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| Oct 2, 2017 | » | Bernoulli Processes
3 min; updated Sep 5, 2022
Bernoulli ProcessA Bernoulli Process is a sequence of independent \({0, 1}\) - valued random variables \(X_1, X_2, X_3, …\), e.g. \(0, 0, 1, 0, 1, 1\) Suppose you flip a coin repeatedly, and record \(0\) for tails and \(1\) for heads. ... |
| Mar 29, 2020 | » | Prologue
1 min; updated Sep 5, 2022
Fall 1990. Simons had spent 12 years searching for a successful investing formula. In 1989, his net returns were -4.0%. In 1988, he had netted 9.0%. In 1990, he netted 55.0% (77.8% before fees). With Elywn Berlekamp, game theorist professor at UCB, Simons built a model for selecting idea trades based on data. Berlekamp knew their approach was alchemic - no cash flows, interest rate forecasts, product research. Some of the trade recommendations didn’t make sense. ... |
A Bernoulli Process does not mandate that the probability distributions of the \(X_i\) be identical. That is up to the model that we choose. For instance, the Binomial Random Variable assumes \(\mathbb{P}\{X_i = 1\} = p \ \ \forall i\)