Statistical inference

start by specifying some parameter of interest

then select a suitable probability model for the data to be collected

in the simple case there is just 1 parameter to be estimated $$\theta$$

the probability model can be written as $$f(x|\theta)$$; where f is a pdf or pmf.

the choice of probability model is generally guided by the quantity of interest, and of the type of data that can be collected, i.e. continuous/discrete, quantitative, categorical, binary. proportion etc.

Some of the key issues are;

1. making a point estimation for a parameter (and the ‘sampling distribution’ thereof. ) 2. confidence intervals for point estimates 3. hypothesis tests and p-values for paramter estimates 4. quantiles 5. likelihood functions

classical inference point estimation confidence intervals asymptotic theory