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I took a course on Applied Bayesian Statistics taught by David Draper in grad school and we covered Bayesian Data Analysis (Gelman et Al.) http://www.stat.columbia.edu/~gelman/book/ and Probability Theory and tbe Logic of Science by Ed Jaynes: https://www.amazon.com/dp/0521592712/ref=cm_sw_r_em_apa_i_v3...

The former is a much recommended book since it's very comprehensive and builds everything from the ground up and was the basis for the entire course. The latter is a beast of it's own and we simply covered what was effectively the first chapter as part of the course.




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