#### Re: Ha

Ha, ha.

Actually, after my coin-toss example, it occurred to me that there is a popular statistical approach you may like that deals explicitly in belief - it's called Bayesian inference*. *But* - "beliefs" in Bayesian inference are not of the yes/no, black/white, I do/I don't variety; rather, they are probabilistic (more precisely, they are probability distributions).

In a nutshell, it works this way: before examining the evidence for a proposition, you start off with a prior belief (probability distribution) about the proposition. You then examine the evidence and "update your prior" on the basis of the evidence, according to a specific mathematical scheme (Bayes' Theorem**). This yields a posterior belief (again a probability distribution). So Bayesian inference yields answers to evaluation of evidence for a hypothesis in the form of probabilities, rather than yes/no answers. The posterior probability distribution also encapsulates the "confidence" (uncertainty, error-bars, etc.) of your evaluation.

For the coin-toss experiment, for example, you may start with the hypothesis: "The coin is unbiased". What form should your prior belief take? Here's where things can become a bit vexed: well, what *do* you believe about the coin - before you've seen the result of the 100 coin tosses? You might say "I don't know anything about the coin - therefore I'll grant equal credence to *every possible* bias that the coin might potentially have. This is called a "flat prior"***. You then crank the data and your prior through Bayes' Theorem, and you have a distribution of posterior belief. (In the coin-toss experiment with flat prior, the posterior will in fact be a Beta distribution, with parameters that reflect the mean and variance of the posterior belief.)

It's worth noting that in fact the alternative so-called "frequentist" (or Fisherian", or "Neyman-Pearson") approach to statistical inference *also* delivers answers in probabilistic form - in this case, the (in)famous p-values. The Bayesian and frequentist approaches to statistical inference have their respective pros and cons, and each has its devotees. Both are prevalent in science, with the frequentist approach more "traditional", particularly in the "hard" sciences (physics, chemistry, etc.). There's nothing to stop one doing both****.

How different does this all feel to the religious (God exists/God doesn't exist) flavour of belief which, sadly, seems to be what by default "belief" means to the lay person (and perhaps to yourself?)

You can have fun with probabilistic belief. E.g., off the top of my head (tomorrow I might give different answers) here are some guesses at my mean Bayesian posteriors (i.e., post evidence-to-date):

Man has set foot on the moon: 99%

The JFK assassination was an FBI/CIA/other-political plot: 15%

Elvis is alive and working in a chip shop in Skegness, Lincolnshire: 1e-20

I'll leave you to play around with your Bayesian (posterior) beliefs on evidence for AGW and it's consequences. Sure they'll look different to mine.

Anyhow... if you want to stick with the whole belief thing, I'd highly recommend you take on board the Bayesian version, rather than the religious all-or-nothing variety you appear to subscribe to. It plays much better with science and the evaluation of evidence. It also reflects much better my own "beliefs" (which you seem so terribly obsessed with) about AGW and its consequences.

Enjoy.

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*_{A misnomer, as it was not devised by Thomas Bayes, after whom it is named.}

**_{A double misnomer, as not only was it not discovered by Bayes, but it is not really a theorem either.}

***_{But... perhaps the flat prior is inappropriate? I mean, most coins you've ever seen are not biased... should you perhaps bias your prior belief towards the coin being unbiased? And if so, by how much? And what do you know about the person who produced the coin? Do you trust them? Etc., etc. (Notably, flat priors don't even exist in many scenarios.) There is thus a built-in ambiguity at the heart of Bayesian inference, which is the reason why I am not a huge fan. It does have some advantages, though, over the alternative and more popular "frequentist" inference approach.}

****_{Bayesian analysis, though, can be mathematically more challenging, often to the point of intractability.}