We express some criticism about the definition of an algorithmic sufficient statistic and, in particular, of an algorithmic minimal sufficient statistic. We propose another definition, which has better properties.

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A fundamental notion in Algorithmic Statistics is that of a stochastic object, i.e., an object having a simple plausible explanation. Informally, a probability distribution is a plausible explanation for $x$ if it looks likely that $x$ was drawn at random with respect to that distribution. In this paper, we ... more >>>