On Information and Sufficiency
Huaiyu Zhu · 1997
The information deviation between any two finite measures cannot be increased by any statistical operations (Markov morphisms). It is invariant if and only if the morphism is sufficient for these two measures. Abbreviated Title: Information and Sufficiency Affiliation: Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA. Email: [email protected], Tel: +1 505 984 8800, Fax: +1 505 982 0565. AMS 1991 Classification: Primary 62B10 (stat info); Secondary 62B20 (meas th), 62B05 (suff stat), 94A17 (meas of info). Keywords: information, sufficiency. Acknowledgment: I thank Kim Sau Chung for pointing out several inaccuracies in a previous version. My work in SFI is sponsored by TXN, Inc. 1 Introduction The ffi-deviations, ffi 2 [0; 1], generalized to the space of finite measures, plays a uniquely important role in statistical inference (Zhu and Rohwer, 1995). One basic requirement for a measure of information is that it should not be increased by any statistical operation, and s...