Class 1
Statistical procedures as robots: input/output. How to apply them to real complex problems is non-trivial. May be used wrongly. They are blind to creator's intent. Non binary: in the sense that a model is not true/false. "All models are wrong, but some of them are useful"
Hipothesis vs Process Models vs Statistical models
Scientific models are intrisically causal/generative on how things happen. Statistical models care about association, not causation. Same statistical model may be associated with more than one process model, each belonging to a different hipothesis.
When running examples:
- Understand theoretical estimand
- Scientific causal model
- User 1 and 2 to build statistical model
- Simulate form 2 to validate 3 yields 1
- Analyze real data
Real problem: connect causal models to statistical procedures.
"No causes in, no causes on": we can't infer causes from data.
Design an study <> causal inference.
Causation: is prediction of intervention or inputation of missing values (two ways of thinking about it).
Correlation doesn't imply causation, causation doesn't imply correlation.
Class 2
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Posterior distribution encodes uncertainty
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Prior predictive encodes a causal model
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Posterior predictive likewise.
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Fiting mechanism is part of the model.
Chapter 3:
Compatibility interval: two parameters whose interval contains certain amount of probability mass Percentile intervals: assign equal probability mass to each tail Highest posterior density interval.
Usages of simulations: model design, research design, software testing, model checking and forecasting.