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\author{Issei Tsunoda}
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\title{Bayesian Models for Free-response Receiver Operating Characteristic Analysis}






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\begin{abstract}
  The free-response receiver operating characteristic method developed by Chakraborty is a generalization of receiver operating characteristic analysis, but Chakraborty used a non-Bayesian approach. This paper aims to reconstruct Chakraborty's technique using a Bayesian approach and to verify that our models fit practical datasets.
  We also develop a Bayesian model for comparing modalities.
\end{abstract}

%% ** Keywords **

(Hierarchical) Bayesian modeling, Signal detection theory, Radiology, FROC analysis, individual differences, observer performance






\section*{References }


[1]. Chakraborty, D.P. (1989). Maximum likelihood analysis of free-response receiver operating characteristic (FROC) data. Med Phys. Jul-Aug;16(4):561-8. DOI: 10.1118/1.596358

[2]. Johnson, T.D.I. \& Johnson, V.E., A Bayesian hierarchical approach to multirater correlated ROC analysis. Stat Med. (2006). Jun 15;25(11):1858-71. DOI: 10.1002/sim.2314


[3] Dorfman, D.D., Berbaum, K.S., \& Metz, C.E. (1992). Receiver operating
characteristic rating analysis: Generalization to the population of
readers and patients with the jackknife method. Investigative Radiology,
27, 723-731.


[4] Swensson, G. (1996). Unified measurement of observer performance in detecting and localizing target
objects on images, Medical Physics 23. pp. 1709-1725 doi: 10.1118/1.597758

[5] Dev Chakraborty; Observer Performance Methods for Diagnostic Imaging, Foundations, Modeling, and Applications with R-Based Examples.

[6] Stan Development Team (2019). RStan: the R interface to Stan. R package
  version 2.19.2. http://mc-stan.org/.

[7] Bayesian data analysis; Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin;Texts in statistical science; Publisher: Chapman \& Hall/CRC, Year: 2004

[8] Bayesian analysis of a ROC curve for categorical data using a skew-binormal model; Balgobin Nandram and Thelge Buddika Peiris (This paper is nice!); 2018 volume 11 369-384; Statistics and its interface





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