Home

Uncertainty

When enough information is available, we use deductive reasoning. In cases where we have incomplete information (as is usually the case in the real world), we must use some form of inductive or plausible reasoning. But which sort?

Dealing With Uncertainty: The Good, the Bad and the Ugly

A note on terminology
To form a judgement about the likely truth or falsity of any proposition A, the correct procedure is to calculate the probability that A is true conditional on all the evidence at hand:
P(A|E1, E2,...)
The vertical bar '|' means 'given' (so that all items to the right of this conditioning symbol are taken as being true).
There is no such thing as an absolute probability. Bayesian

Bayesians condition on the data actually observed and consider the probability distribution on the hypotheses; they believe it reasonable to put probability distributions on hypotheses and they behave accordingly.
P(hypothesis|data, background information) Frequentist

Frequentists condition on a hypothesis of choice and consider the probability distribution on the data, whether observed or not.
P(data|null hypothesis) Fuzzy Logic

Fuzzy terminology would be, for example, truth("Drew is TALL") = 0.38 (see comp.ai.fuzzy newsgroup FAQ).
P(a person would agree with the hypothesis|data, the person is a competent speaker of the language and given the options of "agree" or "disagree")

Likelihood

The likelihood, L(hypothesis|data), of the hypothesis given the data is proportional to P(data|hypothesis)
P(data|hypothesis, background information)/P(data|background information) = constant × P(data|hypothesis)