Skip to content
Merged
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
5 changes: 3 additions & 2 deletions Chapter6_Priorities/Chapter6.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -141,8 +141,9 @@
"A very simple example follows: suppose we wish to estimate the parameter $\\mu$ of a Normal distribution, with $\\sigma = 5$. Since $\\mu$ could range over the whole real line, we can use a Normal distribution as a prior for $\\mu$. How to select the prior's hyperparameters, denoted ($\\mu_p, \\sigma_p^2$)? The $\\sigma_p^2$ parameter can be chosen to reflect the uncertainty we have. For $\\mu_p$, we have two options:\n",
"\n",
"1. Empirical Bayes suggests using the empirical sample mean, which will center the prior around the observed empirical mean:\n",
"\n",
"$$ \\mu_p = \\frac{1}{N} \\sum_{i=0}^N X_i $$\n",
"$$\n",
"\\mu_p = \\frac{1}{N} \\sum_{i=0}^N X_i \n",
"$$\n",
"\n",
"2. Traditional Bayesian inference suggests using prior knowledge, or a more objective prior (zero mean and fat standard deviation).\n",
"\n",
Expand Down