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Chapter 11 - Probability and Statistics

from Section 1 - Basic and Computational Neuroscience

Published online by Cambridge University Press:  04 January 2024

Farhana Akter
Affiliation:
Harvard University, Massachusetts
Nigel Emptage
Affiliation:
University of Oxford
Florian Engert
Affiliation:
Harvard University, Massachusetts
Mitchel S. Berger
Affiliation:
University of California, San Francisco
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Summary

Basic concepts surrounding probability theory and statistics are discussed, beginning with an introduction of experiments, sample spaces, and events. Then, the idea of random variables and probability distributions are introduced, along with the differences between the continuous and discrete cases and thus also probability density functions and probability mass functions. Concepts surrounding conditional probability, dependence, joint distributions, expectation, and variance are also discussed. The important theorems of probability, namely the law of large numbers and the central limit theorem, are also introduced, along with differences between the frequentist and Bayesian interpretations of probability, before moving on to concepts from statistics. Statistical topics introduced include point estimates, confidence intervals, hypothesis testing, and p-values, including frequentist and Bayesian perspectives on these topics. The chapter ends with a brief discussion of topics in modern statistics.

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Chapter
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Publisher: Cambridge University Press
Print publication year: 2024

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References

Further Reading

Blitsztein, JK, Hwang, J. Introduction to Probability. CRC Press, 2019.Google Scholar
MacKay, DJC. Information Theory, Inference and Learning Algorithms. Cambridge University Press, 2003.Google Scholar
Wasserman, L. All of Statistics. Springer, 2004.Google Scholar

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