Ergodic Markov Chain: A Proper Marker for Identification of a Trait

In this paper we present the use of Ergodic Markov Chain as a marker in identification of a trait. We tried to show the Ergodicity properties of a Markov chain and its application on the three markers (Hair Color, Skin Color and Eye Color). The Marker (Eye Color) shows the highest correct classification of 75% and 89% respectively for father to child and mother to child inheritance case and with a smaller % misclassification of 25% and11% respectively. And also the expected number of steps (generations) to return to the given state (Present of Eye Color) is approximately one (1) an indication of Aperiodic state. Furthermore, the Markov chain (Eye Color) consider show that all states communicate, the chains are finite, irreducible, only one class exist and positive recurrent. Hence, the Markov chains (Eye Color) satisfies Ergodic properties which is an indication of good marker for identification of a trait.