Probability (Chance)

A random process is ergodic if all of its statistics can be determined from a sample function of the process. That is, the ensemble averages equal the corresponding time averages with probability one. Role of Ergodicity in Human Inference A newspaper has previously printed some inaccurate information, therefore, the newspaper is going to publish inaccurate information in the future. Fair; ensemble of published articles is more or less ergodic. More crimes are committed by black persons than by white persons, therefore each individual black person is not to be trusted?...

Formal Software Design Alloy is an open-source language and analyzer for software modeling. An Alloy model is a collection of constraints that describe a set of structures, e.g. all possible security configurations of a web application. Alloy’s tool, the Alloy Analyzer is a solver that takes the constraints of a model and finds structures that satisfy them. 📑 The Alloy Analyzer leverages a SAT solver, and this precludes Alloy from analyzing optimization problems....

The Psychology of Money. Morgan Housel. www.collaborativefund.com . Jun 1, 2018. People underestimate the role played by luck. Given \(N\) investors, if \(N\) is large enough, a couple of them will luck their way into billions. But every investor seems to be doing due diligence. The successful ones will be more convinced that their methods really work. Considering the amount of investing books out there, we should be seeing a lot more Warren Buffets in the world....

Debugging 101 Definition? Debugging involves inspecting a program’s internal state. printf Debugging and Logging In printf debugging, one adds print statements and keeps iterating until enough information has been extracted. Using logging has several advantages over printf debugging: varying logging destinations (e.g. standard output, files, sockets, remote servers, etc.); severity levels (e.g. INFO, DEBUG, WARN, ERROR, &c) that support filtering of output; color-coding for readability. Terminals have varying levels of color support: plain color; ANSI escape codes (16 color codes with bold/italic and background); 256 color palette; 24-bit truecolor (“888” colors, aka 16 million, e....

Behavioralists believe that: Investors are not rational in present and future valuations of securities. There are substantial barriers to efficient arbitrage. The Irrational Behavior of Individual Investors Overconfidence People tend to be overconfident, e.g. in a survey, 94% of male respondents believed that their athleticism was above average. Hindsight bias makes the world seem predictable. Investors might think they can beat the market. The tendency of “growth” stocks to underperform “value” stocks shows how overoptimistic growth forecasts are....

Allows us to weight by review population size. Let \(n_i\) be the number of reviews that item \(i\) gets, and let \(r_i\) be the naive average rating of item \(i\) Let \(N\) be the total number of reviews across brands, i.e. \(N = \sum_{i} n_i \) Let \(R\) be the average rating over all items across brands, i.e. \(R = \frac{1}{N} \sum_{i} n_i r_i \)...

Bernoulli Processes; The Binomial Random Variable; Conditional Probability; The Bayes Formula; Probability and Stochastic Systems [ORF 309]; What is Ergodicity?;

The Proper Use of Humility Confessing your fallibility but doing nothing about it braggery, not humility. Designing fail-safe machinery is good humility. Dismissing evidence for evolution because we can’t really know for sure that evolution is correct is misplaced humility. The Third Alternative Sometimes we justify questionable policy by claiming its absence is undesirable, e.g. believing in Santa makes children behave nicely, and therefore Santa-ism is the best of all possible alternatives....