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Log-odds (or logits)

(I wrote this post for my own blog, and given the warm reception, I figured it would also be suitable for the LW audience. It contains some nicely formatted equations/tables in LaTeX, hence I've left it as a dropbox download.) Logarithmic probabilities have appeared previously on LW here, here, and sporadically in the comments. The first is a link to a Eliezer post which covers essentially the same material. I believe this is a better introduction/description/guide to logarithmic probabilities than anything else that's appeared on LW thus far. Introduction: Our conventional way of expressing probabilities has always frustrated me. For example, it is very easy to say nonsensical statements like, “110% chance of working”. Or, it is not obvious that the difference between 50% and 50.01% is trivial compared to the difference between 99.98% and 99.99%. It also fails to accommodate the math correctly when we want to say things like, “five times more likely”, because 50% * 5 overflows 100%. Jacob and I have (re)discovered a mapping from probabilities to log- odds which addresses all of these issues. To boot, it accommodates Bayes’ theorem beautifully. For something so simple and fundamental, it certainly took a great deal of google searching/wikipedia surfing to discover that they are actually called “log-odds”, and that they were “discovered” in 1944, instead of the 1600s. Also, nobody seems to use log-odds, even though they are conceptually powerful. Thus, this primer serves to explain why we need log-odds, what they are, how to use them, and when to use them. Article is here (Updated 11/30 to use base 10)

31Nov 28, 2011

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[LINK] Evidence-based giving by Laura and John Arnold Foundation

http://online.wsj.com/article/SB10001424127887323372504578466992305986654.html Apparently a hedge fundie made 4 billion and is giving most of it away to what the WSJ describes as a "moneyball" approach to giving.

May 18, 20133

What is your true decision metric? A look at medicinal chemists

http://pipeline.corante.com/archives/2012/11/27/how_do_chemist_think_that_they_judge_compounds.php Some background: medicinal chemists are responsible for identifying drug candidates, usually by screening large (10^6) libraries of combinatorially generated molecules. Some of these hits turn out to be biologically active, and then it's up to the medicinal chemists to decide whether these hits are false positives or not, and...

Nov 27, 20125

XKCD - Frequentist vs. Bayesians

http://xkcd.com/1132/ Is this a fair representation of frequentists versus bayesians? I feel like every time the topic comes up, 'Bayesian statistics' is an applause light for me, and I'm not sure why I'm supposed to be applauding.

Nov 9, 201224

Always check your assertions... (Winning the Lottery)

"In 2005, Dr. Zhang was having an ongoing discussion with friends about the Lottery, with Dr. Zhang taking the view that it offered poor odds and was a tax mainly on poor people. To bolster his argument, he began analyzing the Massachusetts Lottery’s various games. But when he got to...

Jul 31, 20127

Four Short Stories on Error Checking

(Cross-posted from my blag) 1. My microwave clock has been broken since a power outage. It now reads something like 7 hours behind the real time. I've been too lazy to fix it, but the bright side is that it's 7 hours behind, and not 15 minutes behind. If it...

Jun 25, 20129

Log-odds (or logits)

Nov 28, 201131

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brilee

Log-odds (or logits)

XKCD - Frequentist vs. Bayesians

Four Short Stories on Error Checking

Always check your assertions... (Winning the Lottery)

brilee

[LINK] Evidence-based giving by Laura and John Arnold Foundation

What is your true decision metric? A look at medicinal chemists

XKCD - Frequentist vs. Bayesians

Always check your assertions... (Winning the Lottery)

Four Short Stories on Error Checking

Log-odds (or logits)

Log-odds (or logits)

XKCD - Frequentist vs. Bayesians

Four Short Stories on Error Checking

Always check your assertions... (Winning the Lottery)

[LINK] Evidence-based giving by Laura and John Arnold Foundation

What is your true decision metric? A look at medicinal chemists

XKCD - Frequentist vs. Bayesians

Always check your assertions... (Winning the Lottery)

Four Short Stories on Error Checking

Log-odds (or logits)