4. Likelihoods

$$p(data|\theta)$$

4.1. What is a Likelihood

Imagine that we flip a coin and record its outcome. The simplest(idealised) model to represent this outcome ignores:

• the angle the coin was thrown at
• its height above the surface
• etc..

Because of our ignorance, our model cannot perfectly predict the behaviour of the coin.

• this uncertainty means that our model is probabilistic rather than deterministic

For

We can use our model to calculate the probability of obtaining two heads in a row: $$Pr(H,H|\theta, Model) = Pr(H|\theta,Model) \times Pr(H|\theta, Model)$$ $$=\theta \times \theta = \theta^2 = (\frac{1}{2})^2 = \frac{1}{4}$$