New thinking about statistical information and its applications to climate prediction
Babbage, Pembroke St.
Bayesian models and methods have arguably been the gold standard for probabilistic assessment of scientific uncertainty for 250 years. The theory of belief functions, also known as Dempster-Shafer (DS) theory referring to its founds in the 1960s and 1970s, has the potential to break through limitations and confusions that are the legacy of the major conceptual and technical advances of the 20th Century. I start with a brief sketch of sources, motivations, and key elements of DS, including why this may be a propitiuous time for a new look at a not-so-new formalism. For statisticians, key ideas are that probabilities are personal and extend beyond the Bayesian paradigm to include probabilities of "don't know," providing new tools for addressing problems of robustification, multiparameter estimation, and nonidentifiability. For climateology, DS opens new ways to think about what is predictable and what is not predictable.