Abstract
Bayesian data analysis is an important and fast-growing discipline within the field of statistics. This chapter provides an elementary introduction to the basics of Bayesian analysis. Here, we use Bayesian inference regarding the population proportion as a simple example to discuss some basic concepts of Bayesian methods. We briefly discuss prior and posterior probability distributions. Prior probability distributions reflect our knowledge regarding the possible values of unknown parameters (e.g., population proportion) before observing data. Posterior probability distributions reflect our updated knowledge about unknown parameters after observing data. We show how posterior probability distributions are used to estimate parameters and perform hypothesis testing.
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References
Christensen, R., Johnson, W., Branscum, A., Hanson, T.E.: Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians. Texts in Statistical Science. Taylor and Francis, London (2010)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall, London (2003)
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Shahbaba, B. (2012). Bayesian Analysis. In: Biostatistics with R. Use R!. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1302-8_13
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DOI: https://doi.org/10.1007/978-1-4614-1302-8_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1301-1
Online ISBN: 978-1-4614-1302-8
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