Kick-off
Decepta-Freak-On Announcements The Doucet book is on reserve at the library The "Get to Know you Survey" is released. New requirement -> you must come to an office hour The entire script is required for assignment 01 Assignment 02 is posted Go over names New Material Markov Models named after Andrei Markov, a Russian mathematician born in 1856 Foundations A Changing World A sequential or temporal process A random variable is sufficient to describe the world at each moment in the sequence The relationship between the variable at different moments in time describes the evolution of the world In a temporal sense we are modeling a dynamic world dynamics are stationary Introduce a single state observable markov model as a graphical model A single random variable concept of a domain a single circle with a self transition directed model or causal model other types of models exist which are undirected. roll it out in time Bad idea to represent coin flips this way. Good idea to represent web site transitions this way. Initial probability distribution Typically uniform Transition probabilities Kind of worthless if uniform stationary process ties the transitions probabilities together at every moment in time. stationary is *not* static Markov assumption current state depends on a finite history of previous states "Markov chain" "Markov process" first-order only depends on previous state second-order depends on previous two states the information that you need to make the current state conditionally independent from all other states transition model first order : P(Xt|Xt-1) second order: P(Xt|Xt-1,Xt-2) show the trick of compressing state histories into a first order model The initial distribution, the transition probability and the length t give a complete probability distribution over all sequences P(s) = P0(s0)*P(s1|s0)*P(s2|s1) etc..... use PI notation Worksheet Genome sequence Charles has a licking problem Introduce Homework 02