"So far we have used a uniform prior, i.e. we assumed a priori that all values of fairness $F \\in [0.1]$ are equally probable. How would our inference about the fairness of the coin have changed if we had chosen a different prior? Let's find out!\n",
"So far we have used a uniform prior, i.e. we assumed a priori that all values of fairness $F \\in [0, 1]$ are equally likely. How would our inference about the fairness of the coin have changed if we had chosen a different prior? Let's find out!\n",
"\n",
"Instead of a uniform prior, we could for example have chosen a normal (Gaussian) distribution peaked at $F=0.5$ with a variance of 0.05, which reflects our background information that most coins are fair.\n",
"\n",
...
...
@@ -202,6 +202,8 @@
"metadata": {},
"outputs": [],
"source": [
"# EVALUATE ME!\n",
"\n",
"# Let's see what we get if our true coin is unbiased:\n",
"\n",
"coin.vary_tosses_Gaussian()"
...
...
@@ -213,6 +215,8 @@
"metadata": {},
"outputs": [],
"source": [
"# EVALUATE ME!\n",
"\n",
"# Let's see what happens if our coin is biased heavily towards tails.\n",
"# In our example the true rate of heads is 1 head in 10 tosses.\n",