I’m reading BDA3 right now, and I’m on chapter 6. You described it well. It takes a lot of thinking to get through, but is very comprehensive. I like how it’s explicitly not just a theory textbook. They demonstrate each major point by describing a real-world problem (measuring cancer rates across populations, comparing test-prep effectiveness), and attacking it with multiple models (usually frequentist to show limitations and then their Bayesian model more thoroughly. It has a focus on learning the tools well enough to apply them to real-world problems.
I plan to start skimming soon. It seems the first two sections are pedagogical, and the remainder covers techniques which I would like to know about but don’t need in detail.
Edit: One example I really enjoyed, and which felt very relevant to today, was on estimating lung-cancer hotspots in America. It broke the country down by county, and first displayed a map of the USA with counties in the top 10% of lung-cancer rates. Much of the highlighted region was in the rural southwest and Rocky mountain region. It asked, what do you think makes these regions have such high rates? It then showed another map, this one of counties in the bottom 10% of lung-cancer rates, and the map focused on the same regions!
Turns out, this was mostly the result of these regions containing many low-population counties, which meant rare-event sampling could skew high very easily, just by chance. If the base rate is 5 per 10,000, and you have 2 cases in a county with 1,000 people, you look like a superfund site. But sample the next year and you might find 0 cases: a county full of young health-freaks.
If you model lung-cancer rates as a hierarchical model with a distribution for county cancer-rates, and each county as being sampled from this, and then sampling cancer events from it’s specific rate, then you can get a Bayes-adjusted incidence rate for each county which will regress small counties to the mean.
This made me read Covid charts which showed hot-spot counties much differently. I noticed that the counties they list are frequently small. Right now, all the counties on the NYTimes list, for example have less than 20,000 people in them, which is, I believe, in the bottom 25% of counties by size roughly.
I loved that example as well, I have heard it elsewhere described as “The law of small numbers”, where small subsets have higher variance and therefore more frequent extreme outcomes. I think it’s particularly good as the most important part of the Bayesian paragdime is the focus on uncertainty.
The appendix on HMC is also a very good supplement to gain a deeper understanding of the algorithm after having read the description in another book first.
I’m reading BDA3 right now, and I’m on chapter 6. You described it well. It takes a lot of thinking to get through, but is very comprehensive. I like how it’s explicitly not just a theory textbook. They demonstrate each major point by describing a real-world problem (measuring cancer rates across populations, comparing test-prep effectiveness), and attacking it with multiple models (usually frequentist to show limitations and then their Bayesian model more thoroughly. It has a focus on learning the tools well enough to apply them to real-world problems.
I plan to start skimming soon. It seems the first two sections are pedagogical, and the remainder covers techniques which I would like to know about but don’t need in detail.
Edit: One example I really enjoyed, and which felt very relevant to today, was on estimating lung-cancer hotspots in America. It broke the country down by county, and first displayed a map of the USA with counties in the top 10% of lung-cancer rates. Much of the highlighted region was in the rural southwest and Rocky mountain region. It asked, what do you think makes these regions have such high rates? It then showed another map, this one of counties in the bottom 10% of lung-cancer rates, and the map focused on the same regions!
Turns out, this was mostly the result of these regions containing many low-population counties, which meant rare-event sampling could skew high very easily, just by chance. If the base rate is 5 per 10,000, and you have 2 cases in a county with 1,000 people, you look like a superfund site. But sample the next year and you might find 0 cases: a county full of young health-freaks.
If you model lung-cancer rates as a hierarchical model with a distribution for county cancer-rates, and each county as being sampled from this, and then sampling cancer events from it’s specific rate, then you can get a Bayes-adjusted incidence rate for each county which will regress small counties to the mean.
This made me read Covid charts which showed hot-spot counties much differently. I noticed that the counties they list are frequently small. Right now, all the counties on the NYTimes list, for example have less than 20,000 people in them, which is, I believe, in the bottom 25% of counties by size roughly.
I loved that example as well, I have heard it elsewhere described as “The law of small numbers”, where small subsets have higher variance and therefore more frequent extreme outcomes. I think it’s particularly good as the most important part of the Bayesian paragdime is the focus on uncertainty.
The appendix on HMC is also a very good supplement to gain a deeper understanding of the algorithm after having read the description in another book first.