A to Z Bayes - Part 1: The Basics

Let's ExperimentURL copied

Step 3: Figuring out the probability of seeing the data under each hypothesis. (Likelihood)URL copied

Once the hypotheses are set, we compute the probability of seeing our data in each of the hypothesis. This is a realitively easy and straight forward step. In the case of an n sided fair dice the probability of seeing a number k show up is 1/n irrespective of k as long as k <= n and 0 if k > n.

\[ P(k|N-sidedDice) = \begin{cases} \ \frac{1}{n} & \text{if}\ k \leq n \\ \ 0 & \text{if}\ k > n \end{cases} \] Hence the probability of a dice showing the above 9 data points is $$\frac{1}{n}$$ for all $$n \geq 7$$. This renders 2, 3, 4, 5 and 6 faced dices to have zero likelihood since probabilty of a 7 occuring in these cases is zero. Thus we have a likelihood for each hypothesis.

Likelihoods of my hypotheses
Probabilities of 2-6 are zero.

2	✦
3	✦ > Let's Experiment
4	✦ > Let's Experiment > Step 1: Figuring out the hypothesis space
5	✦ > Let's Experiment > Step 2: Figuring out the probabilities of hypotheses (Priors)
6	✦ > Let's Experiment > Step 3: Figuring out the probability of seeing the data under each hypothesis. (Likelihood)
7	✦ > Let's Experiment > Step 4: Multiply Priors and Likelihoods (Posterior)
8	✦ > Let's Experiment > Step 5: Profit $$