ppp_MRMC

An S4 object of class <code> <a rd-options="" href="/link/stanfitExtended?package=BayesianFROC&version=0.2.1" data-mini-rdoc="BayesianFROC::stanfitExtended">stanfitExtended</a></code> which is an inherited class from the S4 class <code><a rd-options="rstan" href="/link/stanfit?package=BayesianFROC&version=0.2.1&to=rstan" data-mini-rdoc="rstan::stanfit">stanfit</a></code>. This R object can be passed to the <code><a rd-options="" href="/link/DrawCurves?package=BayesianFROC&version=0.2.1" data-mini-rdoc="BayesianFROC::DrawCurves">DrawCurves</a>()</code>, <code><a rd-options="" href="/link/ppp?package=BayesianFROC&version=0.2.1" data-mini-rdoc="BayesianFROC::ppp">ppp</a>()</code> and ... etc

StanS4class

Logical: <code>TRUE</code> of <code>FALSE</code>. Whether to print the verbose summary, i.e., logical; If <code>TRUE</code> then verbose summary is printed in the R console. If <code>FALSE</code>, the output is minimal. I regret, this variable name should be verbose.

summary

A positive integer, representing $J$ in the following notation.
Now, I think all I needed is love! ttu ttu tututu Love is all I need.
Suppose that $$\theta_1, \theta_2, \theta_3,...,\theta_n$$ is drawn from posterior $\pi(\theta|D)$ of given data $D$.
Let $y_1,y_2,...,y_n$ be samples drawn from$$y_1 \sim likelihood ( . |\theta_1), $$
$$y_2 \sim likelihood ( . |\theta_2),$$
$$y_3 \sim likelihood ( .|\theta_3),$$
$$...,$$
$$y_n \sim likelihood ( . |\theta_N),$$
Then the list of return values retains the following:<dl class="dl-horizontal">
<dt> <code>chisq_at_observed_data</code> </dt><dd>$$\chi (D|\theta_1), \chi (D|\theta_2), \chi (D|\theta_3),...,\chi (D|\theta_n),$$</dd>
<dt> <code>chisq_not_at_observed_data</code> </dt><dd>$$\chi (y_1|\theta_1), \chi (y_2|\theta_2), \chi (y_3|\theta_3),...,\chi (y_n|\theta_n), $$</dd>
<dt> <code>Logical</code> </dt><dd>The i-th component is a logical vector indicating whether $$\chi (y_2|\theta_2) &gt; \chi (D|\theta_2)$$ is satisfied or not. Oppai ga Ippai. If <code>TRUE</code>, then the inequality holds.</dd>
<dt> <code>p.value</code> </dt><dd>From the component <code>Logical</code>, we calculate the so-called Posterior Predictive P value. Note that the author hate this notion!! I hate it!! Akkan Beeeee!!!</dd>
</dl>

replicate.number.from.model.for.each.MCMC.sample

PPP for chi square goodness of fit statistic

Execute BayesianFROC::fit_GUI_Shiny() (or fit_GUI_Shiny_MRMC()) for a graphical user interface via Shiny. The free-response receiver operating characteristic (FROC) method developed by Chakraborty is a generalization of receiver operating characteristic analysis, but Chakraborty used a non-Bayesian approach. This package aims to reconstruct Chakraborty's technique using a Bayesian approach and to verify that our models fit practical datasets. We also develop hierarchical Bayesian models for comparing modalities with new methods. The ultimate aim of FROC analysis is to compare observer performances, which means comparing characteristics, such as area under the curve (AUC) or figure of merit (FOM). In this package, we only use the notion of AUC for modality comparison, where by "modality", we mean imaging methods such as Magnetic Resonance Imaging (MRI), Computed Tomography (CT), Positron Emission Tomography (PET), ..., etc. So there is a problem that which imaging method is better to detect lesions from shadows in radiographs. To solve modality comparison issues, this package provides new methods using hierarchical Bayesian models proposed by the author of this package. Using this package, one can obtain at least one conclusion that which imaging methods are better for finding lesions in radiographs with the case of your data. Fitting FROC statistical models is sometimes not so good, it can easily confirm by drawing FROC curves and comparing these curves and the points constructed by False Positive fractions (FPFs) and True Positive Fractions (TPFs), we can validate the goodness of fit intuitively. Such validation is also implemented by the Chi square goodness of fit statistics in the Bayesian context which means that the parameter is not deterministic, thus by integrating it with the posterior predictive measure, we get a desired value. To compare modalities (imaging methods: MRI, CT, PET, ... , etc), we evaluate AUCs for each modality. FROC is developed by Dev Chakraborty, his FROC model in his 1989 paper relies on the maximal likelihood methodology. The author modified and provided the alternative Bayesian FROC model. Strictly speaking, his model does not coincide with models in this package. In FROC context, we means by multiple reader and multiple case (MRMC) the case of the number of reader or modality is two or more. The MRMC data is available for functions of this package. I hope that medical researchers use not only the frequentist method but also alternative Bayesian methods. In medical research, many problems are considered under only frequentist methods, such as the notion of p-values. But p-value is sometimes misunderstood. Bayesian methods provide very simple, direct, intuitive answer for research questions. Combining frequentist methods with Bayesian methods, we can obtain more reliable answer for research questions. Please execute the following R scripts from the R (R studio) console, demo(demo_MRMC, package = "BayesianFROC"); demo(demo_srsc, package = "BayesianFROC"); demo(demo_stan, package = "BayesianFROC"); demo(demo_drawcurves_srsc, package = "BayesianFROC"); demo_Bayesian_FROC(); demo_Bayesian_FROC_without_pause(). References: Dev Chakraborty (1989) <doi:10.1118/1.596358> Maximum likelihood analysis of free - response receiver operating characteristic (FROC) data. Pre-print: Issei Tsunoda; Bayesian Models for free-response receiver operating characteristic analysis. See the vignettes for more details.

Issei Tsunoda

BayesianFROC

FROC Analysis by Bayesian Approaches

ppp_MRMC function

An S4 object of class <code> <a rd-options='' href='stanfitExtended'>stanfitExtended</a></code> which is an inherited class from the S4 class <code><a rd-options='rstan' href='stanfit'>stanfit</a></code>. This R object can be passed to the <code><a rd-options='' href='DrawCurves'>DrawCurves</a>()</code>, <code><a rd-options='' href='ppp'>ppp</a>()</code> and ... etc

A positive integer, representing $J$ in the following notation.
Now, I think all I needed is love! ttu ttu tututu Love is all I need.
Suppose that $$\theta_1, \theta_2, \theta_3,...,\theta_n$$ is drawn from posterior $\pi(\theta|D)$ of given data $D$.
Let $y_1,y_2,...,y_n$ be samples drawn from

$$y_1 \sim likelihood ( . |\theta_1), $$
$$y_2 \sim likelihood ( . |\theta_2),$$
$$y_3 \sim likelihood ( .|\theta_3),$$
$$...,$$
$$y_n \sim likelihood ( . |\theta_N),$$


Then the list of return values retains the following:<dl class='dl-horizontal'>
<dt> <code>chisq_at_observed_data</code> </dt><dd>$$\chi (D|\theta_1), \chi (D|\theta_2), \chi (D|\theta_3),...,\chi (D|\theta_n),$$</dd>
<dt> <code>chisq_not_at_observed_data</code> </dt><dd>$$\chi (y_1|\theta_1), \chi (y_2|\theta_2), \chi (y_3|\theta_3),...,\chi (y_n|\theta_n), $$</dd>
<dt> <code>Logical</code> </dt><dd>The i-th component is a logical vector indicating whether $$\chi (y_2|\theta_2) &gt; \chi (D|\theta_2)$$ is satisfied or not. Oppai ga Ippai. If <code>TRUE</code>, then the inequality holds.</dd>
<dt> <code>p.value</code> </dt><dd>From the component <code>Logical</code>, we calculate the so-called Posterior Predictive P value. Note that the author hate this notion!! I hate it!! Akkan Beeeee!!!</dd>
</dl>

ppp_MRMC: MRMC: Posterior Predictive P value (PPP) for MRMC,

Description

Usage

Arguments

Value

Details

Examples