draw_latent_signal_distribution: Visualization of Latent Gaussians ( Signal Distribution)
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 the parameter of the latent function, i.e. the normal distribution denoted by Gaussian(z|μ,σ) with posterior mean estimates of its mean μ and standard deviation σ.

draw_latent_signal_distribution(
  StanS4class,
  dark_theme = TRUE,
  dig = 3,
  mesh = 1000,
  new.imaging.device = TRUE,
  hit.rate = TRUE,
  false.alarm.rate = FALSE,
  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 positive integer, indicating the digit for numbers in the R console.
`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 hit rates. That is, each hit rate is defined as follows;

p_5(z_1,...z_C; μ, σ) = \int_{z5}^{∞} Gaussian(z|μ,σ)dz

p_4(z_1,...z_C; μ, σ) = \int_{z4}^{z5} Gaussian(z|μ,σ)dz

p_3(z_1,...z_C; μ, σ) = \int_{z3}^{z4} Gaussian(z|μ,σ)dz

p_2(z_1,...z_C; μ, σ) = \int_{z2}^{z3} Gaussian(z|μ,σ)dz

p_1(z_1,...z_C; μ, σ) = \int_{z1}^{z2} Gaussian(z|μ,σ)dz

For example, in the following data, the number of hit data with the most highest confidence level 5 is regarded as an sample from the Binomial distribution of hit rate p_5(z_1,...z_C; μ, σ) = \int_{z5}^{∞} Gaussian(z|μ,σ)dz with Bernoulli trial number is NL=142.

So, this Gaussian distribution determines hit rate, and this function draw_latent_signal_distribution() plot this Gaussian distribution Gaussian(z|μ,σ). And a reference distribution is the standard Gaussian and do not confuse that it is not the noise distribution, but only reference.

The noise distribution (denoted by d \log Φ) determines the False alarm rates in the similar manner and plotted by using a line of dots. The author thinks the standard Gaussian is more comfortable to compare or confirm the shape of Gaussian(z|μ,σ) and thus, the author implement it in the draw_latent_signal_distribution().

One would want to see the signal distribution and noise distribution simultaneously, then use the function draw_latent_noise_distribution().

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

draw_latent_noise_distribution() Note that the difference of draw_latent_noise_distribution() and draw_latent_signal_distribution() is that the lator use the standard Gaussian for the reference distribution and former uses the d \log Φ() for the reference distribution.

So, the old version draw_latent_signal_distribution() is also important and I like this old version also. Anyway who read this, I think my package size is very large,....ha,,,,I have to reduce it,....but how?

## 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 data examples, one 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)




#--------------------------------------------------------------------------------------
#                         2)      For submission (without color)
#--------------------------------------------------------------------------------------





     fit <-    fit_Bayesian_FROC(
                                 dataList = dataList.Chakra.1.with.explantation
                                 )




# With legends


     draw_latent_signal_distribution(fit,
                   dark_theme  = FALSE,
                   color = TRUE,
                   density = 11
                   )



#' Without legends
draw_latent_signal_distribution(fit,
                                dark_theme           = FALSE,
                                color               = TRUE,
                                mathmatical.symbols = FALSE
)
             # 2019 Sept. 5
             # 2020 March 12



     Close_all_graphic_devices() # 2020 August


## End(Not run)# dottest