Bayesian Statistic

Daniele Scanzi & Dylan Taylor

Statistical Rethinking

If you:

  • Know a bit about regression but are uneasy about statistical modelling
  • Feel like p-values are kind of a strange tool
  • Have heard about Bayesian alternatives but are unsure where to start

Statistical Rethinking

  • Hands-on: coding and practice first rather than mathematical theory
  • Code in R using rethinking package or…
  • … tidyverse + brm explained here

Exercises

Exercises

EASY (E)

The Bayesian statistician Bruno de Finetti (1906–1985) began his 1973 book on probability theory with the declaration: “PROBABILITY DOES NOT EXIST.” The capitals appeared in the original, so I imagine de Finetti wanted us to shout this statement. What he meant is that probability is a device for describing uncertainty from the perspective of an observer with limited knowledge; it has no objective reality. Discuss the globe tossing example from the chapter, in light of this statement. What does it mean to say “the probability of water is 0.7”? (p.46)

MEDIUM (M)

Recall the globe tossing model from the chapter. Compute and plot the grid approximate posterior distribution for each of the following sets of observations. In each case, assume a uniform prior for p. (p.47)

HARD (H)

Use rbinom to simulate 10,000 replicates of 200 births. You should end up with 10,000 numbers, each one a count of boys out of 200 births. Compare the distribution of predicted numbers of boys to the actual count in the data (111 boys out of 200 births). There are many good ways to visualize the simulations, but the dens command (part of the rethinking package) is probably the easiest way in this case. Does it look like the model fits the data well? That is, does the distribution of predictions include the actual observation as a central, likely outcome? (p.70)

Discussion

Is NHST falsificationist? Null hypothesis significance testing, NHST, is often identified with the falsificationist, or Popperian, philosophy of science. However, usually NHST is used to falsify a null hypothesis, not the actual research hypothesis. So the falsification is being done to something other than the explanatory model. This seems the reverse from Karl Popper’s philosophy.

[…] So not only is there “Bayesian” and “frequentist” probability, but there are different versions of Bayesian probability even,relying upon different arguments to justify the approach.[…] How can different interpretations of probability theory thrive?

If we use different statistical approaches, are we doing doing the same “science”?

What is the probability of obtaining head with an unfair coin? Assume you have never seen this coin before and you can throw it only once.

What is the difference between models and hypothesis?

First lecture

Planning

What do you want to focus on?

  • Videos
  • Exercises
  • Tutorials for specific topics
  • Coding skills
Think: What would you like to learn and achieve?

Communication

  • Primary: Slack channel
  • Reminders: emails
  • Got feedback or ideas? Email us!