Difference between independence and correlation – my understanding

Basically, everyone (or almost everyone) knows that independence and correlation equal to zero are different concepts. More importantly, they don’t have two-way relations, which is if you know two random variables X, Y have zero correlation, you cannot imply that … Continue reading Difference between independence and correlation – my understanding

The Poisson and Exponential Distribution

  (1) Poisson and Exponential Distribution have connections. (2) Poisson distribution is used to describe the number of occurrences per unit of time. (3) While exponential distribution can describe the length of time between each occurrence. (4) Therefore, follow this intuition, if you set Poisson to capture the probability of zero occurrence, we should find the bridge to get the same result from the exponential distribution. Continue reading The Poisson and Exponential Distribution

How a Kalman filter works, in pictures

This is a post from http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/ which I believe it is the most intuitive explanation of Kalman filter. I have to tell you about the Kalman filter, because what it does is pretty damn amazing. Surprisingly few software engineers and scientists seem to know about it, and that makes me sad because it is such a general and powerful tool for combining information in the presence of uncertainty. At times its ability to extract accurate information seems almost magical— and if it sounds like I’m talking this up too much, then take a look at this previously posted videowhere I demonstrate … Continue reading How a Kalman filter works, in pictures

Bootstrapping and Monte Carlo Simulation

Bootstrapping is resampling from known samples, Monte Carlo is trying to generate data depend on some parameters. We have samples, for example, 3, 2, 1, 5, 6, but sample size is too small, so we resample from this sample set for 10000 times, then the new sample set is more robust to represent something, this called bootstrapping.so boostrapping is based on unknown distribution, and Monte Carlo based on known distribution. The tie between the bootstrap and Monte Carlo simulation of a statistic is obvious: Both are based on repetitive sampling and then direct examination of the results. A big difference … Continue reading Bootstrapping and Monte Carlo Simulation