Draw a simulated dataset from model distributions with specified parameters from priors
Draw_a_simulated_data_set(
sd = 5,
C = 5,
seed.for.drawing.a.prior.sample = 1111,
fun = stats::var,
NI = 259,
NL = 259,
initial.seed.for.drawing.a.data = 1234,
ModifiedPoisson = FALSE,
ite = 1111
)Standard Deviation of priors
No. of Confidence levels
seed
An one dimensional real valued function defined on the parameter space. This is used in the definition of the rank statistics. Generally speaking, the element of the parameter space is a vector, so the function should be defined on vectors. In my model parameter is mean, standard deviation, C thresholds of the latent Gaussian, so this function should be defined on the C+2 dimensional Euclidean space.
No. of images
No. of Lesions
seed
Logical, that is TRUE or FALSE.
If ModifiedPoisson = TRUE,
then Poisson rate of false alarm is calculated per lesion,
and a model is fitted
so that the FROC curve is an expected curve
of points consisting of the pairs of TPF per lesion and FPF per lesion.
Similarly,
If ModifiedPoisson = TRUE,
then Poisson rate of false alarm is calculated per image,
and a model is fitted
so that the FROC curve is an expected curve
of points consisting of the pair of TPF per lesion and FPF per image.
For more details, see the author's paper in which I explained per image and per lesion. (for details of models, see vignettes , now, it is omiited from this package, because the size of vignettes are large.)
If ModifiedPoisson = TRUE,
then the False Positive Fraction (FPF) is defined as follows
(\(F_c\) denotes the number of false alarms with confidence level \(c\) )
$$ \frac{F_1+F_2+F_3+F_4+F_5}{N_L}, $$
$$ \frac{F_2+F_3+F_4+F_5}{N_L}, $$
$$ \frac{F_3+F_4+F_5}{N_L}, $$
$$ \frac{F_4+F_5}{N_L}, $$
$$ \frac{F_5}{N_L}, $$
where \(N_L\) is a number of lesions (signal). To emphasize its denominator \(N_L\), we also call it the False Positive Fraction (FPF) per lesion.
On the other hand,
if ModifiedPoisson = FALSE (Default), then
False Positive Fraction (FPF) is given by
$$ \frac{F_1+F_2+F_3+F_4+F_5}{N_I}, $$
$$ \frac{F_2+F_3+F_4+F_5}{N_I}, $$
$$ \frac{F_3+F_4+F_5}{N_I}, $$
$$ \frac{F_4+F_5}{N_I}, $$
$$ \frac{F_5}{N_I}, $$
where \(N_I\) is the number of images (trial). To emphasize its denominator \(N_I\), we also call it the False Positive Fraction (FPF) per image.
The model is fitted so that
the estimated FROC curve can be ragraded
as the expected pairs of FPF per image and TPF per lesion (ModifiedPoisson = FALSE )
or as the expected pairs of FPF per image and TPF per lesion (ModifiedPoisson = TRUE)
If ModifiedPoisson = TRUE, then FROC curve means the expected pair of FPF per lesion and TPF.
On the other hand, if ModifiedPoisson = FALSE, then FROC curve means the expected pair of FPF per image and TPF.
So,data of FPF and TPF are changed thus, a fitted model is also changed whether ModifiedPoisson = TRUE or FALSE.
In traditional FROC analysis, it uses only per images (trial). Since we can divide one image into two images or more images, number of
trial is not important. And more important is per signal. So, the author also developed FROC theory to consider FROC analysis under per signal.
One can see that the FROC curve is rigid with respect to change of a number of images, so, it does not matter whether ModifiedPoisson = TRUE or FALSE.
This rigidity of curves means that the number of images is redundant parameter for the FROC trial and
thus the author try to exclude it.
Revised 2019 Dec 8 Revised 2019 Nov 25 Revised 2019 August 28
A variable to be passed to the function rstan::sampling() of rstan in which it is named iter. A positive integer representing the number of samples synthesized by Hamiltonian Monte Carlo method,
and, Default = 1111
A single synthesized data-set
# NOT RUN {
# }
# NOT RUN {
one.dataList <- Draw_a_simulated_data_set()
# }
# NOT RUN {
# dottest
# }
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