What Is the Fourier Transform?

If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform).

This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.

Years ago, I often struggled to choose between Amazon products with high ratings from a few reviews and those with slightly lower ratings but a large volume of reviews. I used the Laplace Rule of Succession to code a browser extension to calculate Laplacian scores for products, helping to make better decisions by balancing high ratings with low review counts. https://greasyfork.org/en/scripts/443773-amazon-ranking-lapl...

Just for reference, in case you find yourself in an optimization under uncertainty situation again: The decision-theoretic right way to do this is generate a bayesian posterior over true ranking given ranking count and a prior on true rankings, add a loss function (it can just be the difference between the true rating of the selected item and the true rating of the non-selected item for simplicity) then choose your option to minimize the expected loss. This produces exactly the correct answer.

Can you please provide an example or link to read more? Seems very interesting.