Over a million developers have joined DZone.

Tweaking Bayes’ Theorem

DZone's Guide to

Tweaking Bayes’ Theorem

· Java Zone
Free Resource

Learn how to troubleshoot and diagnose some of the most common performance issues in Java today. Brought to you in partnership with AppDynamics.

In Peter Norvig’s talk The Unreasonable Effectiveness of Data, starting at 37:42, he describes a translation algorithm based on Bayes’ theorem. Pick the English word that has the highest posterior probability as the translation. No surprise here. Then at 38:16 he says something curious.

So this is all nice and theoretical and pure, but as well as being mathematically inclined, we are also realists. So we experimented some, and we found out that when you raise that first factor [in Bayes' theorem] to the 1.5 power, you get a better result.

In other words, if we change Bayes’ theorem (!) the algorithm works better. He goes on to explain

Now should we dig up Bayes and notify him that he was wrong? No, I don’t think that’s it. …

I imagine most statisticians would respond that this cannot possibly be right. While it appears to work, there must be some underlying reason why and we should find that reason before using an algorithm based on an ad hoc tweak.

While such a reaction is understandable, it’s also a little hypocritical. Statisticians are constantly drawing inference from empirical data without understanding the underlying mechanisms that generate the data. When analyzing someone else’s data, a statistician will say that of course we’d rather understand the underlying mechanism than fit statistical models, that just not always possible. Reality is too complicated and we’ve got to do the best we can.

I agree, but that same reasoning applied at a higher level of abstraction could be used to accept Norvig’s translation algorithm. Here’s this model (derived from spurious math, but we’ll ignore that). Let’s see empirically how well it works.

Understand the needs and benefits around implementing the right monitoring solution for a growing containerized market. Brought to you in partnership with AppDynamics.


Published at DZone with permission of John Cook, DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.


Dev Resources & Solutions Straight to Your Inbox

Thanks for subscribing!

Awesome! Check your inbox to verify your email so you can start receiving the latest in tech news and resources.


{{ parent.title || parent.header.title}}

{{ parent.tldr }}

{{ parent.urlSource.name }}