Probability | Chen Xing

Using Stan to do MCMC

What is Stan? Stan is an intuitive, yet sophisticated, probabilistic programming language that provides an interface to a recently proposed extension to Hamiltonian Monte Carlo (HMC), known as No U-Turn Sampler (NUTS).

Apr 20, 2023 1 min read Probability, tutorial

Bayesian Statistics Self-Study Resources

Here are some good resources for Bayesian Statistics self-learning. Textbooks “A Student’s Guide to Bayesian Statistics”: Easy to understand, also with problem and solution available on the author’s personal blog. There are also lots of other useful Bayesian resources on his blog, for example, the Bayesian lecture slides, definitely deserve to check!

Mar 11, 2023 2 min read Probability, tutorial

A Story Behind Maximum Likelihood

TL;DR What are we actually doing on MLE? What is the motivation for the Maximum Likelihood Estimation? In this post, we will go over the story behind the maximum likelihood.

Aug 31, 2022 3 min read Probability, tutorial

Survival Analysis in R

Here is some tutorial notes for “Survival Analysis in R” course. Do patients taking the new drug survive longer than others? How fast do people get a new job after getting unemployed?

Aug 18, 2022 2 min read R, tutorial, PredictiveAnalytics

Beta Distribution — Intuition, Derivation, and Examples

Motivation Model probabilities The Beta distribution is a probability distribution on probabilities. The Beta distribution can be understood as representing a distribution of probabilities, that is, it represents all the

Aug 3, 2022 3 min read Probability, tutorial

Tutorial Notes for Bayesian Statistics

Bayesian Inference Posterior Distribution The intuition behind the posterior distribution: “It is a weighted version of likelihood! … just weighting the likelihood using my prior belief on theta …” Useful

Jul 26, 2022 1 min read Probability, tutorial

Beta distribution as a prior

Introduction The Beta distribution is a useful probability distribution when you want model uncertainty over a parameter bounded between 0 and 1. In this post, we’ll explore how the two parameters of the Beta distribution determine its shape.

Jul 25, 2022 2 min read Probability, R, tutorial

Some Note for Pareto Distribution

Jul 16, 2022 2 min read PredictiveAnalytics, Probability

CLV Prediction in R

Introduction In the previous posts, we talked about the theoretical part of Pareto/NBD model. This time, we will go over the CLV prediction in R. Customer lifetime value (CLV) is

Jul 10, 2022 5 min read PredictiveAnalytics, Probability, R, tutorial

M4 Forecast Competition Summary

Some Notes for M4 Comp.

Dec 10, 2021 3 min read Forecast, R

CLV小总结

引子 2021春节马上到了，2月4日开始放假，2月9号回家。在

Feb 3, 2021 1 min read Probability, PredictiveAnalytics, tutorial

Gamma-Gamma Spend Model

How to predict a customers mean spending in the future?

Jan 30, 2021 5 min read Probability, tutorial, PredictiveAnalytics

Note for Beta Distribution

Why Beta Distribution?

Jan 30, 2021 3 min read Probability, PredictiveAnalytics, tutorial

Note for Gamma Distribution

Motivation for Gamma Function Definition of Gamma Function Gamma Distribution How to remember the Gamma pdf? Gamma & Exponential Connection Motivation for Gamma Function We all know how to compute the factorial of integer.

Jun 30, 2022 3 min read Probability, tutorial

Probability Theory Study Notes

Online Courses Probability Theory and Stochastic Processes (video lecture). Description: These lectures encompass a full-year course in probability theory and stochastic processes, as taught at the University of California, San Diego (as Math 280).

Dec 17, 2020 1 min read Probability, tutorial

Notes for LP Inequality

Here, I summarize some useful LP Inequalities with proofs. Download PDF file here.

Mar 24, 2023 1 min read Probability

Deriving the conditional distributions of a multivariate normal distribution

Overall, the intuition behind the conditional distribution of a bivariate normal is that even though the two variables are correlated in the joint distribution, they can still be treated as independent when you’re looking at the distribution of one variable, given a fixed value of the other variable.

Mar 31, 2017 1 min read Probability, tutorial