# Algorithmic Minimal Sufficient Statistics: a New Approach

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## Abstract

We introduce the notion of a strong sufficient statistic for a given data string. We show that strong sufficient statistics have better properties than just sufficient statistics. We prove that there are “strange” data strings, whose minimal strong sufficient statistic have much larger complexity than the minimal sufficient statistic.

## Keywords

Algorithmic statistics Minimum description length Randomness deficiency Sufficient statistic Denoising## Notes

### Acknowledgments

The work was in part supported by the RFBR grant 12-01-00864 and the ANR grant ProjetANR-08-EMER-008 Moscow State University, National Research University Higher School of Economics (HSE)

## References

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