Probabilistic models for biological sequences: selection and Maximum Likelihood estimation.

Probabilistic models for biological sequences (DNA and proteins) are frequently used in bioinformatics. We describe statistical tests designed to detect the order of dependency among elements of the sequence and to select the most appropriate probabilistic model for an experimental biological sequence. For a model of given type, the independence model, the first-order Markov chain and the hidden Markov model (HMM), we derive the uniform lower bound for the rate of decay for the errors of the maximum likelihood (ML) estimates of the model parameters and, subsequently, the uniform confidence intervals for the parameters.