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.

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

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