#### WLOG

A question to astronomers. What do you think WLOG is? It has nothing to do with our BLOG or SLOG. Statisticians, please do not say a word.

I do remember the vividity of the first year statistics graduate courses. Not majoring statistics nor mathematics during my college years, everything was interesting, still is, and new. With the language barrier, listening lectures while writing everything down from the board (some professors use quite board space and dirt them a lot) was challenging. Then one day, on the board among equations and theorems, there was WLOG.

Everyone seemed to understand what it is except me. The lecture ran fast and I was too shy to ask what this WLOG was. Astronomers with good math education probably know WLOG already. My first guess was that Americans write some variation of log by WLOG (statisticians tends to write natural log by log, whereas engineers of information theory write log based 2 by log, whereas physical scientist write log based 10 by log, whereas high school students go by the rule). Instead of listing my wild guesses to infer what WLOG is, let’s get to the point.

WLOG: Without Loss Of Generality.

I found it out on my own (I happened to come across a kind book) but it took me some months to get used to this acronym. The concept of shift invariant, scale invariant, and others is almost always barricaded by my doubts about the validity of these invariant properties from the physics viewpoint. Mathematically the invariance is simply assumed for the convenience and does not change the basis of statistics and their inferential characteristics regardless of the reality. As if “it is trivial” implicitly describes and entails a proof, WLOG enables statistical explanation to be concise and general. Nevertheless, I couldn’t accept WLOG for a while. It was like understanding the twin paradox from relativity without math during a high school science class. Perhaps, I was not good at thought experiments or I was too skeptical.

WLOG is a very convenient expression like solving problems in Galileo’s reference frame which save efforts of accounting for details.