Very Very Brief Description

Issei Tsunoda

2019-08-02

Nowadays many people spent very hard days night, working like a dog, so, it is for such doggy.

I love doggy, I want to meet doggy. I do not want to work like a doggy,… I forget that I do not have any job. Please employ me or I have to…

Graphical User Interface: GUI
library(BayesianFROC)
          BayesianFROC::fit_GUI() #   Enjoy fitting!

Or

library(BayesianFROC)
          fit_GUI_dashboard() #   Enjoy fitting!

Or

library(BayesianFROC)
           fit_GUI_simple() #   Enjoy fitting!

\(\color{green}{\textit{Single reader and Single modality }}\)

Data

Confidence Level No. of Hits No. of False alarms
5 = definitely present \(H_{5}\) \(F_{5}\)
4 = probably present \(H_{4}\) \(F_{4}\)
3 = equivocal \(H_{3}\) \(F_{3}\)
2 = probably \(H_{2}\) \(F_{2}\)
1 = questionable \(H_{1}\) \(F_{1}\)

where, \(H_{c},F_c \in \mathbb{N} \cup\{0\}\) for \(c=1,2,...,5\).

Model

\[ H_c \sim \text{Binomial}(p_c(\theta),N_L),\\ F_c \sim \text{Poisson}(q_c(\theta)).\\ \]

\[ p_c(\theta) := \int_{\theta_c}^{\theta_{c+1}}\text{Gaussian}_{}(x|\mu,\sigma)dx,\\ q_c(\theta) := \int_{\theta_c}^{\theta_{c+1}}N_I \times \frac{d \log \Phi(z)}{dz}dz. \]

where model parameter is \(\theta = (\theta_1,\theta_2,\theta_3,...\theta_C; m,v)\) which should be estimated and \(\Phi\) denotes the cumulative distribution functions of canonical Gaussian.

R script

Criticism to classical FROC theory

One notice that our model is use two distribution for hit and false alarm rate, one is the latent Gaussian and the another is a differential logarithmic Gaussian, which differ the so-called bi normal assumption. More precisely, we do not use the canonical Gaussian for the noise distribution, but we use the differential logarithmic Gaussian instead.

Difficulty

My Bayesian models is quite new, and I did not refer any paper except Charaborty 1989 paper. Thus manu people cannot understand where is it difficult to make model. I first make this model with full heterogeniety, but it did not converge, thus I reduce parameters so that MCMC converge.

Making a model is very very simple and easy, but when we try to run MCMC it will fail for many models. We have to construct models so that MCMC converges.