## Calculate the posterior mean

### 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)