mean.Bolstad: Calculate the posterior mean

In Bolstad: Functions for Elementary Bayesian Inference

Description

Calculate the posterior mean of an object of class Bolstad. If the object has a member mean then it will return this value otherwise it will calculate \int_{-∞}^{+∞}θ f(θ|x).dθ using linear interpolation to approximate the density function and numerical integration where θ is the variable for which we want to do Bayesian inference, and x is the data.

Usage

## S3 method for class 'Bolstad'
mean(x, ...)

Arguments

x	An object of class Bolstad
...	Any other arguments. This parameter is currently ignored but it could be useful in the future to deal with problematic data.

Value

The posterior mean of the variable of inference given the data.

Examples

# The useful of this method is really highlighted when we have a general 
# continuous prior. In this example we are interested in the posterior mean of 
# an normal mean. Our prior is triangular over [-3, 3]
set.seed(123)
x = rnorm(20, -0.5, 1)
mu = seq(-3, 3, by = 0.001)
mu.prior = rep(0, length(mu))
mu.prior[mu <= 0] = 1 / 3 + mu[mu <= 0] / 9
mu.prior[mu > 0] = 1 / 3 - mu[mu > 0] / 9
results = normgcp(x, 1, density = "user", mu = mu, mu.prior = mu.prior)
mean(results)

Example output

Attaching package: 'Bolstad'

The following objects are masked from 'package:stats':

    IQR, sd, var

Known standard deviation :1
[1] -0.3414455

Bolstad documentation built on Jan. 8, 2021, 2:03 a.m.