BAYES's Theorem

Charles François (2004). BAYES's Theorem, International Encyclopedia of Systems and Cybernetics, 2(1): 246.

Collection	International Encyclopedia of Systems and Cybernetics
Year	2004
Vol. (num.)	2(1)
ID	◀ 246 ▶
Object type	Methodology or model

R. MATTHEWS (1997, p.38) explains Bayes's theorem as follows: “(The) theorem shows how to update your belief in a particular theory in the light of new data . Mathematically, it states:

'

where Odds (Theory, given observed data) are the odds on the correctness of the theory, given the new data , and Odds (Theory) are the so-called prior odds that the theory is correct - that is, a measure of the plausibility of the theory before the new data emerged. Precisely how that new data changes your beliefs is captured by the so-called “Likehood Ratio ” (LR), which is made up of two factors:

''''Prob (getting the data, given theory is correct) \term{}

Prob (getting the data, given theory is wrong)“

BAYES's Theorem helps dealing with statements “that lie somewhere between absolute truth and falsity” (R. MATTHEWS, 2000, p.45). This is crucial for the evaluation of the soundness of any scientific result (and any belief in general), because, as observers , we have no way to appreciate “absolute” truth or falsity.

MATTHEWS explains: “… as you accumulate more information , BAYES's theorem shows that your original thoughts - flaky or well founded, right or wrong - become progressively less important… The scientific process contains an ineluctable amount of subjectivity at the onset, but… it gives way to objectivity as the information accumulates. In other words, scientific objectivity is ”emergent“ (p.45).

It would be possibly better to say that it is “asymptotically emergent”, because it is impossible to totally eliminate subjectivity . This process is closely related to POPPER'S falseability . It is also obvious that asymptotic objectivity is better reached by recurrent debate and consensus .

See also