Learning about the Parameter of the Bernoulli Model
We consider the problem of learning as much information as possible about the parameter?of the Bernoulli model {P????0, 1} from the statistical datax?{0, 1}n,n?1 being the sample size. Explicating this problem in terms of the Kolmogorov complexity and Rissanen's minimum description length principle, we construct a computable point estimator which (a) extracts from x all information it contains about?, and (b) discards all sample noise inx. Our result is closely connected with Rissanen's theorem about the optimality of his scheme of coding statistical data.