Bayesian calculations often depend on sampling methods such as Markov Chain Monte Carlo?

(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: lawrence@krubner.com

I really wish I understood this article. I need to commit to spending some serious time studying statistics, so I can catch up with the modern boom in data analysis. Because 90% of this article is over my head. But from what I can glean, it is very informative:

You’ll noticed that I glossed over something here: the prior, P(Ftrue). The prior allows inclusion of other information into the computation, which becomes very useful in cases where multiple measurement strategies are being combined to constrain a single model (as is the case in, e.g. cosmological parameter estimation). The necessity to specify a prior, however, is one of the more controversial pieces of Bayesian analysis.

A frequentist will point out that the prior is problematic when no true prior information is available. Though it might seem straightforward to use a noninformative prior like the flat prior mentioned above, there are some surprisingly subtleties involved. It turns out that in many situations, a truly noninformative prior does not exist! Frequentists point out that the subjective choice of a prior which necessarily biases your result has no place in statistical data analysis.

A Bayesian would counter that frequentism doesn’t solve this problem, but simply skirts the question. Frequentism can often be viewed as simply a special case of the Bayesian approach for some (implicit) choice of the prior: a Bayesian would say that it’s better to make this implicit choice explicit, even if the choice might include some subjectivity.

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