Laplacian Approximation & Bayesian Logistic Regression

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Laplacian Approximation

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Method for approximating integrals

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Bayesian Logistic Regression

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Combines Bayesian inference with logistic regression

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Purpose of Laplacian Approximation

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Simplifies complex integrals

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Logistic Regression

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Predicts binary outcomes

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Likelihood Function

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Probability of data given parameters

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Normal Distribution

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Common assumption in Laplacian Approximation

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MAP Estimation

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Maximum a posteriori estimation

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Hessian Matrix

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Second derivative matrix

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Conjugate Priors

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Simplifies Bayesian updating

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Predictive Distribution

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Future data prediction