Bayesian inference is one of two dominant approaches to statistical inference. The word Bayesian refers to the influence of Reverend Thomas Bayes. Bayesian inference is a modern revival of the classical definition of probability.
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Comment: 39 pages, 11 figures, 1 table, accepted by ApJ. IDL routines
(linmix_err.pro) for performing the Markov Chain Monte Carlo are available at
the IDL astronomy user's library, http://idlastro.gsfc.nasa.gov/homepage.html.