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You're reading from  Bayesian Analysis with Python - Third Edition

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Published inJan 2024
Reading LevelExpert
PublisherPackt
ISBN-139781805127161
Edition3rd 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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10.2 The grid method

The grid method is a simple brute-force approach. Even if you are not able to compute the whole posterior, you may be able to compute the prior and the likelihood point-wise; this is a pretty common scenario, if not the most common one.

Let’s assume we want to compute the posterior for a model with a single parameter. The grid approximation is as follows:

  1. Define a reasonable interval for the parameter (the prior should give you a hint).

  2. Place a grid of points (generally equidistant) on that interval.

  3. For each point in the grid, multiply the likelihood and the prior.

Optionally, we may normalize the computed values, that is, we divide each value in the posterior array by the total area under the curve, ensuring that the total area equals 1.

The following code block implements the grid method for the coin-flipping model:

Code 10.1

def posterior_grid(grid_points=50, heads=6, tails=9): 
    """ 
 ...
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Bayesian Analysis with Python - Third Edition
Published in: Jan 2024Publisher: PacktISBN-13: 9781805127161

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