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This documentation is for astroML version 0.4

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Chapter 5: Bayesian Statistical Inference

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Chapter 5: Bayesian Statistical Inference¶

This chapter develops the fundamentals of Bayesian statistical inference, and finishes with some examples of computing statistics in this manner.

../../_images/fig_odds_ratio_coin_1_thumb.png

Coin Toss Odds Ratio¶

../../_images/fig_malmquist_bias_1_thumb.png

Malmquist Bias Example¶

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Eddington-Malmquist & Lutz-Kelker Biases¶

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Log-likelihood for Gaussian Distribution¶

../../_images/fig_posterior_gaussian_1_thumb.png

Posterior for Gaussian Distribution¶

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Gaussian/Gaussian distribution¶

../../_images/fig_likelihood_gaussgauss_1_thumb.png

Gaussian Distribution with Gaussian Errors¶

../../_images/fig_posterior_gaussgauss_1_thumb.png

Gaussian Distribution with Gaussian Errors¶

../../_images/fig_posterior_binomial_1_thumb.png

Binomial Posterior¶

../../_images/fig_likelihood_cauchy_1_thumb.png

Log-likelihood for Cauchy Distribution¶

../../_images/fig_posterior_cauchy_1_thumb.png

Posterior for Cauchy Distribution¶

../../_images/fig_likelihood_uniform_1_thumb.png

Log-likelihood for Uniform Distribution¶

../../_images/fig_likelihood_gausslin_1_thumb.png

Log-likelihood for Gaussian plus linear background¶

../../_images/fig_poisson_continuous_1_thumb.png

Unbinned Poisson Data¶

../../_images/fig_poisson_likelihood_1_thumb.png

Binned Regression: Poisson vs Gaussian¶

../../_images/fig_poisson_comparison_1_thumb.png

Poisson Statistics with arbitrarily small bins¶

../../_images/fig_outlier_likelihood_1_thumb.png

Plot the posterior of mu vs g1 with outliers¶

../../_images/fig_outlier_marginalized_1_thumb.png

Plot the Outlier Probability¶

../../_images/fig_odds_ratio_cauchy_1_thumb.png

Odds Ratio for Cauchy vs Gaussian¶

../../_images/fig_hist_binsize_1_thumb.png

Selection of Histogram bin size¶

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Distribution Representation Comparison¶

../../_images/fig_cauchy_mcmc_1_thumb.png

MCMC for the Cauchy distribution¶

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Histogram for Double-gaussian model test¶

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MCMC Model Comparison¶

../../_images/fig_gaussgauss_mcmc_1_thumb.png

Gaussian Distribution with Gaussian Errors¶

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Finding a signal in a background¶

../../_images/fig_hierarchical_bayes_RV_1_thumb.png

Hierarchical Bayes modeling for Gaussian distribution with Gaussian errors¶

../../_images/fig_hierarchical_bayes_sources_1_thumb.png

An illustration of Hierarchical Bayes modeling for a Gaussian burst with background¶

../../_images/fig_ABCexample_1_thumb.png

Approximate Bayesian Computation for Gaussian location parameter¶