Interval Estimation

Suppose that we have 100 coin tosses and observe 60 successes.

MLE:

where:

But what about a reasonable range?

We have: , independent

We are interested in: . lies within this interval at same level (???) of likelihood our confidence.

likelihood interval means

Likelihood Interval

Definition

A likelihood interval is

(see set builder notation)

say we want , then we want , a interval likelihood.

Any value in is at a minimum of the likelihood of the MLE. "50% todo"

Plausibility

Definition

  1. : very plausible
  2. : plausible
  3. : implausible
  4. : very implausible

What does a 50% likelihood interval mean? It's hard to communicate that.

[!example]
A coin is tossed 200 times with . Suppose that we observe successes. Find the 10% likelihood interval for .

todo wtf