Validate our Bayesian model for the case of a single reader and single modality.
Radiograph
For the user it is sufficient to know only one function validation.dataset_srsc_for_different_NI_NL()
. This function replicate many data-sets from known distributions which user specified before execution. In FROC data, the number of lesions and images corresponds samples size. So, large number of image gives us more small bias which will be confirmed by the function validation.dataset_srsc_for_different_NI_NL()
.
The following, the important variables of validation.dataset_srsc_for_different_NI_NL()
are shown.
NLvector
: A vector, whose each component means No. of lesions. We fit models to the replicated data withs these fixed lesions specified this vector NLvector
.ratio
: The ratio of image:lesions. It bother for me to input both the images and lesions. Thus I construct so that it is sufficient to input only one of them, that is if lesion is specified, then the noumber of images are automatically generated by satisfying this ratio
replicate.datset
: For fixed number of lesions, images, the dataset of hits and false alarms are replicated, and the number of replicated data sets are specified by this variable.mean.truth
: The mean of signal distribution.sd.truth
: The standard deviation of signal distribution.z.truth
: The threshold of the bi-normal assumptionite
: The Hamiltonian Monte Carlo iterations used in each fitting for replicated data-sets.Each number in table means the errors of parameter, i.e., the mean values of estimates minus true parameter over all replications. We can see that the number of images and lesions become more large, then these error tends to zero. That is, in FROC models, the number of lesions and images corresponds sample size, so if these values are larger, then the hits and false alarms also become larger, and it leads us to smaller biases.
validation.dataset_srsc_for_different_NI_NL()
Name.of.Parameters | 1-th model | 2-th model | 3-th model | 4-th model |
---|---|---|---|---|
Number of Images | 200.0000000 | 20000.0000000 | 2.00000e+06 | 2.0000e+08 |
Number of Lesions | 100.0000000 | 10000.0000000 | 1.00000e+06 | 1.0000e+08 |
z[ 1 ] | 0.1055186 | 0.0103358 | 1.01020e-03 | 1.0720e-04 |
z[ 2 ] | 0.1956183 | 0.0132404 | 1.20850e-03 | 1.3030e-04 |
z[ 3 ] | 1.1307551 | 0.0309471 | 2.52580e-03 | 2.9210e-04 |
mean.of.signal | -0.4843169 | -0.0463222 | -4.95890e-03 | -4.2730e-04 |
sd.of.signal | 3.8036830 | 0.1160011 | 1.07218e-02 | 1.0843e-03 |
AUC | -0.0348429 | -0.0041814 | -4.49200e-04 | -4.0100e-05 |
dz[ 1 ] | 0.0900996 | 0.0029046 | 1.98300e-04 | 2.3100e-05 |
dz[ 2 ] | 0.9351368 | 0.0177067 | 1.31730e-03 | 1.6170e-04 |
p[ 1 ] | -0.0384759 | -0.0019671 | -1.90400e-04 | -1.9200e-05 |
p[ 2 ] | -0.0119591 | -0.0015342 | -1.72000e-04 | -1.5200e-05 |
p[ 3 ] | -0.0121365 | -0.0026324 | -2.75400e-04 | -2.5300e-05 |
lambda[ 1 ] | -0.0384759 | -0.0019671 | -1.90400e-04 | -1.9200e-05 |
lambda[ 2 ] | -0.0119591 | -0.0015342 | -1.72000e-04 | -1.5200e-05 |
lambda[ 3 ] | -0.0121365 | -0.0026324 | -2.75400e-04 | -2.5300e-05 |