There is more than Monte Carlo when talking about randomized algorithms. It is not uncommon to see the expresions "Monte Carlo Approach" and "randomized approach" used interchangeably. More than once you start reading a paper or listening to a presentation, in which the words "Monte Carlo" appear on the keywords and even on the title, … Continue reading On types of randomized algorithms
Remember your friend from our very first post? . Well, I am sorry to say that he never really reached French Guyana. He ended up in Carcass, one of the Malvinas/Falkland islands. And his boat was (peacefully) captured by overly friendly pirate penguins. Now he spends his days counting penguins and sheep. He did keep a coin and … Continue reading Basic Statistics with Sympathy – Part 4: Building arbitrary RNGs in Sympathy
Or "Martingales are awesome!". In a previous post, we talked about bounds for the deviation of a random variable from its expectation that built upon Martingales, useful for cases in which the random variables cannot be modeled as sums of independent random variables (or in the case in which we do not know if they are … Continue reading Studying random variables with Doob-Martingales
In the previous post we looked at Chebyshev's, Markov's and Chernoff's expressions for bounding (under certain conditions) the divergence of a random variable from its expectation. Particularly, we saw that the Chernoff bound was a tighter bound for the expectation, as long as your random variable was modeled as sum of independent Poisson trials. In … Continue reading Useful rules of thumb for bounding random variables (Part 2)
This post is my interpretation of Chapter 10 of the book "Advanced Data Analysis from an Elementary point of view". It is one of the most interesting reads I have found in quite some time (together with this). Actually, the original title for the post was "Book Chapter review: Using non-parametric models to test parametric model … Continue reading Book Chapter Review: If your model is mis-specified, are you better off?
Allow me to introduce you to your new best friend from Sympathy 1.2.x: The improved calculator node. The node takes a list of tables, from which you can establish a new signal with the output for a calculation. There is already a menu with the most popular calculations and a list of signals from the … Continue reading Basic Statistics with Sympathy – Part 2: Plotting and using the Calculator Node for common functions.
Statistics and expectations: When your data is incomplete, somewhat corrupted or you simply need to use a black-box tool, you can help yourself by using statistics...