# Processing consistency in non-Bayesian inference

*Xue Dong He* and
*Di Xiao*

*Journal of Mathematical Economics*, 2017, vol. 70, issue C, 90-104

**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 (search for similar items in EconPapers)

**Date:** 2017

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:70:y:2017:i:c:p:90-104

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