2020/02/18 by Russell J. Bowater, Bowater, Russell J. · 1 citation
Arts and Humanities · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Methodology (stat.ME) #Other Statistics (stat.OT) #Philosophy and History of Science #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2002.07966
openalex publication_date 2020/02/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
It is recognised that the Bayesian approach to inference can not adequately\ncope with all the types of pre-data beliefs about population quantities of\ninterest that are commonly held in practice. In particular, it generally\nencounters difficulty when there is a lack of such beliefs over some or all the\nparameters of a model, or within certain partitions of the parameter space\nconcerned. To address this issue, a fairly comprehensive theory of inference is\nput forward called integrated organic inference that is based on a fusion of\nFisherian and Bayesian reasoning. Depending on the pre-data knowledge that is\nheld about any given model parameter, inferences are made about the parameter\nconditional on all other parameters using one of three methods of inference,\nnamely organic fiducial inference, bispatial inference and Bayesian inference.\nThe full conditional post-data densities that result from doing this are then\ncombined using a framework that allows a joint post-data density for all the\nparameters to be sensibly formed without requiring these full conditional\ndensities to be compatible. Various examples of the application of this theory\nare presented. Finally, the theory is defended against possible criticisms\npartially in terms of what was previously defined as generalised subjective\nprobability.\n