Statistical inference
Statistical inference is the process of deducing properties of an underlying distribution by analysis of data. Inferential statistical analysis infers properties about a population; this includes testing hypotheses and deriving estimates.
There are three types of inference:
Estimation of the most appropriate single value of a parameter.
Interval estimation to assess what region of parameter values is most consistent with the given data.
Hypothesis testing to decide, between two options, what parameter values are most consistent with the data.
There are mainly three approaches to attack these problems:
Frequentist: Inference is judged based upon performance in repeated sampling.
Bayesian: Inference must be subjective. A prior distribution is chosen for the parameter we seek, and we combine the density of the data prior to obtain a joint distribution. A further application of Bayes Theorem gives us a distribution of the parameter, given the data. To perform computations...
