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…

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

## Data

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.

## 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.