<jupyter_start><jupyter_text>Bayesian Methods  Environment setup<jupyter_code>import platform

print(f"Python version: {platform.python_version()}")
assert platform.python_version_tuple() >= ("3", "6")

import numpy as np

print(f"NumPy version: {np.__version__}")

from IPython.display import YouTubeVideo<jupyter_output>Python version: 3.7.5
NumPy version: 1.18.1<jupyter_text>Bayes' theorem  <NAME> (1701-1761)English statistician, philosopher and presbyterian minister.[![<NAME>](images/Thomas_Bayes.gif)](https://en.wikipedia.org/wiki/Thomas_Bayes)  Bayes' legacy- <NAME> (1623-1662) pioneered the study of probabilies of *effects* given *causes*.- On the contrary, <NAME> proposed a formula, known as **Bayes's theorem**, for computing the probability of a *cause* given an *effect*.  Intuitive explanation<jupyter_code>YouTubeVideo("HZGCoVF3YvM")<jupyter_output><empty_output><jupyter_text>Quick proof<jupyter_code>YouTubeVideo("U_85TaXbeIo")<jupyter_output><empty_output>
{'fraction_non_alphanumeric': 0.12768130745658834, 'fraction_numerical': 0.028600612870275793, 'mean_word_length': 8.333333333333334, 'pattern_counts': {'":': 0, '<': 16, '<?xml version=': 0, '>': 17, 'https://': 1, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'chain_length': '3', 'dir': 'jupyter-structured-clean-dedup', 'id': '609412', 'license': 'MIT', 'n_tokens_mistral': 360, 'n_tokens_neox': 333, 'n_words': 73, 'path': 'algorithms/bayesian_methods.ipynb', 'repo_name': 'bpesquet/machine-learning-handbook', 'size': '1004'}