Probability | Chen Xing

Motivation Semiparametric models contain both a finite-dimensional parameter of interest (

θ

) and an infinite-dimensional nuisance parameter (

η

). The goal is to estimate

θ

as efficiently as possible while filtering out the impact of

η

.

Feb 5, 2025 2 min read Probability, econometrics, causal inference

From Donsker Classes to Neyman Orthogonality: The Power of DML

Motivation & Intuition In classical semiparametric theory, we want to estimate a low‑dimensional target parameter (say, a treatment effect) while controlling for high‑dimensional nuisance functions (like nonparametric regressions). However, in order to use the central limit theorem (CLT) and to characterize the asymptotic behavior, classical results require that the space of functions in which these nuisance functions lie is “small” in a technical sense.

Feb 20, 2025 2 min read causal inference, econometrics, Probability

Learning Resource: Causal Machine Learning with DoubleML

Here are some study notes for Double Machine Learning in causal inference. Introduction Double machine learning, as introduced by (Chernozhukov et al. 2018), is a methodology used in causal inference, which is particularly useful when dealing with high-dimensional data.

Nov 21, 2023 3 min read tutorial, Probability, causal inference, ML

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

Probabilistic Models for Computing Customer-Centric Metrics

Introduction In this post, I will summarize the common statistical methods to describe and predict customers’ purchase behavior in non-contractual settings. It fits probabilistic models to historical transaction records for computing customer-centric metrics of managerial interest.

Aug 27, 2022 3 min read Probability, PredictiveAnalytics, tutorial

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

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

Theory Behind Pareto/NBD Part 1

Theoretical proof behind PNBD Modeling Part 1.

Jan 31, 2021 4 min read PredictiveAnalytics, Probability, tutorial

Theory Behond Pareto/NBD Part 2

Theoretical proof behind PNBD Modeling Part 2.

Jan 31, 2021 4 min read PredictiveAnalytics, Probability, 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