Towards an Algorithmic

While Kolmogorov complexity is the accepted absolute measure of information content of an individual nite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing the information in the data, for example, a nite set where the data sample typically came from. The statistical theory based on such relations between individual objects can be called algorithmic statistics, in contrast to ordinary statistical theory that deals with relations between probabilistic ensembles. We develop a new algorithmic theory of typical statistic, suucient statistic, and minimal suucient statistic.