This textbook explains the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency‎.‎ It defines the likelihood function‎,‎ prior distributions and posterior distributions‎.‎ It explains how posterior distributions are the basis for inference and explores their basic properties‎.‎ Various methods of specifying prior distributions are considered‎,‎ with special emphasis on subject‎-matter considerations and exchange ability‎.‎ The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions‎.‎ The remainder of the book is concerned with applications of the theory to important models that are used in economics‎,‎ political science‎,‎ biostatistics and other applied fields‎.‎ New to the second edition is a chapter on semiparametric regression and new sections on the ordinal probit‎,‎ item response‎,‎ factor analysis‎,‎ ARCH‎-GARCH and stochastic volatility models‎.‎ The new edition also emphasizes the R programming language‎.‎