### Statistical and Inductive Inference by Minimum Message Length (Information Science and Statistics)

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## Inductive probability - Wikipedia

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Fisher , and C. There is a non-Technical Introduction [ here ]. Now in inductive inference one often wants the hypothesis H with the largest posterior probability. MsgLen H can usually be estimated well, for some reasonable prior on hypotheses.

## Minimum message length

MsgLen D H can also usually be calculated. However, for two rival hypotheses, H and H'. Consider a transmitter T and a receiver R connected by one of Shannon's communication channels. T must transmit some data D to R.

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T and R may have previously agreed on a code book for hypotheses, using common knowledge and prior expectations. If T can find a good hypothesis, H, theory, structure, pattern, The message paradigm keeps us "honest": Any information that is not common knowledge must be included in the message for it to be decipherable by the receiver; there can be no hidden parameters.

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This issue extends to inferring and stating real-valued parameters to the "appropriate" level of precision. The method is "safe": If we use an inefficient code it can only make the hypothesis look less attractive than otherwise.

There is a natural hypothesis test: The null-theory corresponds to transmitting the data "as is". That does not necessarily mean in 8-bit ascii; the language must be efficient.

If a hypothesis cannot better the null-theory then it is not acceptable. A more complex hypothesis fits the data better than a simpler model, in general. Approximations to SMML. Structural Models Feathers on the Arrow of Time.

## Statistical and Inductive Inference by Minimum Message Length (Information Science and Statistics)

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