# How much saving do you need in the end? zero?

Dec 30, 2022       4 mins     Tag: zombie
I came across this book called “Die with zero”. Along with many other yolo ideas, the book prompts the attitude that one must maximize net fulfillment over net worth to the extent of “DIE WITH...

# control variate other than the score

Dec 08, 2022       1 min     Tag: computing
In Bayesian computation, we use control variate to reduces Monte Carlo (MC) variance. The idea if we want to compute $E_{p} h(x)$ from MC draws $x_{1, \dots, S}$, instead of computing the sample mean of...

# What is wrong with this marginalize-out trick

Aug 23, 2022       2 mins     Tag: stan
Consider a normal-normal model with vector data $y$ and scalar parameter $\mu$ and $\sigma$ written in the following stan code1: Bob Carpenter wrote the code. Bob, Charles and I wasted one hour discussing this toy...

# Alternaitves to two stage modeling

Aug 22, 2022       3 mins     Tag: modeling
Sometimes a model can be decomposed into modules and we may run inference separately. This task comes a lot in cut-feedback, SMC, causal inference (two stage regression), multiple imputation, and PK-PD modeling.

# Score matching, Bayesian predictions, tempering, and invariance

Aug 20, 2022       5 mins     Tag: prediction
Score matching Suppose that we observe a sequence of data $y={y_i \in R_m \mid 1\leq i \leq n}$ coming independently from an unknown distribution $p_{true}$; we would like to evaluate a forecast given by a...

# How to generate unbiased estimate of 1/E[x] using one random draw?

Apr 19, 2022       2 mins     Tag: computing
Quiz: you are given ONE random draw $x$ that was drawn from a density $p(x)$. Could you produce an unbiased estimate of $1/E_p[X]$?

# Statistics intuitions for intergals

Mar 29, 2022       3 mins     Tag: computing
I have not done any math for a long while. Today I happen to need to compute an integral

# Marginal liklihood and the Lindley paradox

Nov 22, 2021       3 mins     Tag: modeling
I read an arxiv preprint “History and Nature of the Jeffreys-Lindley Paradox” by Eric-Jan Wagenmakers and Alexander Ly. It is a comprehensive journey that reviews the development of the “Jeffreys-Lindley Paradox”, or what is typically...

Oct 05, 2021       2 mins     Tag: computation
I come across a paper “The Adaptive Biasing Force Method: Everything You Always Wanted To Know but Were Afraid To Ask” by Jeffrey Comer et al. When comparing the adaptive biasing force method (gradient based...

# How do we compare two numbers

Sep 15, 2021       2 mins     Tag: visualization
Why do we automatically read that 6'3 >> 5'8, while 52% ≈ 47%?

# MEBA—Make Empirical-Bayes Bayes again

Aug 19, 2021       3 mins     Tag: modeling
Assuming there are some hyperparameters $\beta$ in the model involving data $y$. We have four ways to get some inference of $\beta$.

# Decision theory is hard

Jun 04, 2021       4 mins     Tag: decision theory
One mental challenge is decision-making with more than two options. To simplify the dilemma that your humble author is encountering, assume that it is on a long haul flight and you are asked by a...

# Who is more Bayesian, Rubin or Pearl?

May 23, 2021       6 mins     Tag: causal