A quick post today to let you know what's on my mind this week - I'm still chewing on these ideas, so if you have opinions, feel free to comment below. Will follow up on some of these in future posts.

**Four Quick Takes on the Election Aftermath**

- In 2016, we mocked most election forecasters who said Hillary Clinton would win with 99% probability while agreeing that Nate Silver won the least bad award. Fast forward to 2020. Nate gave Biden a 89% chance of winning while the Economist said 96%. Who's got bragging rights here?
- A former colleague pointed out to me that people mistakenly confuse a high chance of winning with a wide margin of victory. In a simulation model, a 96 percent chance of winning just means that Biden was predicted to win the most electoral votes in 96 percent of the simulated scenarios -- the 96 percent number does not contain information about the margin of victory in any scenario.
- What Trump voters witnessed in Wisconsin, Michigan, Georgia and Pennsylvania was "
**statistical gravity**." - In a Bayesian forecasting model, we get a posterior probability distribution as the output. This is typically explained as the proportion of scenarios in a simulation that end up with a given electoral-vote share. Tail events are rare and capture unusual scenarios - e.g. James Comey in the last days of 2016. Within this framework, how does one express the view that in the forthcoming election, one expects to see a tail event?

**Four Quick Takes on the Coronavirus Vaccine**

We finally got some news yesterday via Pfizer*, which sent out a press release claiming that its vaccine candidate may have "over 90 percent efficacy". They have not published a formal report, so there isn't much we can go on right now. Given the urgent need for a viable vaccine, this is one step in the right direction.

- The claim is based on what happened seven days after the second dose so what the statement meant was that people who got the vaccine was 10 times less likely to be counted as a case within seven days of the second dose than those who got the placebo. This is an impressive early finding. Will "statistical gravity" kick in later?
- People keep misinterpreting vaccine efficacy. The leader of the current White House coronavirus task force tweeted that the Pfizer vaccine "prevented infection in 90% of its volunteers". As I said before, this is not what it means. The case rate for vaccinated volunteers was about 0.1 percent while that for unvaccinated volunteers was 1 percent (99 percent of placebo takers did not get infected in the first 7 days). The former is 90% smaller than than latter.
- I was scrambling to read the Pfizer protocol. I had assumed theirs and Moderna's would be similar since their vaccine candidates belong to the same family. I was surprised to learn that Pfizer was going to measure efficacy based on seven days as I already knew that Moderna doesn't count cases until 14 days after the second dose. So if we had run these two clinical trials side by side, Pfizer's analysis would have been finished before Moderna even started theirs. When both trials report results, we will have a much richer understanding of this type of vaccines.
- People are calling for subgroup analysis. That will take time. This interim analysis is based on a total of about 90 infections. If you break that number down to subgroup level, there's not enough data yet to provide a useful anaswer. Be patient. Allow statistical gravity to work.

* Should give credit to BioNTech which is the company in Germany that develops this vaccine. Pfizer is running the vaccine trial.

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