Unfortunately, our grant has run out, so we can only afford to sample 10 people:

1. Pick an estimator (such as sample proportion) of the probability
2. Generate a point estimate of :

3. Use an approximation of the sampling distribution to quantify uncertainty:

4. Generate a confidence interval (e.g. for standard 95% CI)

1. Pick a prior (such as a uniform distribution) for the probability

1. Pick a prior (such as a uniform distribution) for the probability
2. Update prior with data (one at a time or all at once)

1. Pick a prior (such as a uniform distribution) for the probability
2. Update prior with data (one at a time or all at once)

1. Pick a prior (such as a uniform distribution) for the probability
2. Update prior with data (one at a time or all at once)

1. Pick a prior (such as a uniform distribution) for the probability
2. Update prior with data (one at a time or all at once)

1. Pick a prior (such as a uniform distribution) for the probability
2. Update prior with data (one at a time or all at once)

1. Pick a prior (such as a uniform distribution) for the probability
2. Update prior with data (one at a time or all at once)

1. Pick a prior (such as a uniform distribution) for the probability
2. Update prior with data (one at a time or all at once)
3. The posterior distribution describes the relative posterior probability for different values of

Posterior probability:

The posterior probability is our answer. It tells us everything we know about the probability of unemployment rate () given what we’ve learned from our sample ().

Prior probability:

The prior probability is everything we claim to know about the probability of unemployment () before we ask anybody about their employment. It is the unconditional distribution of .

Evidence:

The evidence is just the average probability of seeing our sample across all possible values of (normalizing the posterior). It is often the hardest part of a posterior to calculate.

Fortunately we can almost always ignore it.

Likelihood:

The likelihood is where our model lives.

In reality we know and want to learn about :

In our model we know and want to describe :

Binomial distribution

The probability of getting ‘successes’ in trials if the probability of success is :

Likelihood:

The likelihood is where our model lives.
In this case, a binomial distribution is a good choice. Given a particular probabily of unemployment (and a sample size ), tells us how likely our sample is.