Verónica González-López (IMECC-UNICAMP)

Title: A Family of Metrics based on the Efficient Determination Criterion

We address the problem of determining whether two independent samples, each drawn from discrete Markovian processes, are governed by the same underlying stochastic law, with respect to a specific state in the state space. To this end, we introduce a family of metrics (in the mathematical sense) between samples, derived from the Efficient Determination Criterion (EDC). For each proposed metric, we establish a corresponding decision threshold. Since the EDC depends on penalization terms, we identify conditions on these terms under which it is possible to demonstrate that each metric is statistically consistent: it converges to zero as the sample sizes increase, provided the stochastic laws are identical. Conversely, when the samples are drawn from distinct stochastic laws, the metrics diverge, assuming arbitrarily large values as the sample sizes grow. We present applications that demonstrate the usefulness of the family of metrics (joint work with J. Garcia and E. Santos).