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...

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...

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...

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 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...

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

I have not done any math for a long while. Today I happen to need to compute an integral

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...

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...

Why do we automatically read that 6'3 >> 5'8, while 52% ≈ 47%?

Assuming there are some hyperparameters $\beta$ in the model involving data $y$. We have four ways to get some inference of $\beta$.

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...

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...

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: