The Bactra Review   Stochastic Complexity in Statistical Inquiry

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To toot my own horn while rolling some logs, see: J. P. Crutchfield and K. Young, ``Inferring Statistical Complexity,'' Physical Review Letters 63 (1989) 105--108 and J. P. Crutchfield, ``The Calculi of Emergence: Computation, Dynamics, and Induction,'' Physica D 75 (1994) 11--54 for the essence of how to do this, and various programmatic statements. For proofs of optimality, see C. R. Shalizi and J. P. Crutchfield, ``Computational Mechanics: Pattern and Prediction, Structure and Simplicity,'' SFI Working Paper 99-07-044.