## Georgia on my mind

Posted in Books, Kids, Statistics, Travel with tags , , , , , , , , on May 12, 2021 by xi'an

The riddle of this week was inspired by the latest presidential elections when one State after another flipped the winner from Trump to Biden. Incl. Georgia.

On election night, the results of the 80 percent who voted on Election Day are reported out. Over the next several days, the remaining 20 percent of the votes are then tallied. What is the probability that the candidate who had fewer votes tallied on election night ultimately wins the race?

Assuming many votes, perfect balance between both candidates (p=½), and homogeneity between early and late ballots, the question boils down to the probability of a sum of two normals, X+Y, ending up being of the opposite sign from X, when the variances of X and Y are α and 1-α. Which writes as the expectation

$2 \mathbb{E}_\alpha[\Phi(-X/\sqrt{1-\alpha})]$

equal to

$\frac{2}{2\pi}\left(\frac{\pi}{2} + \arctan\{\sqrt{\alpha/(1-\alpha)|}\}\right)$

which returns a probability of about 0.14 when α=0.8. When looking at the actual data for Georgia, out of 5 million voters, at some point 235,000 ballots remained to be counted with Trump on the lead. This means an α about 0.05 and implies a probability of 7% (not accounting for the fact that the remaining mail-in-ballots were more favourable to Biden.)

## Xs Xplain’d

Posted in Statistics with tags , , , , , , , , , , on January 31, 2021 by xi'an

David Spiegelhalter is starting a column in The Guardian about COVID-19, the first installment being about excess death statistics. Arguing rightly that it is “fairer to look at what has happened to the total number of deaths”, since this is an objective quantity (in countries with trustworthy death statistics). The discussion on how many of the excess deaths can be attributed to the pandemic is somewhat confusing, though, as little can be said with enough confidence, between the positive impact (flu deaths have plummeted, 30% less traffic deaths in France, &tc.) and the negative impact (stress, harsher economic or social conditions, &tc.) A worthy warning: the deficit in “other” deaths during the second wave is partly due to the extra deaths during the first wave, esp. for fragile and elderly persons.

## it was the season of Light, it was the season of Darkness

Posted in Kids, Travel with tags , , , , , , , , , on January 30, 2021 by xi'an

## it was the best of times, it was the worst of times

Posted in Books, pictures, Travel with tags , , , , , , , , , , , , , , , on January 7, 2021 by xi'an

## solidarność z Polkami

Posted in Statistics with tags , , , , , , , , , , on October 30, 2020 by xi'an