3 ms·

The biggest historical obstacle to Bayesian stats was low amounts of data available and difficulty of computation. Frequentist stats is optimised around these.

by jordigh 10y ago

The biggest historical obstacle to Bayesian stats was low amounts of data available and difficulty of computation. Frequentist stats is optimised around these. With 30 samples and very easy computations, you are able to produce a reasonable frequentist confidence interval, sometimes even with less data. On the other hand, even the simplest Bayesian analysis of determining the probability of heads in a coin flip requires some interesting integration and the somewhat obscure Beta distribution. Now that we have lots of data and lots of computing power, Bayesian stats can show its results, after getting rebranded as "machine learning".

tgb 10y ago
> On the other hand, even the simplest Bayesian analysis of determining the probability of heads in a coin flip requires some interesting integration and the somewhat obscure Beta distribution. Isn't this kind of misleading? The end result of the Beta distribution, etc. is just the extremely simple-to-compute Rule of Succession [1]. [1] https://en.wikipedia.org/wiki/Rule_of_succession https://en.wikipedia.org/wiki/Rule_of_succession
- jordigh 10y ago
  A bit, but in general, computing posterior distributions tends to very quickly lead to more complicated integrals. It just so happens that the Beta distribution is somewhat nice and symmetrical, if a bit obscure.
  - XFrequentist 10y ago
    More generally, this is why there's (still) a mild obsession with "conjugate" prior/likelihood distribution pairs - i.e. combinations of prior and likelihood that give analytically tractable posteriors[1] - despite the ability to get easily get results with MCMC. [1] Yes, everyone wants a nice posterior. You're very clever.
eli_gottlieb 10y ago
>Now that we have lots of data and lots of computing power, Bayesian stats can show its results, after getting rebranded as "machine learning". Partly lots of computing power, and partly the Monte Carlo revolution that enabled us to replace intractable integrals with lots of cheap CPU time.

by jordigh 10y ago

tgb 10y ago

> On the other hand, even the simplest Bayesian analysis of determining the probability of heads in a coin flip requires some interesting integration and the somewhat obscure Beta distribution. Isn't this kind of misleading? The end result of the Beta distribution, etc. is just the extremely simple-to-compute Rule of Succession [1]. [1] https://en.wikipedia.org/wiki/Rule_of_succession https://en.wikipedia.org/wiki/Rule_of_succession

jordigh 10y ago
A bit, but in general, computing posterior distributions tends to very quickly lead to more complicated integrals. It just so happens that the Beta distribution is somewhat nice and symmetrical, if a bit obscure.
- XFrequentist 10y ago
  More generally, this is why there's (still) a mild obsession with "conjugate" prior/likelihood distribution pairs - i.e. combinations of prior and likelihood that give analytically tractable posteriors[1] - despite the ability to get easily get results with MCMC. [1] Yes, everyone wants a nice posterior. You're very clever.

eli_gottlieb 10y ago

>Now that we have lots of data and lots of computing power, Bayesian stats can show its results, after getting rebranded as "machine learning". Partly lots of computing power, and partly the Monte Carlo revolution that enabled us to replace intractable integrals with lots of cheap CPU time.