# Very Very Brief Description

#### 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 $$c=1,2,...,5$$.

• $$N_I$$: Number of images
• $$N_L$$: Number of lesions

## 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

d   <- BayesianFROC::d
fit <- fit_Bayesian_FROC(  dataList = d )

## 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.