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Processing consistency in non-Bayesian inference |
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| Institution: | 1. Room 505, William M.W. Mong Engineering Building, Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;2. Department of Industrial Engineering and Operations Research, Columbia University, United States;1. Department of Industrial Engineering and Operations Research, Columbia University, S. W. Mudd Building, 500 W. 120th Street, New York, NY 10027, USA;2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Room 609, William M.W. Mong Engineering Building, Shatin, N.T., Hong Kong;1. IAB, Germany;2. DSE, Università di Bologna, Italy;1. Department of Economics and Management, University of Pisa, Italy;2. CNRS, CMAP - Ecole Polytechnique, France |
| Abstract: | We propose a coherent inference model that is obtained by distorting the prior density in Bayes’ rule and replacing the likelihood with a so-called pseudo-likelihood. This model includes the existing non-Bayesian inference models as special cases and implies new models of base-rate neglect and conservatism. We prove a sufficient and necessary condition under which the coherent inference model is processing consistent, i.e., implies the same posterior density however the samples are grouped and processed retrospectively. We further show that processing consistency does not imply Bayes’ rule by proving a sufficient and necessary condition under which the coherent inference model can be obtained by applying Bayes’ rule to a false stochastic model. |
| Keywords: | Non-Bayesian inference Processing consistency Distortion Pseudo-likelihood False-Bayesian models Conservatism and base-rate neglect |
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