- '/Users/rgmartin/Dropbox/Research/mybib.bib'
title: 'Conditional inferential models: combining information for prior-free probabilistic inference'
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Introduction {#S:intro}
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Fisher’s brand of statistical inference [@fisher1973] is often viewed as a middle-ground between the Bayesian and frequentist approaches. Two important examples are his fiducial argument and his ideas on conditional inference. Perhaps influenced by Fisher’s ideas, a current focus in foundational research is on achieving some kind of compromise between the Bayesian and frequentist ideals. See, for example, recent work on fiducial inference [@hannig2009; @hannig2012; @hannig.lee.2009], confidence distributions [@xie.singh.strawderman.2011; @xie.singh.2012], Dempster–Shafer theory [@dempster2008; @shafer2011], and objective Bayes with default, reference, and/or data-dependent priors [@berger2006; @bergerbernardosun2009; @fraser2011; @fraser.reid.marras.yi.2010]. Recently @imbasics have laid out the details of a promising new *inferential model* (IM) approach. IMs take the usual input—sampling model and observed data—and produce prior-free, probabilistic measures of certainty about any assertion/hypothesis of interest, with an almost automatic calibration property. The fundamental idea is that uncertainty about the parameter of interest $\theta$, given observed data $X=x$, is fully characterized by the of an unobservable auxiliary variable $U$. So, the problem of inference about $\theta$ can be translated into one of predicting this unobserved $U$ with a random set. In Section \[S:ims\] we briefly review the construction 