Bayes Theorem Bayess theorem Pr [ A | B ] = Pr [ B | A ] Pr [ A ] - PowerPoint PPT Presentation

Dec 02, 2022 •6 likes •86 views

Bayes Theorem Bayess theorem Pr [ A | B ] = Pr [ B | A ] Pr [ A ] Pr [ B ] Note: This is very useful in both this course and in life. Example of Application of Bayess theorem Pr [ A | B ] = Pr [ B | A ] Pr [ A ] Pr [ B ] . There

Bayes Theorem
Bayes’s theorem ◮ Pr [ A | B ] = Pr [ B | A ] · Pr [ A ] Pr [ B ] Note: This is very useful in both this course and in life.
Example of Application of Bayes’s theorem Pr [ A | B ] = Pr [ B | A ] · Pr [ A ] Pr [ B ] . There are two coins: 1) Coin F is fair: Pr ( H ) = Pr ( T ) = 1 2 . 2) Coin B is biased: Pr ( H ) = 3 4 , Pr ( T ) = 1 4 . Alice picks coin at random, flips 10 times, gets all H. Is the coin definitely biased?
Example of Application of Bayes’s theorem Pr [ A | B ] = Pr [ B | A ] · Pr [ A ] Pr [ B ] . There are two coins: 1) Coin F is fair: Pr ( H ) = Pr ( T ) = 1 2 . 2) Coin B is biased: Pr ( H ) = 3 4 , Pr ( T ) = 1 4 . Alice picks coin at random, flips 10 times, gets all H. Is the coin definitely biased? No.
Example of Application of Bayes’s theorem Pr [ A | B ] = Pr [ B | A ] · Pr [ A ] Pr [ B ] . There are two coins: 1) Coin F is fair: Pr ( H ) = Pr ( T ) = 1 2 . 2) Coin B is biased: Pr ( H ) = 3 4 , Pr ( T ) = 1 4 . Alice picks coin at random, flips 10 times, gets all H. Is the coin definitely biased? No. What is Prob that it is biased? VOTE: 1. Between 0.99 and 1.0 2. Between 0.98 and 0.99 3. Between 0.97 and 0.98 4. Less than 0.97
Example of Application of Bayes’s theorem Pr [ A | B ] = Pr [ B | A ] · Pr [ A ] Pr [ B ] . There are two coins: 1) Coin F is fair: Pr ( H ) = Pr ( T ) = 1 2 . 2) Coin B is biased: Pr ( H ) = 3 4 , Pr ( T ) = 1 4 . Alice picks coin at random, flips 10 times, gets all H. Is the coin definitely biased? No. What is Prob that it is biased? VOTE: 1. Between 0.99 and 1.0 2. Between 0.98 and 0.99 3. Between 0.97 and 0.98 4. Less than 0.97 We will see that it is 0.982954, so between 0.98 and 0.99.
Example of Application of Bayes’s theorem Pr ( B | H 10 ) = Pr ( B ) Pr ( H 10 | B ) P ( H 10 ) Pr ( B ) = 1 2 Pr ( H 10 | B ) = ( 3 4 ) 10 Pr ( H 10 ) = Pr ( H 10 ∩ F ) + Pr ( H 10 ∩ B ) Pr ( H 10 ∩ F ) = Pr ( H 10 | F ) Pr ( F ) + Pr ( H 10 | B ) Pr ( B ) = � � 2 ) 10 + ( 3 1 ( 1 4 ) 10 2 Put it together to get 1 Pr ( B | H 10 ) = 1 + (2 / 3) 10 = 0 . 982954 .
Example of Application of Bayes’s theorem Pr ( B | H 10 ) = Pr ( B ) Pr ( H 10 | B ) P ( H 10 ) Pr ( B ) = 1 2 Pr ( H 10 | B ) = ( 3 4 ) 10 Pr ( H 10 ) = Pr ( H 10 ∩ F ) + Pr ( H 10 ∩ B ) Pr ( H 10 ∩ F ) = Pr ( H 10 | F ) Pr ( F ) + Pr ( H 10 | B ) Pr ( B ) = � � 2 ) 10 + ( 3 1 ( 1 4 ) 10 2 Put it together to get 1 Pr ( B | H 10 ) = 1 + (2 / 3) 10 = 0 . 982954 . 1 Pr ( B | H n ) = 1 + (2 / 3) n .

Download Presentation

Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Bayes Theorem Thomas Bayes (1701-1761) Simple form of Bayes Theorem, for

Nave Bayes Classifica/on Debapriyo Majumdar Data Mining Fall 2014 Indian Statistical Institute Kolkata August 14, 2014 Bayes Theorem Thomas Bayes (1701-1761) Simple form of Bayes Theorem, for two

1.04k views • 20 slides

Formal Modeling in Cognitive Science Independence Lecture 23: Conditional Probability; Bayes

Conditional Probability and Independence Conditional Probability and Independence Bayes Theorem Bayes Theorem An Application of Bayes Theorem An Application of Bayes Theorem 1 Conditional Probability and Independence Conditional

247 views • 6 slides

Frequentist example An entomologist spots what might be a rare subspecies of beetle, due to the

CS201 Bayes Theorem Excerpts from WikiPedia http://en.wikipedia.org/wiki/Bayes%27_theorem http://en.wikipedia.org/wiki/Bayesian_inference Bayes's theorem is stated mathematically as the following simple form: [1] For an epistemological

333 views • 5 slides

1 Problem with Brute force Nave Bayes ( ) ( ) ( ) It cannot generalize to unseen

Outline Bayes theorem Discrete Bayesian classifiers Maximum likelihood classification Brute force Bayesian learning Nave Bayes Lecture 5 Bayesian Belief Networks Bayes theorem Maximum likelihood ( ) ( ) ( ) P x

72 views • 4 slides

Bayesian Learning Bayes Theorem MAP, ML hypotheses MAP learners Minimum description

Bayesian Learning Bayes Theorem MAP, ML hypotheses MAP learners Minimum description length principle Bayes optimal classifier Naive Bayes learner Example: Learning over text data Bayesian belief networks

1.11k views • 51 slides

Statistical Reasoning Probability and Bayes' Theorem Certainty Factors and Rule- Based

Statistical Reasoning Probability and Bayes' Theorem Certainty Factors and Rule- Based Systems Bayesian Networks Dempster-Shafer Theory Fuzzy Logic Chapter 8 1 Probability and Bayes' Theorem P(H i|E) = the probability that

281 views • 13 slides

Formal Modeling in Cognitive Science Lecture 18: Conditional Probability; Bayes Theorem Steve

Conditional Probability and Independence Bayes Theorem Formal Modeling in Cognitive Science Lecture 18: Conditional Probability; Bayes Theorem Steve Renals (notes by Frank Keller) School of Informatics University of Edinburgh

169 views • 13 slides

Data Mining Lecture 06: Bayes Theorem Theses slides are based on the slides by Tan,

CISC 4631 Data Mining Lecture 06: Bayes Theorem Theses slides are based on the slides by Tan, Steinbach and Kumar (textbook authors) Eamonn Koegh (UC Riverside) Andrew Moore (CMU/Google) 1 Nave Bayes Classifier Thomas

657 views • 36 slides

Independence, Variance, Bayes Theorem Russell Impagliazzo and Miles Jones Thanks to Janine

Independence, Variance, Bayes Theorem Russell Impagliazzo and Miles Jones Thanks to Janine Tiefenbruck http://cseweb.ucsd.edu/classes/sp16/cse21-bd/ June 1, 2016 Independence Rosen p. 486 Theorem : If X and Y are independent random

1.26k views • 92 slides

Statistical classification Lecture notes Naive Bayes Bayes' theorem P ( c|a ) P ( a ) = P ( a|c

Statistical classification Lecture notes Naive Bayes Bayes' theorem P ( c|a ) P ( a ) = P ( a|c ) P (c) P ( c|f ) % of class c given feature(s) a Posterior This will be our target P ( f|c ) % of feature f given class c

676 views • 36 slides

Unit2: Probabilityanddistributions 2. Bayes theorem and Bayesian inference If you

Announcements Unit2: Probabilityanddistributions 2. Bayes theorem and Bayesian inference If you received an email from me about your clicker registration being missing and you still have not given me your info on the Sta 101 - Fall

298 views • 4 slides

Another Walkthrough of Variational Bayes Bevan Jones ML for NLP Reading Group The University of

Another Walkthrough of Variational Bayes Bevan Jones ML for NLP Reading Group The University of Edinburgh 18 th of October, 2012 2 Variational Bayes? Bayes Bayes Theorem But the integral is intractable! Sampling Gibbs,

1.51k views • 140 slides

Unit2: Probabilityanddistributions 2. Bayes theorem and Bayesian inference Sta 101 - Spring

Announcements Unit2: Probabilityanddistributions 2. Bayes theorem and Bayesian inference Sta 101 - Spring 2017 PS 2 is posted Start reviewing Unit 3 materials Duke University, Department of Statistical Science Dr. Mukherjee Slides

354 views • 4 slides

Formal Modeling in Cognitive Science Lecture 19: Application of Bayes Theorem; Discrete Random

Application of Bayes Theorem Discrete Random Variables Distributions Formal Modeling in Cognitive Science Lecture 19: Application of Bayes Theorem; Discrete Random Variables; Distributions Steve Renals (notes by Frank Keller) School of

453 views • 21 slides

Conditional and Small Sample Probability August 6, 2019 August 6, 2019 1 / 63 Bayes Theorem

Conditional and Small Sample Probability August 6, 2019 August 6, 2019 1 / 63 Bayes Theorem Bayes Theorem will help us more easily calculate P (statement about variable 1 | statement about variable 2) when we have information about P

759 views • 63 slides

Spam Filtering with Naive Bayes Classifier Yuriy Arabskyy June 6, 2017 Table of contents What

Spam Filtering with Naive Bayes Classifier Yuriy Arabskyy June 6, 2017 Table of contents What is spam? Different spam types Anti-Spam Techniques Probability theory basics Conditional probability Bayes Theorem Naive Bayes Theorem Spam

1.04k views • 27 slides

Making Change Making Change Goal. Given currency coin denominations, e.g., {100, 25, 10, 5, 1}

Making Change Making Change Goal. Given currency coin denominations, e.g., {100, 25, 10, 5, 1} devise a method to pay an integer amount using the fewest coins. Example: 34. 25 5 1 1 1 1 Cashier's algorithm. At each

346 views • 9 slides

The Mach System Abraham Silberschatz, Peter Baer Galvin, and Greg Gagne Presented by: Jee Vang

The Mach System Abraham Silberschatz, Peter Baer Galvin, and Greg Gagne Presented by: Jee Vang Outline - Context - Goals - History - Overview of Mach - Kernel - System Components - Process Management - IPC - Memory Management -

564 views • 27 slides

1 Department of Computer Science Lehman College, City University of New York Fall 2019 CMP 426

1 Department of Computer Science Lehman College, City University of New York Fall 2019 CMP 426 (Section 01) CMP 697 (Section 01): Operating Systems Syllabus Instructor: Steven Fulakeza Email: steven.fulakeza@lehman.cuny.edu Phone: 718-960-5581

179 views • 4 slides

Topic Presenter / Facilitator CA Web Publishing Update Kevin Paddock Michael Chen, WUG

Topic Presenter / Facilitator CA Web Publishing Update Kevin Paddock Michael Chen, WUG Web Survey Results Eric Kauffman CA State Template Update Artem Khomishen Accessibility Resources on Webtools Michael Chen 2

725 views • 46 slides

ADVANCED ALGORITHMS Lecture 11: Review, flows/cuts ANNOUNCEMENTS 5 Hong g HW 1 grades out

ADVANCED ALGORITHMS Lecture 11: Review, flows/cuts ANNOUNCEMENTS 5 Hong g HW 1 grades out (?) Maheshakya 2 Amin 034 HW 2 due this Friday, 11:59 PM sravein I 43 gIouglegroups.com utah algo ta way ym.nu gym TODAYS PLAN Quick

394 views • 21 slides

Module 3: XML Query and Manipulati Key XML query and manipulation languages include XPath

Module 3: XML Query and Manipulati Key XML query and manipulation languages include XPath XQuery XSLT SQL/XML c Munindar P. Singh, CSC 513, Spring 2010 p.45 Metaphors for Handling XML: 1 How we conceptualize XML documents determines

441 views • 28 slides

Betweenness relation orientated by Guttman effect in critical edition M. Le Pouliquen 1 M. Csernel

Betweenness relation orientated by Guttman effect in critical edition M. Le Pouliquen 1 M. Csernel 2 1 Telecom Bretagne, Labsticc UMR 3192 , BP 832, 29285 Brest Cedex - France 2 AXIS Inria-Rocqencourt, BP-105- 78180 Le Chesnay Cedex - France CARME

567 views • 32 slides

PIAF Workshop, Sydney, February 2008 Quantum measurement and quantum reality from a topos

PIAF Workshop, Sydney, February 2008 Quantum measurement and quantum reality from a topos theoretical perspective. John V Corbett Department of Mathematics, Macquarie Uni- versity, N.S.W. 2109, Australia, Centre for Time, Philosophy

403 views • 16 slides