%>>%                    Fit a model
AFROC                   AF*ROC* curve (alternative free-response *ROC*
                        curve)
AFROC_curve             FROC curve as an embedding map
Author_vs_classic_for_AUC
                        validation of AUC calculation
BayesianFROC            Theory of FROC Analysis via Bayesian Approaches
Chi_square_goodness_of_fit_in_case_of_MRMC_Posterior_Mean
                        Chi square statistic (goodness of fit) in the
                        case of MRMC at the pair of given data and each
                        MCMC sample
Close_all_graphic_devices
                        Close the Graphic Device
ConfirmConvergence      Check R hat criterion
Confirm_hit_rates_are_correctly_made_in_case_of_MRMC
                        Check whether each hit-rate is defined
                        correctly
CoronaVirus_Disease_2019
                        Who should be inspected?
CoronaVirus_Disease_2019_prevalence
                        Who should be inspected?
Credible_Interval_for_curve
                        Draw FROC curves which means credible interval.
DrawCurves              Draw FROC curves
DrawCurves_MRMC         Draw the FROC curves for all modalities and
                        readers
DrawCurves_MRMC_pairwise
                        Draw the FROC curves with Colour
DrawCurves_MRMC_pairwise_BlackWhite
                        Draw the FROC curves without colour
DrawCurves_MRMC_pairwise_col
                        Draw the FROC curves with Colour
DrawCurves_srsc         Draw the FROC curves
Draw_AUC                Draw the Region of AUC of AFROC
Draw_a_prior_sample     Draw One Sample from Prior
Draw_a_simulated_data_set
                        Draw a simulated dataset from model
                        distributions with specified parameters from
                        priors
Draw_a_simulated_data_set_and_Draw_posterior_samples
                        Draw a dataset and MCMC samples
Draw_an_area_of_AUC_for_srsc
                        Draw a Region of the area under the AFROC curve
Empirical_FROC_via_ggplot
                        Empirical FROC curve via ggplot2
FROC_curve              FROC curve as an embedding map
Phi                     The Cumulative distribution function Phi(x) of
                        the Standard Gaussian, namely, mean = 0 and
                        variance =1.
Phi_inv                 Inverse function of the Cumulative distribution
                        function Phi(x) of the Standard Gaussian.
                        where x is a real number.
ROC_curve               Title
ROC_data_creator        Synthesize ROC data
ROC_data_creator2       Synthesize ROC data
R_hat_max               Max R hat
Simulation_Based_Calibration_histogram
                        Draw a histogram of the rank statistics
Simulation_Based_Calibration_single_reader_single_modality_via_rstan_sbc
                        Simulation Based Calibration (SBC) for a single
                        reader and a single modality case
Simulation_Based_Calibration_via_rstan_sbc_MRMC
                        Simiulation Based Calibration (SBC) for a
                        single reader and a single modality case
Stan_code_validation    stan code
StatisticForANOVA       Statistic for ANOVA
TRUE.Counter.in.vector
                        Count 'TRUE' in a Vector whose components are
                        all Logical R objects
Test_Null_Hypothesis_that_all_modalities_are_same
                        Test the Null hypothesis that all modalities
                        are same
argMax                  Arg Max: Extract a subscript corresponding
                        component is a max
argMin                  Arg Min: Extract a subscript corresponding
                        component is a minimal
array_easy_example      Example array
array_of_hit_and_false_alarms_from_vector
                        Array of hits and false alarms; 2019 Jun 18
caseID_m_q_c_vector_from_NI_M_Q_C
                        Creats vectors: 'm,q,c' from integers: 'M,Q,C'
check_hit_is_less_than_NL
                        Chech total hit is less than NL for each reader
                        and each modality
check_rhat              Diagnosis of MCMC sampling
chi_square_at_replicated_data_and_MCMC_samples_MRMC
                        chi square at replicated data drawn (only one
                        time) from model with each MCMC samples.
chi_square_goodness_of_fit
                        _*Chi square goodness of fit statistics*_ at
                        each MCMC sample w.r.t. a given dataset.
chi_square_goodness_of_fit_from_input_all_param
                        Calculates the Goodness of Fit (Chi Square)
chi_square_goodness_of_fit_from_input_all_param_MRMC
                        Chi square in the case of MRMC at a given
                        dataset and a given parameter.
clearWorkspace          Clear Work Space
color_message           message with colored item
compare                 model comparison
comparison              model comparison
compile_all_models_in_pkg_BayesianFROC
                        Compile all stanfiles in pkg BayesianFROC
create_dataList_MRMC    Creates a _Single_ Dataset in Case of MRMC
create_dataset          Creates a dataset
d                       Data: A Single Reader and A Single Modality
dark_theme              Dark Theme
data.MultiReaderMultiModality
                        Multiple reader and Multiple modality data
data.SingleReaderSingleModality
                        Data: A Single Reader and A Single Modality
data.bad.fit            Data: Single reader and Single modality
data.hier.ficitious     Multiple reader and Multiple modality data
data.nonconverge.srsc   *Non-Convergent* Data: Single reader and Single
                        modality
dataList.Chakra.1       Data: A Single Reader and A Single Modality
dataList.Chakra.1.with.explantation
                        Data: A Single Reader and A Single Modality
dataList.Chakra.2       Data: A Single Reader and A Single Modality
dataList.Chakra.3       Data: A Single Reader and A Single Modality
dataList.Chakra.4       Data: A Single Reader and A Single Modality
dataList.Chakra.Web     An FROC Data of Multiple-Reader and
                        Multiple-Modality
dataList.Chakra.Web.orderd
                        An FROC Data of Multiple-Reader and
                        Multiple-Modality
dataList.High           Data: Single reader and Single modality
dataList.Low            Data: Single reader and Single modality
dataList.divergent.transition.in.case.of.srsc
                        An FROC Dataset with *_Divergent Transitions_*
                        in case of A Single reader and A Single
                        modality
dataList.high.ability   Data: A Single Reader and A Single Modality
dataList.low.ability    Data: A Single Reader and A Single Modality
dataList.one.modality   dataset of Multiple reader and one modality
data_2modaities_2readers_3confidence
                        data: 2 readers, 2 modalities and 3
                        confideneces
data_generate_NaN_in_fit_with_iteration1111_seed1234
                        *NaN in samplings* A Single Reader and A Single
                        Modality
data_low_p_value        *low p-value = 0.012* Data: Single reader and
                        Single modality
data_much_low_p_value   *low p-value = 0.002* A Single Reader and A
                        Single Modality
data_of_36_readers_and_a_single_modality
                        36 readers and a sinle modality data
dataset_creator_by_specifying_only_M_Q
                        Creates dataset
dataset_creator_for_many_Readers
                        create data for MRMC
dataset_creator_new_version
                        Create a Dataset (version 2) Interactively
dcasewise               An casewised FROC Data of Multiple-Reader and
                        Multiple-Modality
dd                      Multiple Reader and Multiple Modality Data
dd.orderd               Multiple Reader and Multiple Modality Data
ddd                     Multiple reader and Multiple modality data
dddd                    One reader and Multiple modality data
ddddd                   Data of MRMC; Model * _ does _* converge.
dddddd                  Multiple reader and single modality data
ddddddd                 Multiple reader and 2 modalities data such that
                        all modalities have same AUC.
demo_Bayesian_FROC      demonstration
demo_Bayesian_FROC_without_pause
                        demonstration without pausing
draw.CFP.CTP.from.dataList
                        Plot the pairs of CFPs and CTPs
draw_ROC_Curve          Title
draw_ROC_Curve_from_fitted_model
                        Title
draw_latent_noise_distribution
                        Visualization of the Latent Gaussian for false
                        rates
draw_latent_signal_distribution
                        Visualization of Latent Gaussians ( Signal
                        Distribution)
dz                      Threshold: parameter of an MRMC model
error_MRMC              Comparison of Estimates and Truth in case of
                        MRMC
error_message           Error Message for Data Format
error_message_on_imaging_device_rhat_values
                        Error message *on a plot plane* (imaging
                        device)
error_srsc              Validation via replicated datasets from a model
                        at a given model parameter
error_srsc_error_visualization
                        Visualization for Error of Estimator
error_srsc_variance_visualization
                        Visualization Of variance Analysis
explanation_about_package_BayesianFROC
                        Explanation of this package
explanation_for_what_curves_are_drawn
                        Print out about what curves are drawn
extractAUC              Extract AUC
extract_EAP_CI          Extracts Estimates as vectors from stanfit
                        objects
extract_EAP_by_array    Extract Etimates Preserving Array Format.
extract_data_frame_from_dataList_MRMC
                        Extract sub data frame from list of FROC data
extract_data_frame_from_dataList_srsc
                        extract data frame from datalist in case of
                        srsc
extract_estimates_MRMC
                        MRMC: Extract All Posterior Mean Estimates from
                        stanfitExtended object
extract_parameters_from_replicated_models
                        Extract Estimates From Replicated MRMC Model
false_and_its_rate_creator
                        False Alarm Creator for both cases of MRMC and
                        srsc
false_and_its_rate_creator_MRMC
                        MRMC: False Alarm Creator For each Modality and
                        each Reader.
fffaaabbb               Package Development tools and memo.
file_remove             Execute before submission to delete redandunt
                        files.
fit_Bayesian_FROC       Fit a model to data
fit_GUI                 Fit with GUI via Shiny
fit_GUI_MRMC            Fit with GUI via Shiny in case of MRMC
fit_GUI_MRMC_new        Fit an MRMC model to data with Shiny GUI
fit_GUI_ROC             Fit (very bad, MCMC not converge) ROC model
                        with GUI via Shiny
fit_GUI_Shiny           Fit a model with GUI of Shiny
fit_GUI_Shiny_MRMC      Fit with GUI via Shiny (in case of MRMC)
fit_GUI_dashboard       Fit with GUI via Shiny (Simple version)
fit_GUI_simple_from_apppp_file
                        Fit with GUI via Shiny
fit_MRMC                Fit and Draw the FROC models (curves)
fit_MRMC_casewise       Fit and Draw the FROC models (curves)
fit_MRMC_versionTWO     Fit and Draw the FROC models (curves) version2.
fit_Null_hypothesis_model_to_
                        Fit the null model
fit_a_model_to          Fit a model to data
fit_srsc                fit a model to data in the case of A Single
                        reader and A Single modality (srsc).
fit_srsc_ROC            fit a model to data in the case of A Single
                        reader and A Single modality (srsc).
flat_one_par            Makes array names
flatnames               from rstan package
foo                     without double quote
foo_of_a_List_of_Arrays
                        Apply functions by each Array in a list
fooo                    taboo or
from_array_to_vector    Transform from an * _array_* to a * _vector_*
get_posterior_variance
                        Alternative of 'rstan::get_posterior_mean()'
get_samples_from_Posterior_Predictive_distribution
                        Synthesizes Samples from Predictive Posterior
                        Distributions (PPD).
get_treedepth_threshold
                        get treedepth threshold
ggplotFROC              Draw FROC curves by two parameters a and b
ggplotFROC.EAP          Draw FROC curves by two parameters a and b
give_name_srsc_CFP_CTP_vector
                        Give a Name For CTP CFP vector
give_name_srsc_data     Give a name for srsc data list component
hit_generator_from_multinomial
                        Under Const
hit_rate_adjusted_from_the_vector_p
                        hit rate adjusted from a vector p
hits_creator_from_rate
                        MRMC Dataset Creator From Hit Rate.
hits_false_alarms_creator_from_thresholds
                        Hits and False Alarms Creator
hits_from_thresholds    MRMC Hit Creator from thresholds, mean and S.D.
hits_rate_creator       MRMC Hit Rates Creator from Thresholds, Mean
                        and S.D.
horizontal_from_vertical_in_each_case
                        Transfer From Vertical placement into
                        Horizontal placement for casewise vectors
initial_values_specification_for_stan_in_case_of_MRMC
                        Initial values for HMC (Hamiltonian Moncte
                        Carlo Markov Chains)
install_imports         Installer.
inv_Phi                 Inverse function of the Cumulative distribution
                        function Phi(x) of the Standard Gaussian.
                        where x is a real number.
is_length_zero          Is argument of length zero ?
is_logical_0            is.logical(0)
is_na_in_vector         Detect NA in a vector
is_na_list              Check whether a list contains NA or not.
is_stanfitExtended      Check whether class is _stanfitExtended_ for
                        any R object
m_q_c_vector_from_M_Q_C
                        Creats vectors: 'm,q,c' from integers: 'M,Q,C'
make_TeX                Make a TeX file for summary
make_true_parameter_MRMC
                        Make a true model parameter and include it in
                        this package
metadata_srsc_per_image
                        Create metadata for MRMC data.
metadata_to_DrawCurve_MRMC
                        Create metadata for MRMC data
metadata_to_fit_MRMC    Create metadata for MRMC data
metadata_to_fit_MRMC_casewise
                        Create metadata for MRMC data
mu                      Mean of signal: parameter of an MRMC model
mu_truth                Mean of signal: parameter of an MRMC model
mu_truth_creator_for_many_readers_MRMC_data
                        mu of MRMC model paramter
name_of_param_whose_Rhat_is_maximal
                        Extract a name of parameter from
                        StanfitExtended object (or stanfit object.)
names_argMax            Extract name from a real vector whose component
                        is the maximal one
p                       Hit Rate: parameter of an MRMC model
p_truth                 Hit Rate: parameter of an MRMC model
p_value_of_the_Bayesian_sense_for_chi_square_goodness_of_fit
                        P value for goodness of fit : No longer used in
                        2019 Oct
pairs_plot_if_divergent_transition_occurred
                        Pairs plot for divergent transition
pause                   Pause for Demo
plot,stanfitExtended,missing-method
                        A generic function 'plot()'
plotFROC                Draw FROC curves by two parameters a and b
plot_FPF_TPF_via_dataframe_with_split_factor
                        Scatter Plot of FPFs and TPFs via Splitting
                        Factor
plot_FPF_and_TPF_from_a_dataset
                        Plot FPF and TPF from MRMC data
plot_ROC_empirical_curves
                        Empirical ROC curve
plot_curve_and_hit_rate_and_false_rate_simultaneously
                        Curve and signal distribution and noise d log
                        Phi() for a single reader and a single modality
plot_dataset_of_ppp     plot datasets using calculation of ppp
plot_dataset_of_ppp_MRMC
                        plot datasets using calculation of ppp
plot_empirical_FROC_curves
                        Plot empirical FROC Curves by traditional ways
                        of 'ggplot2'
plot_test               # Definition of a method for the inherited
                        class stanfitExtended from stanfit
pnorm_or_qnorm          pnorm or qnorm
print,stanfitExtended-method
                        A method for a generic function 'print()' for
                        class "'stanfitExtended'"
print_minimal_reproducible_code_in_case_of_MRMC
                        Show minimal code in MRMC
print_stanfitExtended   Definition of a method for the inherited class
                        stanfitExtended from stanfit
priorResearch           Research for Prior
prior_predictor         Predict some estimates of parameter
prior_print_MRMC        Print What Prior Are Used
prior_print_srsc        Print What Prior Are Used
rank_statistics_with_two_parameters
                        Rank Statistics
replicate_MRMC_dataList
                        MRMC: Replicates Datasets From Threshold, Mean
                        and S.D.
replicate_model_MRMC    Replicate Models
sbcc                    SBC
seq_array_ind           Makes a Matrix from a vector of itegers
showGM                  the Graphical Model via PKG 'DiagrammeR' for
                        the case of a single reader and a single
                        modality
show_codes_in_my_manuscript
                        Show R codes used in my manuscript
size_of_return_value    Size of R object
small_margin            Margin
snippet_for_BayesianFROC
                        Edit Snippet
sortAUC                 Prints a Ranking for AUCs for MRMC Data
stan_model_of_sbc       Creates an object of class stanfit of SBC
stan_trace_of_max_rhat
                        a trace plot for a paramter whose R hat is
                        largest
stanfitExtended         'stanfitExtended', an S4 class inherited from
                        the S4 class *_'stanfit'_*
stanfit_from_its_inherited_class
                        Chage S4 class to stanfit
summarize_MRMC          Summarize the estimates for MRMC case
summary_EAP_CI_srsc     Summary
the_row_number_of_logical_vector
                        Extract the row number from a logical vector
trace_Plot              Trace plot
v                       Standard Deviation: parameter of an MRMC model
v_truth                 Standard Deviation: parameter of an MRMC model
v_truth_creator_for_many_readers_MRMC_data
                        v of MRMC model paramter
validation.dataset_srsc
                        Errors of Estimator for any Given true
                        parameter
validation.draw_srsc    Draw Curves for validation dataset
vertical_from_horizontal_in_each_case
                        Transfer From Horizontal placement into
                        Vertical placement for casewise vectors
viewdata                Build a table of FROC data
viewdata_MRMC           View MRMC data
viewdata_MRMC_casewise
                        View MRMC data
viewdata_srsc           Build a table of data in the case of A Single
                        reader and A Single modality (srsc)
waic                    WAIC Calculator
z                       Threshold: parameter of an MRMC model
z_from_dz               Thresholds from its difference
z_truth                 Threshold : parameter of an MRMC model
