DescriptionThis dissertation focuses on developing efficient Fusion Learning methodologies for combining information from non-independent sources using {it confidence distribution} (CD). The sources hereby are broadly construed as different pieces of information extracted from possibly correlated datasets. This situation typically arises when multiple inferences are performed over different times, locations or experiment settings due to computational and statistical considerations, which encompasses a wide range of scientific and engineering applications (e.g. seismic monitoring and detection, computer experiments). In this dissertation, we develop a general framework to effectively and efficiently combine these correlated information using CD, and furthermore, explore the advantages of this framework in different problems that are of theoretical and practical interests.