(ML 7.1) Bayesian inference - A simple example

Illustration of the main idea of Bayesian inference, in the simple case of a univariate Gaussian with a Gaussian prior on the mean (and known variances).

Category:

Education

Tags:

• machine learning
• statistics
• math

[phatdaddy9]

why are you using x bar instead of mu? Wouldn't the measurement be the population instead of the sample size?

[mathematicalmonk]

@phatdaddy9 I'm having difficulty understanding your question. Can you restate it in a different way?

[phatdaddy9]

@mathematicalmonk

Sure no problem. Why are you using the mathematical notation for the sample distribution, when you are taking the population distribution? Am i missing something?

[mathematicalmonk]

@phatdaddy9 I'm using the usual notation for the sample mean: given random variables X_1,...,X_n, the sample mean is \bar X = (1/n) sum_i X_i.

There's not really a "population" here. The closest thing to a population distribution in this example would be the Normal(theta,1) distribution we are assuming for the measurements. But note that in fact theta itself is a random variable in our model. (I haven't used "mu" anywhere in this video, but I could have used "mu" instead of "theta".)

[awimagic]

great presentation! keep up the good work :)

[shuaiyuanchn]

but, you really don't need to give a 2-min story and draw figures of "Tom" and "Coach".

[rrenaudrrenaud]

Bah, I meant, "that you should think the football field is _smaller_ than ..."

[rrenaudrrenaud]

Isn't the coaches willingness to bet against you more information that you should think the football field than you believed before you heard the bet?

Consider that I want to bet against you. There are 100 things that we both think we know well enough to bet on. You honestly list your beliefs on those 100 things. Then I choose the 5 that I am most willing to bet against you on. I'd guess you are going to lose money.

[fel27]

Wow! Thanks for this great video