# 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

# AIC vs. BIC

I often use fit criteria like AIC and BIC to choose between models. I know that they try to balance good fit with parsimony, but beyond that I’m not sure what exactly they mean. What are they really doing? Which … Continue reading AIC vs. BIC

# Double Mersenne number

From Wikipedia, the free encyclopedia Double Mersenne primes Number of known terms 4 Conjectured number of terms 4 First terms 7, 127, 2147483647 Largest known term 170141183460469231731687303715884105727 OEIS index A077586 In mathematics, a double Mersenne number is a Mersenne number … Continue reading Double Mersenne number

# Taylor rule

In economics, a Taylor rule is a reduced form approximation of the responsiveness of the nominal interest rate, as set by the central bank, to changes in inflation, output, or other economic conditions. In particular, the rule describes how, for … Continue reading Taylor rule

# 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