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

Description Usage Arguments Details Value See Also Examples

View source: R/draw_latent_distribution.R

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

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
)

`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()` ... 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.

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

——————————————————————————————————

`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

—————————————————————————————————

* false alarms = False Positives = FP

* hits = True Positives = TP

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

draw_latent_signal_distribution()

## 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