Prior Probability

About of prior probabilities

Prior probabilities represent the proportion of observations in each group before observing new data.

For $k$ groups $G_1,G_2,\dots ,G_k$:

• $p_i$: Proportion of observations in group $G_i$, calculated as:
  $p_i=\frac{n_i}{N}$

Variables:

• $n_i$: Number of observations in group $G_i$.
• $N$: Total number of observations across all groups, $N=n_1+n_2+\cdots +n_k$.
• $p_i$: Satisfies ${\sum }_{i=1}^k{p}_i=1$.

Example:

Suppose 70% of freshmen at a university graduate ($G_1$) and 30% do not ($G_2$)

Then:

• $p_1=0.7$
• $p_2=1-p_1=0.3$