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Understanding Joint Distributions and Conditioning in Probability Theory

This text explores the fundamental concepts of joint distributions and the various methods of conditioning in probability theory. It covers essential topics such as the reduction and renormalization processes involved in conditioning, along with marginalization techniques for factors within joint distributions. The significance of conditional probability distributions (CPD) and un-normalized measures is discussed in detail, providing a comprehensive insight into factor products and the manipulation of distributions necessary for statistical analysis.

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Understanding Joint Distributions and Conditioning in Probability Theory

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Presentation Transcript

  1. Preliminaries: Distributions, Factors

  2. Joint Distribution

  3. Joint Distribution

  4. Conditioning

  5. Conditioning: Reduction

  6. Conditioning: Renormalization

  7. Conditioning: Renormalization

  8. Conditioning: Renormalization

  9. Marginalization

  10. Marginalization

  11. Marginalization

  12. Factors

  13. Joint Distribution

  14. Un-normalized Measure

  15. Conditional Probability Distribution (CPD)

  16. General Factors

  17. Factor Product

  18. Factor Marginalization

  19. Factor Reduction

  20. Factor Reduction

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