^2)Normal(mu2,tau2^2),
where Normal(mu,tau^2) is Normal density with mean mu
and variance
tau^2
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 theta
, as well as constructing
the Bayes Factor and determining the sample size via an average error based
approach.
The arguments of norm2KV.2sided
are passed to each of the additional
functions upon their creation as default values. That is, if mu0
is
set to 1 in the call to norm2KVV.2sided
, each of the functions returned
will have the defaualt value of 1 for mu0
. If an argument is not
specified in the call to norm2KV.2sided
, then it remains a required
parameter in all functions created.
norm2KV.2sided
returns a list of 5 functions:
logm 
Returns a list of three vectors: the log marginal density under
the null hypothesis ( logm(xbar, n, sigma, prob, mu0, tau0, mu1, tau1, mu2, tau2)

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, n, sigma, prob, mu0, tau0, mu1, tau1, mu2, tau2) For details on the arguments, see 
prior 
Returns a vector. The value of the prior density. The function takes the following usage: prior(theta, prob, mu0, tau0, mu1, tau1, mu2, tau2)

post 
Returns a vector. The value of the posterior density. The function takes the following usage: post(theta, xbar, n, sigma, prob, mu0, tau0, mu1, tau1, mu2, tau2)

ssd.norm2KV.2sided 
Sample size calculations for this particular setup. The function has the following usage: ssd.norm2KV.2sided(alpha, w, sigma, prob, mu0, tau0, mu1, tau1, mu2, tau2, m = 2500, minn = 2, maxn = 1000, all = FALSE) See 
binom1.1sided
,binom1.2sided
,
binom2.1sided
,binom2.2sided
,
norm1KV.1sided
,norm1KV.2sided
,
norm1UV.2sided
,ssd
,BAEssd
############################################################ # Generate the suite of functions for a twosample normal # with a twosided test. Consider the hypothesis # H0: theta[1]==theta[2] vs. H1: theta[1]!=theta[2] # # with a known variance of 3. # generate suite f7 < norm2KV.2sided(sigma=3,prob=0.5,mu0=0,tau0=1,mu1=2,tau1=1,mu2=2,tau2=1) # attach suite attach(f7) # calculate the Bayes Factor for the following observed data # n = 30, xbar[1] = 1, xbar[2] = 1 logbf(xbar=matrix(c(1,1),nrow=1,ncol=2),n=30) # perform sample size calculation with TE bound of 0.5 and weight 0.9 #  due to a need for a Monte Carlo implementation of this procedure, this # problem can take significantly longer to solve, compared to other examples. # Thus, for this example, a large error bound and weight were chosen to # decrease computation time while illustrating the function. ssd.norm2KV.2sided(alpha=0.5,w=0.9) # detain suite detach(f7)