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OVERVIEW OF BAYESIAN INFERENCE: PART 1

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Presentation on theme: "OVERVIEW OF BAYESIAN INFERENCE: PART 1"— Presentation transcript:

1 OVERVIEW OF BAYESIAN INFERENCE: PART 1

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4 THE BAYESIAN APPROACH IN A NUTSHELL

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7 HOW DOES ONE DO THIS?

8 HISTORICAL NOTES

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10 Example: Infer mean of normal distribution with known variance

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16 Example: model for allelic count with Beta prior

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31 Mixtures of conjugate densities

32 Joint, Conditional and Marginal Posterior Distributions

33 Marginal posterior densities

34 Conditional posterior distributions

35 BAYESIAN ANALYSIS OF CLASSICAL LINEAR REGRESSION MODEL (normal distribution of residuals, “uninformative” priors)

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45 2) Model for allelic count with Beta prior

46 Binary Data: Predictive distribution

47 Example of predictive distribution: beta-binomial model with composition sampling

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49 Bayes factor for 2 beta-binomial models

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51 Posterior Predictive Distributions


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