<p>People often deviate from Bayesian updating by processing information in an optimistic manner. In such optimistic information processing, people tend to selectively incorporate information that is favorable to them. Furthermore, it is known that such selective belief updating imposes psychological costs on them. In this paper, we model optimistic belief updating with psychological costs and provide axiomatic foundations for it. Our model includes Bayesian updating as a special case while allowing for a unified axiomatization of various forms of optimistic information processing by modifying certain axioms.</p>