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Probability

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Abstract

Probability is tricky to understand and trickier to apply. Through a detailed series of examples that we work using multiple methods using Python modules, we illustrate how to use geometrical projections to develop intuition regarding conditional probability and how to apply them to difficult problems. We also discuss the concept of information entropy, which will become important for certain machine learning methods.

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Notes

  1. 1.

    See appendix for proof using the Cauchy-Schwarz inequality.

  2. 2.

    The best, easy-to-understand presentation of this material is chapter four of Mackay’s text [7]. Another good reference is chapter four of [8].

  3. 3.

    Cumulative density function. Namely, \(F(x)=\mathbb {P}(X < x)\).

  4. 4.

    Note that this example density does not exactly integrate out to one like a probability density function should, but the normalization constant for this is distracting for our purposes here.

References

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Authors and Affiliations

  1. West Health Institute, San Diego, California, USA

    José Unpingco

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  1. José Unpingco
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Correspondence to José Unpingco .

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© 2016 Springer International Publishing Switzerland

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Unpingco, J. (2016). Probability. In: Python for Probability, Statistics, and Machine Learning. Springer, Cham. https://doi.org/10.1007/978-3-319-30717-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-30717-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30715-2

  • Online ISBN: 978-3-319-30717-6

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