# FROC Analysis by Bayesian Approaches

## Documentation for package ‘BayesianFROC’ version 1.0.0

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Code demos. Use demo() to run them.

## Help Pages

A B C D E F G H I M N P R S T V W Z misc

## -- A --

AFROC | AF*ROC* curve (alternative free-response *ROC* curve)
AFROC_curve | FROC curve as an embedding map
argMax | Arg Max: Extract a subscript corresponding component is a max
argMin | Arg Min: Extract a subscript corresponding component is a minimal
array | Transform from an * _array_* to a * _vector_*
array_easy_example | Example array
array_of_hit_and_false_alarms_from_vector | Array of hits and false alarms; 2019 Jun 18
Author_vs_classic_for_AUC | validation of AUC calculation

## -- B --

BayesianFROC | Theory of FROC Analysis via Bayesian Approaches

## -- C --

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.
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
clearWorkspace | Clear Work Space
Close_all_graphic_devices | Close the Graphic Device
color_message | message with colored item
compare | model comparison
comparison | model comparison
compile_all_models_in_pkg_BayesianFROC | Compile all stanfiles in pkg BayesianFROC
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?
create_dataList_MRMC | Creates a _Single_ Dataset in Case of MRMC
create_dataset | Creates a dataset
Credible_Interval_for_curve | Draw FROC curves which means credible interval.

## -- D --

d | Data: A Single Reader and A Single Modality
dark_theme | Dark Theme
data.bad.fit | Data: Single reader and Single modality
data.hier.ficitious | Multiple reader and Multiple modality data
data.MultiReaderMultiModality | Multiple reader and Multiple modality data
data.nonconverge.srsc | *Non-Convergent* Data: Single reader and Single modality
data.SingleReaderSingleModality | Data: A Single Reader and A 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.divergent.transition.in.case.of.srsc | An FROC Dataset with *_Divergent Transitions_* in case of A Single reader and A Single modality
dataList.High | Data: Single reader and Single modality
dataList.high.ability | Data: A Single Reader and A Single Modality
dataList.Low | Data: Single reader and Single modality
dataList.low.ability | Data: A Single Reader and A Single Modality
dataList.one.modality | dataset of Multiple reader and one modality
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
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
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
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_an_area_of_AUC_for_srsc | Draw a Region of the area under the AFROC curve
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_latent_noise_distribution | Visualization of the Latent Gaussian for false rates
draw_latent_signal_distribution | Visualization of Latent Gaussians ( Signal Distribution)
draw_ROC_Curve | Title
draw_ROC_Curve_from_fitted_model | Title
dz | Threshold: parameter of an MRMC model

## -- E --

Empirical_FROC_via_ggplot | Empirical FROC curve via ggplot2
error_message | Error Message for Data Format
error_message_on_imaging_device_rhat_values | Error message *on a plot plane* (imaging device)
error_MRMC | Comparison of Estimates and Truth in case of MRMC
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_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_EAP_by_array | Extract Etimates Preserving Array Format.
extract_EAP_CI | Extracts Estimates as vectors from stanfit objects
extract_estimates_MRMC | MRMC: Extract All Posterior Mean Estimates from stanfitExtended object
extract_parameters_from_replicated_models | Extract Estimates From Replicated MRMC Model

## -- F --

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_a_model_to | Fit a model to data
fit_Bayesian_FROC | Fit a model to data
fit_GUI | Fit with GUI via Shiny
fit_GUI_dashboard | Fit with GUI via Shiny (Simple version)
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_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_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).
flatnames | from rstan package
flat_one_par | Makes array names
foo | without double quote
fooo | taboo or
foo_of_a_List_of_Arrays | Apply functions by each Array in a list
FROC_curve | FROC curve as an embedding map
from_array_to_vector | Transform from an * _array_* to a * _vector_*

## -- G --

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

## -- H --

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.
hit_generator_from_multinomial | Under Const
hit_rate_adjusted_from_the_vector_p | hit rate adjusted from a vector p
horizontal_from_vertical_in_each_case | Transfer From Vertical placement into Horizontal placement for casewise vectors

## -- I --

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 --

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
m_q_c_vector_from_M_Q_C | Creats vectors: 'm,q,c' from integers: 'M,Q,C'

## -- N --

names_argMax | Extract name from a real vector whose component is the maximal one
name_of_param_whose_Rhat_is_maximal | Extract a name of parameter from StanfitExtended object (or stanfit object.)

## -- P --

p | Hit Rate: parameter of an MRMC model
pairs_plot_if_divergent_transition_occurred | Pairs plot for divergent transition
pause | Pause for Demo
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.
plot-method | A generic function 'plot()'
plotFROC | Draw FROC curves by two parameters a and b
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_FPF_and_TPF_from_a_dataset | Plot FPF and TPF from MRMC data
plot_FPF_TPF_via_dataframe_with_split_factor | Scatter Plot of FPFs and TPFs via Splitting Factor
plot_ROC_empirical_curves | Empirical ROC curve
plot_test | # Definition of a method for the inherited class stanfitExtended from stanfit
pnorm_or_qnorm | pnorm or qnorm
print-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
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

## -- R --

rank_statistics_with_two_parameters | Rank Statistics
replicate_model_MRMC | Replicate Models
replicate_MRMC_dataList | MRMC: Replicates Datasets From Threshold, Mean and S.D.
ROC_curve | Title
ROC_data_creator | Synthesize ROC data
ROC_data_creator2 | Synthesize ROC data
R_hat_max | Max R hat

## -- S --

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
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
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
stanfitExtended | 'stanfitExtended', an S4 class inherited from the S4 class *_'stanfit'_*
stanfit_from_its_inherited_class | Chage S4 class to stanfit
Stan_code_validation | stan code
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
StatisticForANOVA | Statistic for ANOVA
summarize_MRMC | Summarize the estimates for MRMC case
summary_EAP_CI_srsc | Summary

## -- T --

Test_Null_Hypothesis_that_all_modalities_are_same | Test the Null hypothesis that all modalities are same
the_row_number_of_logical_vector | Extract the row number from a logical vector
to | Transform from an * _array_* to a * _vector_*
trace_Plot | Trace plot
TRUE.Counter.in.vector | Count 'TRUE' in a Vector whose components are all Logical R objects

## -- V --

v | Standard Deviation: parameter of an MRMC model
validation.dataset_srsc | Errors of Estimator for any Given true parameter
validation.draw_srsc | Draw Curves for validation dataset
vector | Transform from an * _array_* to a * _vector_*
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)
v_truth | Standard Deviation: parameter of an MRMC model
v_truth_creator_for_many_readers_MRMC_data | v of MRMC model paramter

## -- W --

waic | WAIC Calculator

## -- Z --

z | Threshold: parameter of an MRMC model
z_from_dz | Thresholds from its difference
z_truth | Threshold : parameter of an MRMC model

## -- misc --

%>>% | Fit a model
====== | A generic function 'plot()'