"Math Wonders to Inspire Teachers and Students" Book Scanning
Book Scanning :Math Wonders to Inspire Teachers and StudentsAlfred S. PosamentierBook Publishing Company :Association for Supervision and Curriculum Development Alexandria, Virginia USADownload Now
____________________________________________________________________________________
CONTENTS :
____________________________________________________________________________________
SAMPLE CONTENT :
"Mathematics : A Tutorial on Learning Bayesian Networks" Book Scanning
Book Scanning :Mathematics : A Tutorial on Learning Bayesian NetworksDavid HeckermanBook Publishing Company :___Download Now
____________________________________________________________________________________
CONTENTS :
____________________________________________________________________________________
SAMPLE CONTENT :
The Bayesian Philosophy
Before we discuss Bayesian Networks and how to learn the from data, it will help to review the Bayesian interpretation of probability. A primary element of the language of probability (Bayesian or otherwis) is the event. By event, we mean a state of some part of our world in some time interval in the past, present, or future. A classic examplpe of an even is that a particular flip of a coin will come up heads. A perhaps more interesting event is that gold will close at more than $400 per ounce on Januari 1, 2001.
Given an event e, the prevalent conception of its probality is that it is a measure of the frequency with which e occurs, when we repeat many times an experiment with possible outcomes e and e (not e). A different notion is tat the probability of e represents the degree of belief held by a person that the event e will occur in a single experiment. If a person assigns a probability between 0 and l to e, then he is to some degree unsure about wheter or not e will occur.
The interpretation of a probalitiy as a frequency in a series of repeat experiments is traditionally of probability as a degree of belief is called the subjective or Beyesian interpretation, in honor of Reverend Thomas Bayes, a scientist from the mid 1700s who helped to pioneer the theory of probabilistic inference (bayes 1958; Hacking, 1975). As we shall see in Section $, the frequentist interpretation is special case of Bayesian interpretation.
In the Bayesian interpretation, a probability or belief will always depend on state of knowledge of the person who provides thhat probability. For example, if we were to give someone a coin, he would likely assign a probability of 1/2 to the event thhat the coin would show heads on the next toss. If, however, we conviced that person that the coin was weighted in favor of head, he would assign a higher probability of e given "?". The Symbol "?" represents the state of knowledge of the person who provides the probability.
Also, in this interpretation, a person can assess a probability that the coin would show heads on the elevent thos, under the assumtion that the same coin comes up heads n each of the first ten losses. We write p(e2|e1,?) to denote the probability of event e2 given that event e1 is true and given backgound knowledge ?.
.....................
