Wednesday, 28 April 2010

Bayesian inference

http://en.wikipedia.org/wiki/Bayesian_inference
'One of the crucial features of the Bayesian view is that a probability is assigned to a hypothesis, whereas under the frequentist view, a hypothesis is typically rejected or not rejected without directly assigning a probability.'
Most people have a truth and change it when enough evidence has accumulated. Some people learn to treat truths as more or less probable, but have to do this consciously. This leads to paradigm-shifting, because people stubbornly resist new evidence until it's really overwhelming.

Some experiments on belief revision have suggested that humans change their beliefs faster when using Bayesian methods than when using informal judgement. If I say I am intuitively Bayesian, I am claiming that I more naturally accept a certain level of uncertainty in statements of 'fact'; that my informal judgement typically involves subconscious assignation of probabilities of truth to certain statements rather than a binary system of accepting or rejecting it.
I'm sure that most people do this to an extent. But studies show that it's certainly not an everyday mode of thought.I believe that this approach to science is very important. Scientists currently test whether a hypothesis is true by seeing if the data pass an arbitrary limit of probability. If, given that the hypothesis is not true, the probability of getting the data is too small, they conclude that the hypothesis is true. The Bayesian method would be to assign a probability of truth to that hypothesis, using the data to measure that degree of probability.

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