 He who knows not and knows not he knows not: he is a fool - shun him. He who knows not and knows he knows not: he is simple - teach him. He who knows and knows not he knows: he is asleep - wake him. He who knows and knows he knows: he is wise - follow him.

# Normal Likelihood with Normal Prior

Often, it is useful to simulate the Bayesian updating process, to study how the posterior changes with the sample moments of $x$ . Therefore I have written a R function, which takes a vector of normally distributed data $x$ , a prior (the hyper-parameters) mean $\mu$ and variance $\tau^2$ , and then calculates the posterior.

# Examples

## Example 1: Basic usage

For instance, suppose 10 observations are coming from $N(\theta,100)$ . Assume that the prior on $\theta$ is $N(20,20)$ . Using the numerical example in the R code below, the posterior is $N(1.322028, 1.086328)$. These three densities are shown in Figure 1. # Example 2: Sample Size Simulation

You can also easily make a sample size Monte Carlo simulation ## Example 3: Recursive Bayesian Updating

Simulate the updating process for recursive Bayesian updating 