{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

prob-models - A Little Probability Coding and Information...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
A Little Probability . . . . . . Coding and Information Theory Fall, 2004 Tom Carter http://astarte.csustan.edu/˜ tom/ October, 2004 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Some probability background There are two notions of the probability of an event happening. The two general notions are: 1. A frequentist version of probability: In this version, we assume we have a set of possible events, each of which we assume occurs some number of times. Thus, if there are N distinct possible events ( x 1 , x 2 , . . . , x N ) , no two of which can occur simultaneously, and the events occur with frequencies ( n 1 , n 2 , . . . , n N ), we say that the probability of event x i is given by P ( x i ) = n i N j =1 n j This definition has the nice property that N X i =1 P ( x i ) = 1 2
Image of page 2
2. An observer relative version of probability: In this version, we take a statement of probability to be an assertion about the belief that a specific observer has of the occurrence of a specific event. Note that in this version of probability , it is possible that two different observers may assign different probabilities to the same event. Furthermore, the probability of an event, for me, is likely to change as I learn more about the event, or the context of the event. 3
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3. In some (possibly many) cases, we may be able to find a reasonable correspondence between these two views of probability. In particular, we may sometimes be able to understand the observer relative version of the probability of an event to be an approximation to the frequentist version, and to view new knowledge as providing us a better estimate of the relative frequencies. 4
Image of page 4
I won’t go through much, but some probability basics, where a and b are events: P ( not a ) = 1 - P ( a ) . P ( a or b ) = P ( a ) + P ( b ) - P ( a and b ) . We will often denote P ( a and b ) by P ( a, b ). If P ( a, b ) = 0, we say a and b are mutually exclusive. Conditional probability: P ( a | b ) is the probability of a , given that we know b . The joint probability of both a and b is given by: P ( a, b ) = P ( a | b ) P ( b ) .
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern