Bayesian Statistics

The Frequentist Approach

• Observe data.
• Assume the data were generated randomly, e.g. by nature, by designing a survey, etc.
• Make assumptions on the generating process, e.g. i.i.d., Gaussian, etc.
• Associate the generating process to some object of interest, e.g. a parameter, a density, etc.
• Assuming that the object is unknown but fixed, try to find it, e.g. estimate it, test a hypothesis about it, etc.

The Bayesian Approach

• Observe data.
• Assume the data are generated randomly by some process.
• Under some assumptions, e.g. parametric distribution, associate the process with some fixed object.
• We have a prior belief about the object.
• Using the data, we want to update that belief into a posterior belief.