# 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...

# Terrace and gradient

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

# I passed my defense today

May 07, 2021       5 mins     Tag: zombie
I passed my thesis defense today. The capability of passing the defense per se appeared less exciting than I had imagined, in part because everyone passes the dissertation defense anyway. It is like the p-value...

# Bipartisan vaccination?

Apr 17, 2021       4 mins     Tag: modeling causal
I read a NYT graph article entitled Least Vaccinated U.S. Counties Have Something in Common: Trump Voters. Apart from beautiful visualizations, their graph comparison seems persuading to draw two conclusions: