# What is the optimal design of regression covariates?

Feb 23, 2021       2 mins     Tag: modeling

# A Bayesian reflection of "Invariance, Causality and Robustness"

Feb 23, 2021       5 mins     Tag: causal
I was reading Peter Bühlmann’s statistical science article “Invariance, Causality and Robustness”. To be fair, he gave a short course in 2020 here in Columbia, but after reading this paper I guess I did not...

# Best point mass approximation

Feb 20, 2021       1 mins     Tag: computation
It comes a lot that we often summarize a continuous distribution (often, posterior distribution of parameter estimation or of predictions) by a point mass (or a sharpe spike) for (1) computation or memory cost, (2)...

# Measuring extrapolation

Feb 19, 2021       7 mins     Tag: modeling causal
Cramér–Rao lower bound I will not call myself a theoretic statistician but sometimes I still find mathematical statistics amusing especially when they have practical implications. To start this blog post, I will go from Cramér–Rao...

# The likelihood principle in model check and model evaluation

Dec 16, 2020       9 mins     Tag: modeling
The likelihood principle is often phrase as an axiom in Bayesian statistics. My interpretation of the likelihood principle reads:

# Monte Carlo estimate of quantile

Nov 24, 2020       4 mins     Tag: computation
This comes a lot in Monte Carlo computation: we are only given finite draws but we want to compute extreme quantiles.

# Book review "Discrete Distribution"

Nov 21, 2020       2 mins     Tag: book
Today I was reading the book “Discrete Distribution” by Johnson and Kotz. I did not realize it has a newer version until I started this blog post—-the edition I read was published in 1969 by...

# Does MAP estimate always overfit?

Oct 21, 2020       1 mins     Tag: modeling
This is wrong. Indeed it can be opposite.

# Why Bayesian models could have better predictions.

Sep 28, 2020       2 mins     Tag: modeling
In a predictive paradigm, no one really cares about how I obtain the estimation or the prediction. It can come from some MLE, MAP of risk minimization, or some Bayes procedure. Also, when we talk...

# Some difficulty of fitting splines on latent variables

Sep 16, 2020       3 mins     Tag: modeling
in general B-spline is sensitive to the boundary knots, while the unknown support of latent variable models amplifies such sensitivity.

# Gaussian process regressions having opinions or speculation.

May 19, 2020       3 mins     Tag: zombie modeling
I occasionally read Howard Marks’s memo, and in my recent infrequent visit, I have constantly encountered him citing Marc Lipsitch, Professor of Epidemiology at Harvard, that (in Lipsitch’s covid research and in Marks’s money making)...

# A very short introduction on the large deviation principle

May 06, 2020       15 mins     Tag: tutorial
I took this seminar class on Large Deviation Principle (LDP) by Sumit. I summarize some following results that I personally think most relevant (to what I am doing now). Most results are from the book...

# Sample sd of indirect effects in a multilevel mediation model

May 03, 2020       1 mins     Tag: modeling
M asked me a question which essentially looks like this: In a mediation model a and b are regression coefficient through the mediation path, and the final quantity of interest is therefore the product $ab$....