Validation for a Single Reader and Single Modality case via p value of Bayesian sence

Issei Tsunoda

2019-05-04

p value

In this vignettes, we explain the p value of the chi square goodness of fit statistics for Bayesian version. In classical p values are calculated by data using fixed parameter, e.g., such as maximal likelihood estimates. However, in Bayesian context, the parameter of model is not deterministic, so, the p values in Bayesian context also depend on the parameter of model. To obtain the p values in deterministic way in Bayesian context, we integrate a p values by the posterior predictive distribution. The posterior predictive distribution is defined by the posterior mean of the likelihood. For the detail, please see the Gelman’s book “ Bayesian Data Analysis”.

The package BayesianFROC implement the calculation of the posterior probability p value for the chi square goodness of fit statistics for a single reader and single modality FROC model.

In this vignette, we explain how to run the function which calculate the posterior predictive p value.

First, user should prepare a single reader and single modality data. And using this data, we get the object from fitting by running the function.

Second, using this object, we run the function which calculate the posterior predictive p value. So all we have to do is simple, that is, merely run only two functions.

The resulting outputs contained p values. Also the replicated data and the plot for replicated data are available.

Example Code to Calculate the Posterior Predictive P value


# Prepare a dataset
dat <- BayesianFROC::dataList.Chakra.1


# Fitting
fit <- BayesianFROC::fit_Bayesian_FROC(dat)


# Calculation of the P value 
p_value_of_the_Bayesian_sense_for_chi_square_goodness_of_fit(fit)

Outputs

In the graphic devices, the replicated data from the posterior predictive distribution are drawn when user run the function.

This replicated data means cumulative hits and false alarms pre lesions or images. So user see how the FROC data is distributed from the true distribution.