# draw_latent_noise_distribution: Visualization of the Latent Gaussian for false rates In BayesianFROC: FROC Analysis by Bayesian Approaches

## Description

Plot the posterior mean of model parameter θ and and the latent function, i.e. the differential logarithmic Gaussian d \log Φ(z).

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 draw_latent_noise_distribution( StanS4class, dark_theme = TRUE, dig = 3, mesh = 1000, new.imaging.device = TRUE, hit.rate = FALSE, false.alarm.rate = TRUE, both.hit.and.false.rate = FALSE, density = 22, color = TRUE, mathmatical.symbols = TRUE, type = 3, summary = FALSE ) 

## Arguments

 StanS4class An S4 object of class  stanfitExtended which is an inherited class from the S4 class stanfit. This R object is a fitted model object as a return value of the function fit_Bayesian_FROC(). To be passed to DrawCurves(), ppp() and ... etc dark_theme TRUE or FALSE dig A variable to be passed to the function rstan::sampling() of rstan in which it is named ...??. A positive integer representing the Significant digits, used in stan Cancellation. Default = 5, mesh Mesh for painting the area new.imaging.device Logical: TRUE of FALSE. If TRUE (default), then open a new device to draw curve. Using this we can draw curves in same plain by new.imaging.device=FALSE. hit.rate whether draws it. Default is TRUE. false.alarm.rate whether draws it. Default is TRUE. both.hit.and.false.rate whether draws it. Default is TRUE. density A natural number, indicating the density of shading lines, in lines per inch. color A color region is selected from black and white only. For more colors, put FALSE. For publication, the mono color is allowed in many case, so the author made this for such publication. mathmatical.symbols A logical, whether legend is in plot. type An integer, for the color of background and etc. summary Logical: TRUE of FALSE. Whether to print the verbose summary. If TRUE then verbose summary is printed in the R console. If FALSE, the output is minimal. I regret, this variable name should be verbose.

## Details

Our FROC model use a latent Gaussian random variable to determine false rates which are defined as follows;

q_5(z_1,...z_C) = \int_{z5}^{∞} d \log Φ(z)dz

q_4(z_1,...z_C) = \int_{z4}^{z5} d \log Φ(z)dz

q_3(z_1,...z_C) = \int_{z3}^{z4} d \log Φ(z)dz

q_2(z_1,...z_C) = \int_{z2}^{z3} d \log Φ(z)dz

q_1(z_1,...z_C) = \int_{z1}^{z2} d \log Φ(z)dz

For example, in the following data, the number of false alarm data with confidence level 5 41 which is considered as an sample from the Poisson distribution of its rate

q_5(z_1,...z_C) = \int_{z5}^{∞} d \log Φ(z)dz

So, this Gaussian distribution determines false rate, and this function draw_latent_noise_distribution() plot this Gaussian distribution d \log Φ and the density Gaussian(z|μ,σ) is also plotted to compare hit rates and false rates. thus, the author implement it in the draw_latent_signal_distribution(),

Example data:

A single reader and single modality case

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 NI=63,NL=124 confidence level No. of false alarms No. of hits In R console ->  c f  h ----------------------- ----------------------- ----------------------------- ------------- definitely present 5 1 41 probably present 4 2 22 equivocal 3 5 14 subtle 2 11 8 very subtle 1 13 1

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* false alarms = False Positives = FP

* hits = True Positives = TP

## Value

Information of Latent Gaussians, such as mean and S.D. of the signal distributions and thresholds.

draw_latent_signal_distribution()
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ## Not run: #======================================================================================== # Shape of signal distribution strongly influences the value of AUC, so in the following # the author shows how it affects the estimates of AUCs. # We consider two dataset, one of which is a low AUC and the other is a high AUC. # In the high AUC case, the Signal Gaussain will be low variance and # in the low AUC case, the variance will desperse. 2019 August 4, 2019 Dec 17 #======================================================================================== # ----- High AUC case -------- viewdata(dataList.High) fit.High <- fit_Bayesian_FROC(dataList.High,ite=111) draw_latent_signal_distribution(fit.High) # ----- Low AUC case -------- viewdata(dataList.Low) fit.Low <- fit_Bayesian_FROC(dataList.Low) draw_latent_signal_distribution(fit.Low) Close_all_graphic_devices() # 2020 August ## End(Not run)# dottest