Fixed some typos

[zaxtax]

I didn't like the wording in some parts.

There are more substantial changes that would want to make but don't want to mess up the voice of the document.

Namely:

1. Highlight MCMC is just a means of performing Bayesian Inference. There are other algorithms for doing it that are beyond the scope of the book.

2. MCMC roughly moves towards regions of high probability, but the goal is not to find the Maximum A-Posterior point. MH moves are designed so as to make sure our samples are still from the target distribution.

3. The mixture models example will have an exponential number of peaks, but because they are all isomorphic to each other, sampling around any of them is not a big deal.

I am including this here more to clarify how much detail do you believe is appropriate for this book.

[CamDavidsonPilon]

Thanks for the comments, Rob.

1. I'll address that MCMC is indeed one way of performing Bayesian inference.
2. I did try to acknowledge this, but I will add more clarification on this this point.
3. Could you expand on this point, please?

[zaxtax]

For point 3) I am referring to things like this: http://normaldeviate.wordpress.com/2012/08/04/mixture-models-the-twilight-zone-of-statistics/

The idea is that there is random variable saying which mixture to assign a given data point. These random variables can be permuted and it wouldn't change the underlying representation, but it does mean for each permutation there will be a peak. Luckily since these permutations are all essentially the same distribution it doesn't matter which peak you hover around. It does though mean multiple chains will not always converge the same peak.

Let me write some text addressing 1) and 2)

[CamDavidsonPilon]

Very interesting read. You know I did observe this sort of behaviour in the example. (Especially the non-identifiable and convergence to different modes). Perhaps this is the worst example to demonstrate convergence of MCMC haha.

I welcome your comments about 1) and 2).