
1. Parameter - unobserved quantity describing a statistical population
2. Observed variable - measurements taken by researcher in order to make predictions about a parameter

Parameters and observed variables

A prior is the probability distribution of a parameter that reflects analyst’s personal beliefs.

Prior

- Observed variables given a distribution function likelihood 
- Unobserved variables or parameters 

University of Michigan - Ann Arbor

Steps to designing a simple Bayesian model:

1. Data story: Motivate the model by narrating how the data might arise.
2. Update: Educate your model by feeding it the data.
3. Evaluate: All statistical models require supervision, leading to model revision. 

Designing a simple Bayesian model 

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd ed.). Chapman and Hall/CRC.

Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd edition)

The data story is the underlying reality of the data. Particularly, it focuses on the sampling process: the probability of each outcome (p) and the independence or dependence of events. 


In the example where a globe is tossed and where (land or water) the index finger lands is recorded:

1. True probability of water covering the globe is p
2. True probability. of land covering the globe is 1-p
3. Each event is considered independent of each other

Data Story 

Bayesian updating is the process of going from a prior probability to a future one based on the new data presented

Bayesian Updating

When reviewing model and its underlying assumptions, two principles should be kept in mind:

1. An accurate model is not necessarily a good one.
2. Critiquing and supervising model is necessary to arrive at a better model.


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