1. What have you learned? What did we miss?
Amazing! You are now at the end of this course on the fundamentals of Bayesian data analysis using R. And we’ve come far!
2. We have covered
We have seen Bayesian modeling as a way of quantifying uncertainty using probability, and we have covered what is needed to do Bayesian inference. You need
3. We have covered
data,
4. We have covered
a Bayesian model that consists of a generative model and prior probability distributions over parameters and unknowns, and finally you need
5. We have covered
a computational method to fit the model.
6. We have covered
We looked at two basic computational methods: Rejection sampling, where you directly sample from the generative model and then condition on the data by filtering away all samples that don’t match. And grid approximation, where you directly use Bayes theorem to calculate the probability over a grid of parameter combinations. But while we never explained it, we also used a Markov chain Monte Carlo method under the hood when we tried out that BEST model. We mainly looked at two generative models:
7. We have covered
The binomial distribution and the normal distribution. But, we briefly used the Poisson distribution and touched on the t-distribution in the last exercise.
8. We have covered
We learned how to work with samples representing the posterior probability distribution, and how to calculate new interesting measures, like the probability that zombies have an IQ over 60. Useful stuff. But this was a quick introduction, and there are many many
9. Things we didn't cover
things we didn’t cover. We only looked at rather simple Bayesian models, and you might be left with the impression that Bayes is for these simple situations. But a Bayesian approach can be used all over machine learning and statistics, and there are Bayesian versions of things like time series models and deep learning. A great strength with Bayes is that you have great flexibility when setting prior distributions. But to be honest, we didn’t talk much about how to decide what priors and models to use. There is a lot to learn there, but there are also many good default priors and models you can use, like, for example, the BEST model. We didn’t contrast Bayesian statistics with classical statistics, which is so often done. One reason for this is that I don’t think it is that useful, it’s two different approaches, and better to learn the good things with both of them. We didn’t look at more advanced computational methods, like the many Markov chain Monte Carlo algorithms there are, and we didn’t look at the many good computational tools and packages that now exist, like Stan and JAGS. And to explore one of these tools would be a good next step after this course.
10. Things we didn't cover
Aaaand we didn’t really explain how Allan Turing used Bayesian statistics to break the German Enigma code. But he really did use Bayes! And while it’s not too complicated to explain, it does require you to learn all the specific details of how the Enigma machine worked. Maybe next time!
11. Go explore Bayes!
Bayesian data analysis is increasingly being used all over data science and machine learning, and even if we just scratched the surface, you should now have the necessary knowledge to explore this exciting topic further.
12. Bye and thanks!
I’m Rasmus Bååth, Data Scientist, and Bayesian enthusiast, and thank you for staying with me to the end. Bye!
13. Let's practice!