Jan

26

First, Prof. Tau on the Philippines Grand Lotto.

An unusual lottery result made the news recently: on October 1, 2022, the PCSO Grand Lotto in the Philippines, which draws six numbers from {1} to {55} at random, managed to draw the numbers {9, 18, 27, 36, 45, 54} (though the balls were actually drawn in the order {9, 45,36, 27, 18, 54}). In other words, they drew exactly six multiples of nine from {1} to {55}.

Then, Prof. Tau on Bayes.

The Bayesian updating makes me think of predictions for the S&P for 2024 and how one would have updated these as the year progressed.

Asindu Drileba wonders:

Suppose the S&P can only return two values +1% and -1%. If it has returned +1% for day one and -1% for day two. The dataset would day the s&p returns are +1%, -1% so:

- Probability of going up (+1%) is 0.5
- Probability of going down (-1%) is also 0.5

Given the 2 day dataset of +1%, -1%. Now, suppose it is day 3 and the market goes up (+1%). How do we use Bayesian techniques to update the probability? In the ordinary way. The dataset would be (+1%, -1%, +1%). So update probability:

- Probability of going up, 2/3 (0.666..)
- Probability of going down, 1/3 (0.3)

I am not saying this is how Bayesian updates work. I am trying to ask members how it work's given the above toy dataset. There is a related video by Julia Galef called Bayesian thinking.

Khilav Majmudar writes:

I've learnt more about Bayesian probability from these two Tao posts than anything else I've encountered online. Thank you.

George McPherson responds:

I think this falls into the category of the law of small numbers. Relatedly, I just finished reading The Hot Hand by Ben Cohen and enjoyed it very much.


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