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You're reading from  Bayesian Analysis with Python. - Second Edition

Product typeBook
Published inDec 2018
Reading LevelIntermediate
PublisherPackt
ISBN-139781789341652
Edition2nd Edition
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Osvaldo Martin
Osvaldo Martin
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Osvaldo Martin

Osvaldo Martin is a researcher at CONICET, in Argentina. He has experience using Markov Chain Monte Carlo methods to simulate molecules and perform Bayesian inference. He loves to use Python to solve data analysis problems. He is especially motivated by the development and implementation of software tools for Bayesian statistics and probabilistic modeling. He is an open-source developer, and he contributes to Python libraries like PyMC, ArviZ and Bambi among others. He is interested in all aspects of the Bayesian workflow, including numerical methods for inference, diagnosis of sampling, evaluation and criticism of models, comparison of models and presentation of results.
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WAIC in depth

If we expand equation 5.6, we get the following:

Both terms in this expression look very similar. The first one, the lppd (log point-wise predictive density), is computing the mean likelihood over the posterior samples. We do this for each data point and then we take the logarithm and sum up over all data points. Please compare this term with equations 5.3 and 5.4. This is just what we call deviance, but computed, taking into account the posterior. Thus, if we accept that computing the log-likelihood is a good way to measure the appropriateness of the fit of a model, then computing it from the posterior is a logic path for a Bayesian approach. As we already said, the lddp of observed data is an overestimate of the lppd for future data. Thus, we introduce a second term to correct the overestimation. The second term computes the variance of the log-likelihood over...

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Bayesian Analysis with Python. - Second Edition
Published in: Dec 2018Publisher: PacktISBN-13: 9781789341652

Author (1)

author image
Osvaldo Martin

Osvaldo Martin is a researcher at CONICET, in Argentina. He has experience using Markov Chain Monte Carlo methods to simulate molecules and perform Bayesian inference. He loves to use Python to solve data analysis problems. He is especially motivated by the development and implementation of software tools for Bayesian statistics and probabilistic modeling. He is an open-source developer, and he contributes to Python libraries like PyMC, ArviZ and Bambi among others. He is interested in all aspects of the Bayesian workflow, including numerical methods for inference, diagnosis of sampling, evaluation and criticism of models, comparison of models and presentation of results.
Read more about Osvaldo Martin