bayes_goal_func {bayesassurance}

Decision Making using Rate of Correct Classification

Description

Determines the rate of correctly classifying the linear hypothesis as true or false, where the hypothesis test is specified as

H0: u'\beta = c0

vs.

H1: u'\beta = c1

. See vignette for more details.

Usage

bayes_goal_func(n, Xn = NULL, K, pi, sigsq, u, beta_0, beta_1)

Arguments

n

sample size (vector or scalar).

Xn

design matrix that characterizing the data. This is specifically given by the normal linear regression model

yn = Xn\beta + \epsilon,

\epsilon ~ N(0, \sigma^2 I_n),

where I_n is an n by n identity matrix. When set to NULL, an appropriate Xn is automatically generated bayesassurance::gen_Xn(). Note that setting Xn = NULL also enables user to pass in a vector of sample sizes to undergo evaluation as the function will automatically adjust Xn accordingly based on the sample size.

K

The amount of utility associated with H0 being correctly accepted.The null hypothesis is not rejected if the posterior probability of H0 is at least 1/(1+K).

pi

constant corresponding to the prior on parameter \beta such that P(u'\beta_0) = 1 - P(u'\beta_1) = \pi.

sigsq

variance constant of the linear regression model

u

fixed scalar or vector of the same dimension as \beta_0 and \beta_1

beta_0

fixed scalar or vector that null hypothesis is set to

beta_1

fixed scalar or vector that alternative hypothesis is set to

Value

a list of objects corresponding to the rate of classifications

• rc_table: table of sample size and corresponding correct classification rates

• rc_plot: plot of correct classification rates for varying sample sizes

Examples

## Example
n <- seq(100, 1200, 10)
out <- bayesassurance::bayes_goal_func(n, Xn = NULL, K = 1, pi = 0.5,
sigsq = 1, u = 1, beta_0 = 0.5, beta_1 = 0.6)
out$rc_plot