This paper proposes a formal characterization of extended Bayesian updating for complementarily additive subjective beliefs under ambiguity, which are compatible with a wide range of choice behavior toward ambiguity. The main result shows that, based on the biseparability of Ghirardato and Marinacci (2001), extended Bayesian updating characterizes the update rule which is a step-by-step composite updating for priors, where one of Dempster-Shafer rule, Bayes' update rule and Fagin-Halpern rule is applied to each step. As applications, more specific preference relations are examined, such as the maxmin expected utility, the rank-dependent expected utility, and the concave expected utility preferences by Lehrer (2009).
