Package 'qch' reference manual

Title:	Query Composite Hypotheses
Description:	Provides functions for the joint analysis of Q sets of p-values obtained for the same list of items. This joint analysis is performed by querying a composite hypothesis, i.e. an arbitrary complex combination of simple hypotheses, as described in Mary-Huard et al. (2021) <doi:10.1093/bioinformatics/btab592> and De Walsche et al.(2023) <doi:10.1101/2024.03.17.585412>. In this approach, the Q-uplet of p-values associated with each item is distributed as a multivariate mixture, where each of the 2^Q components corresponds to a specific combination of simple hypotheses. The dependence between the p-value series is considered using a Gaussian copula function. A p-value for the composite hypothesis test is derived from the posterior probabilities.
Authors:	Tristan Mary-Huard [aut, cre] , Annaig De Walsche [aut] , Franck Gauthier [ctb]
Maintainer:	Tristan Mary-Huard <[email protected]>
License:	GPL-3
Version:	2.0.0
Built:	2024-11-25 06:37:24 UTC
Source:	CRAN

Gaussian copula density for each Hconfiguration.

Description

Gaussian copula density for each Hconfiguration.

Usage

Copula.Hconfig_gaussian_density(Hconfig, F0Mat, F1Mat, R)
Copula.Hconfig_gaussian_density(Hconfig, F0Mat, F1Mat, R)

Arguments

`Hconfig`	A list of all possible combination of H0 and H1 hypotheses generated by the `GetHconfig()` function.
`F0Mat`	a matrix containing the evaluation of the marginal cdf under H0 at each items, each column corresponding to a p-value serie.
`F1Mat`	a matrix containing the evaluation of the marginal cdf under H1 at each items, each column corresponding to a p-value serie.
`R`	the correlation matrix.

Value

A matrix containing the evaluation of the Gaussian density function for each Hconfiguration in columns.

EM calibration in the case of the gaussian copula (unsigned)

Description

EM calibration in the case of the gaussian copula (unsigned)

Usage

EM_calibration_gaussian(
  Hconfig,
  F0Mat,
  F1Mat,
  fHconfig,
  R.init,
  Prior.init,
  Precision = 1e-06
)
EM_calibration_gaussian(
  Hconfig,
  F0Mat,
  F1Mat,
  fHconfig,
  R.init,
  Prior.init,
  Precision = 1e-06
)

Arguments

`Hconfig`	A list of all possible combination of H0 and H1 hypotheses generated by the `GetHconfig()` function.
`F0Mat`	a matrix containing the evaluation of the marginal cdf under H0 at each items, each column corresponding to a p-value serie.
`F1Mat`	a matrix containing the evaluation of the marginal cdf under H1 at each items, each column corresponding to a p-value serie.
`fHconfig`	a matrix containing config densities evaluated at each items, each column corresponding to a configurations.
`R.init`	the initialization of the correlation matrix of the gaussian copula parameter.
`Prior.init`	the initialization of prior probabilities for each of the H-configurations.
`Precision`	Precision for the stop criterion. (Default is 1e-6)

Value

A list of 2 objects 'priorHconfig' and 'Rcopula'. Object 'priorHconfig' is a vector of estimated prior probabilities for each of the H-configurations. Object 'Rcopula' is the estimated correlation matrix of the gaussian copula.

EM calibration in the case of the gaussian copula (unsigned) with memory management

Description

EM calibration in the case of the gaussian copula (unsigned) with memory management

Usage

EM_calibration_gaussian_memory(
  Logf0Mat,
  Logf1Mat,
  F0Mat,
  F1Mat,
  Prior.init,
  R.init,
  Hconfig,
  Precision = 1e-06,
  threads_nb
)
EM_calibration_gaussian_memory(
  Logf0Mat,
  Logf1Mat,
  F0Mat,
  F1Mat,
  Prior.init,
  R.init,
  Hconfig,
  Precision = 1e-06,
  threads_nb
)

Arguments

`Logf0Mat`	a matrix containing the log(f0(xi_q))
`Logf1Mat`	a matrix containing the log(f1(xi_q))
`F0Mat`	a matrix containing the evaluation of the marginal cdf under H0 at each items, each column corresponding to a p-value serie.
`F1Mat`	a matrix containing the evaluation of the marginal cdf under H1 at each items, each column corresponding to a p-value serie.
`Prior.init`	the initialization of prior probabilities for each of the H-configurations.
`R.init`	the initialization of the correlation matrix of the gaussian copula parameter.
`Hconfig`	A list of all possible combination of H0 and H1 hypotheses generated by the `GetHconfig()` function.
`Precision`	Precision for the stop criterion. (Default is 1e-6)
`threads_nb`	The number of threads to use.

Value

EM calibration in the case of conditional independence

Description

EM calibration in the case of conditional independence

Usage

EM_calibration_indep(fHconfig, Prior.init, Precision = 1e-06)
EM_calibration_indep(fHconfig, Prior.init, Precision = 1e-06)

Arguments

`fHconfig`	a matrix containing config densities evaluated at each items, each column corresponding to a configurations.
`Prior.init`	the initialization of prior probabilities for each of the H-configurations.
`Precision`	Precision for the stop criterion. (Default is 1e-6)

Value

a vector of estimated prior probabilities for each of the H-configurations.

EM calibration in the case of conditional independence with memory management (unsigned)

Description

EM calibration in the case of conditional independence with memory management (unsigned)

Usage

EM_calibration_indep_memory(
  Logf0Mat,
  Logf1Mat,
  Prior.init,
  Hconfig,
  Precision = 1e-06,
  threads_nb
)
EM_calibration_indep_memory(
  Logf0Mat,
  Logf1Mat,
  Prior.init,
  Hconfig,
  Precision = 1e-06,
  threads_nb
)

Arguments

`Logf0Mat`	a matrix containing the log(f0(xi_q))
`Logf1Mat`	a matrix containing the log(f1(xi_q))
`Prior.init`	the initialization of prior probabilities for each of the H-configurations.
`Hconfig`	A list of all possible combination of H0 and H1 hypotheses generated by the `GetHconfig()` function.
`Precision`	Precision for the stop criterion. (Default is 1e-6)
`threads_nb`	The number of threads to use.

Value

a vector of estimated prior probabilities for each of the H-configurations.

Signed case function: Separate f1 into f+ and f-

Description

Signed case function: Separate f1 into f+ and f-

Usage

f1_separation_signed(XMat, f0Mat, f1Mat, p0, plotting = FALSE)
f1_separation_signed(XMat, f0Mat, f1Mat, p0, plotting = FALSE)

Arguments

`XMat`	a matrix of probit-transformed p-values, each column corresponding to a p-value serie.
`f0Mat`	a matrix containing the evaluation of the marginal density functions under H0 at each items, each column corresponding to a p-value serie.
`f1Mat`	a matrix containing the evaluation of the marginal density functions under H1 at each items, each column corresponding to a p-value serie.
`p0`	the proportions of H0 items for each series.
`plotting`	boolean, should some diagnostic graphs be plotted. Default is FALSE.

Value

A list of 4 objects 'f1plusMat', 'f1minusMat', 'p1plus', 'p1minus'. Object 'f1plusMat' is a matrix containing the evaluation of the marginal density functions under H1plus at each items, each column corresponding to a p-value serie. Object 'f1minusMat' is a matrix containing the evaluation of the marginal density functions under H1minus at each items, each column corresponding to a p-value serie. Object 'p1plus' is an estimate of the proportions of H1plus items for each series. Object 'p1minus' is an estimate of the proportions of H1minus items for each series.

FastKerFdr signed

Description

FastKerFdr signed

Usage

FastKerFdr_signed(X, p0 = NULL, plotting = FALSE, NbKnot = 1e+05, tol = 1e-05)
FastKerFdr_signed(X, p0 = NULL, plotting = FALSE, NbKnot = 1e+05, tol = 1e-05)

Arguments

`X`	a vector of probit-transformed p-values (corresponding to a p-value serie)
`p0`	a priori proportion of H0 hypotheses
`plotting`	boolean, should some diagnostic graphs be plotted. Default is FALSE.
`NbKnot`	The (maximum) number of knot for the kde procedure. Default is 1e5
`tol`	a tolerance value for convergence. Default is 1e-5

Value

A list of 3 objects. Object 'p0' is an estimate of the proportion of H0 hypotheses, Object 'tau' is the vector of H1 posteriors, Object 'f1' is a numeric vector, each coordinate i corresponding to the evaluation of the H1 density at point xi, where xi is the ith item in X. Object 'F1' is a numeric vector, each coordinate i corresponding to the evaluation of the H1 ;cdf at point xi, where xi is the ith item in X.

FastKerFdr unsigned

Description

FastKerFdr unsigned

Usage

FastKerFdr_unsigned(
  X,
  p0 = NULL,
  plotting = FALSE,
  NbKnot = 1e+05,
  tol = 1e-05
)
FastKerFdr_unsigned(
  X,
  p0 = NULL,
  plotting = FALSE,
  NbKnot = 1e+05,
  tol = 1e-05
)

Arguments

`X`	a vector of probit-transformed p-values (corresponding to a p-value serie)
`p0`	a priori proportion of H0 hypotheses
`plotting`	boolean, should some diagnostic graphs be plotted. Default is FALSE.
`NbKnot`	The (maximum) number of knot for the kde procedure. Default is 1e5
`tol`	a tolerance value for convergence. Default is 1e-5

Value

Computation of the sum sum_c(w_c*psi_c) using Gaussian copula parallelized version

Description

Computation of the sum sum_c(w_c*psi_c) using Gaussian copula parallelized version

Usage

fHconfig_sum_update_gaussian_copula_ptr_parallel(
  Hconfig,
  NewPrior,
  Logf0Mat,
  Logf1Mat,
  zeta0,
  zeta1,
  R,
  Rinv,
  threads_nb = 0L
)
fHconfig_sum_update_gaussian_copula_ptr_parallel(
  Hconfig,
  NewPrior,
  Logf0Mat,
  Logf1Mat,
  zeta0,
  zeta1,
  R,
  Rinv,
  threads_nb = 0L
)

Arguments

`Hconfig`	list of vector of 0 and 1, corresponding to the configurations
`NewPrior`	a double vector containing the prior w_c
`Logf0Mat`	a double matrix containing the log(f0(xi_q))
`Logf1Mat`	a double matrix containing the log(f1(xi_q))
`zeta0`	a double matrix containing the qnorm(F0(x_iq))
`zeta1`	a double matrix containing the qnorm(F1(x_iq))
`R`	a double matrix corresponding to the copula parameter
`Rinv`	a double matrix corresponding to the inverse copula parameter
`threads_nb`	an int the number of threads

Value

a double vector containing sum_c(w_c*psi_c)

Computation of the sum sum_c(w_c*psi_c) parallelized version

Description

Computation of the sum sum_c(w_c*psi_c) parallelized version

Usage

fHconfig_sum_update_ptr_parallel(
  Hconfig,
  NewPrior,
  Logf0Mat,
  Logf1Mat,
  threads_nb = 0L
)
fHconfig_sum_update_ptr_parallel(
  Hconfig,
  NewPrior,
  Logf0Mat,
  Logf1Mat,
  threads_nb = 0L
)

Arguments

`Hconfig`	list of vector of 0 and 1, corresponding to the configurations
`NewPrior`	a double vector containing the prior w_c
`Logf0Mat`	a double matrix containing the log(f0(xi_q))
`Logf1Mat`	a double matrix containing the log(f1(xi_q))
`threads_nb`	an int the number of threads

Value

a double vector containing sum_c(w_c*psi_c)

Gaussian copula density

Description

Gaussian copula density

Usage

gaussian_copula_density(zeta, R, Rinv)
gaussian_copula_density(zeta, R, Rinv)

Arguments

`zeta`	the matrix of probit-transformed observations.
`R`	the correlation matrix.
`Rinv`	the inverse correlation matrix.

Value

A numeric vector, each coordinate i corresponding to the evaluation of the Gaussian copula density function at observation zeta_i.

Specify the configurations corresponding to the composite $H_1$ test "AtLeast".

Description

Specify which configurations among Hconfig correspond to the composite alternative hypothesis : {at least "AtLeast" $H_1$ hypotheses are of interest }

Usage

GetH1AtLeast(Hconfig, AtLeast, Consecutive = FALSE, SameSign = FALSE)
GetH1AtLeast(Hconfig, AtLeast, Consecutive = FALSE, SameSign = FALSE)

Arguments

`Hconfig`	A list of all possible combination of $H_0$ and $H_1$ hypotheses generated by the `GetHconfig()` function.
`AtLeast`	How many $H_1$ hypotheses at least for the item to be of interest ? (an integer or a vector).
`Consecutive`	Should the significant test series be consecutive ? (optional, default is `FALSE`).
`SameSign`	Should the significant test series have the same sign ? (optional, default is `FALSE`).

Value

A vector 'Hconfig.H1' of components of Hconfig that correspond to the 'AtLeast' specification.

Examples

GetH1AtLeast(GetHconfig(4),2)

GetH1AtLeast(GetHconfig(4),2)

Specify the configurations corresponding to the composite $H_1$ test "Equal".

Description

Specify which configurations among Hconfig correspond to the composite alternative hypothesis :{Exaltly "Equal" $H_1$ hypotheses are of interest }

Usage

GetH1Equal(Hconfig, Equal, Consecutive = FALSE, SameSign = FALSE)
GetH1Equal(Hconfig, Equal, Consecutive = FALSE, SameSign = FALSE)

Arguments

`Hconfig`	A list of all possible combination of H0 and H1 hypotheses generated by the `GetHconfig()` function.
`Equal`	What is the exact number of $H_1$ hypotheses for the item to be of interest? (an integer or a vector).
`Consecutive`	Should the significant test series be consecutive ? (optional, default is FALSE).
`SameSign`	Should the significant test series have the same sign ? (optional, default is FALSE).

Value

A vector 'Hconfig.H1' of components of Hconfig that correspond to the 'Equal' specification.

Examples

GetH1Equal(GetHconfig(4),2)

GetH1Equal(GetHconfig(4),2)

Generate the $H_0$ / $H_1$ configurations.

Description

Generate all possible combination of simple hypotheses $H_0$ / $H_1$ .

Usage

GetHconfig(Q, Signed = FALSE)
GetHconfig(Q, Signed = FALSE)

Arguments

`Q`	The number of test series to be combined.
`Signed`	Should the sign of the effect be taken into account? (optional, default is `FALSE`).

Value

A list 'Hconfig' of all possible combination of $H_0$ and $H_1$ hypotheses among $Q$ hypotheses tested.

Examples

GetHconfig(4)

GetHconfig(4)

Update of the prior estimate in EM algo parallelized version

Description

Update of the prior estimate in EM algo parallelized version

Usage

prior_update_arma_ptr_parallel(
  Hconfig,
  fHconfig_sum,
  OldPrior,
  Logf0Mat,
  Logf1Mat,
  threads_nb = 0L
)
prior_update_arma_ptr_parallel(
  Hconfig,
  fHconfig_sum,
  OldPrior,
  Logf0Mat,
  Logf1Mat,
  threads_nb = 0L
)

Arguments

`Hconfig`	list of vector of 0 and 1, corresponding to the configurations
`fHconfig_sum`	a double vector containing sum_c(w_c*psi_c), obtained by fHconfig_sum_update_ptr_parallel()
`OldPrior`	a double vector containing the prior w_c
`Logf0Mat`	a double matrix containing the log(f0(xi_q))
`Logf1Mat`	a double matrix containing the log(f1(xi_q))
`threads_nb`	an int the number of threads

Value

a double vector containing the new estimate of prior w_c

Update of the prior estimate in EM algo using Gaussian copula, parallelized version

Description

Update of the prior estimate in EM algo using Gaussian copula, parallelized version

Usage

prior_update_gaussian_copula_ptr_parallel(
  Hconfig,
  fHconfig_sum,
  OldPrior,
  Logf0Mat,
  Logf1Mat,
  zeta0,
  zeta1,
  R,
  Rinv,
  threads_nb = 0L
)
prior_update_gaussian_copula_ptr_parallel(
  Hconfig,
  fHconfig_sum,
  OldPrior,
  Logf0Mat,
  Logf1Mat,
  zeta0,
  zeta1,
  R,
  Rinv,
  threads_nb = 0L
)

Arguments

`Hconfig`	list of vector of 0 and 1, corresponding to the configurations
`fHconfig_sum`	a double vector containing sum_c(w_c*psi_c), obtained by fHconfig_sum_update_ptr_parallel()
`OldPrior`	a double vector containing the prior w_c
`Logf0Mat`	a double matrix containing the log(f0(xi_q))
`Logf1Mat`	a double matrix containing the log(f1(xi_q))
`zeta0`	a double matrix containing the qnorm(F0(x_iq))
`zeta1`	a double matrix containing the qnorm(F1(x_iq))
`R`	a double matrix corresponding to the copula parameter
`Rinv`	a double matrix corresponding to the inverse copula parameter
`threads_nb`	an int the number of threads

Value

a double vector containing the new estimate of prior w_c

Synthetic example to illustrate the main qch functions

Description

PvalSets is a data.frame with 10,000 rows and 3 columns. Each row corresponds to an item, columns 'Pval1' and 'Pval2' each correspond to a test serie over the items, and column 'Class' provides the truth, i.e. if item $i$ belongs to class 1 then the H0 hypothesis is true for the 2 tests, if item $i$ belongs to class 2 (resp. 3) then the H0 hypothesis is true for the first (resp. second) test only, and if item $i$ belongs to class 4 then both H0 hypotheses are false (for the first and the second test).

Usage

PvalSets
PvalSets

Format

A data.frame

Synthetic example to illustrate the main qch functions using gaussian copula

Description

PvalSets_cor is a data.frame with 10,000 rows and 3 columns. Each row corresponds to an item, columns 'Pval1' and 'Pval2' each correspond to a test serie over the items, and column 'Class' provides the truth, i.e. if item $i$ belongs to class 1 then the H0 hypothesis is true for the 2 tests, if item $i$ belongs to class 2 (resp. 3) then the H0 hypothesis is true for the first (resp. second) test only, and if item $i$ belongs to class 4 then both H0 hypotheses are false (for the first and the second test). The correlation between the two pvalues series within each class is 0.3.

Usage

PvalSets_cor
PvalSets_cor

Format

A data.frame

Infer posterior probabilities of $H_0$ / $H_1$ configurations.

Description

For each item, estimate the posterior probability for each configuration. This function use either the model accounting for the dependence structure through a Gaussian copula function (copula=="gaussian") or assuming the conditional independence (copula=="indep"). Utilizes parallel computing, when available. For package documentation, see qch-package.

Usage

qch.fit(
  pValMat,
  EffectMat = NULL,
  Hconfig,
  copula = "indep",
  threads_nb = 0,
  plotting = FALSE,
  Precision = 1e-06
)
qch.fit(
  pValMat,
  EffectMat = NULL,
  Hconfig,
  copula = "indep",
  threads_nb = 0,
  plotting = FALSE,
  Precision = 1e-06
)

Arguments

`pValMat`	A matrix of p-values, each column corresponding to a p-value serie.
`EffectMat`	A matrix of estimated effects corresponding to the p-values contained in pValMat. If specified, the procedure will account for the direction of the effect. (optional, default is `NULL`)
`Hconfig`	A list of all possible combination of $H_0$ and $H_1$ hypotheses generated by the `GetHconfig()` function.
`copula`	A string specifying the form of copula to use. Possible values are "`indep`"and "`gaussian`". Default is "`indep`" corresponding to the independent case.
`threads_nb`	The number of threads to use. The number of thread will set to the number of core available by default.
`plotting`	A boolean. Should some diagnostic graphs be plotted ? Default is `FALSE`.
`Precision`	The precision for EM algorithm to infer the parameters. Default is `1e-6`.

Value

A list with the following elements:

`prior`	vector of estimated prior probabilities for each of the H-configurations.
`Rcopula`	the estimated correlation matrix of the Gaussian copula. (if applicable)
`Hconfig`	the list of all configurations.

If the storage permits, the list will additionally contain:

`posterior`	matrix providing for each item (in row) its posterior probability to belong to each of the H-configurations (in columns).
`fHconfig`	matrix containing $\psi_c$ densities evaluated at each items, each column corresponding to a configuration.

Else, the list will additionally contain:

`f0Mat`	matrix containing the evaluation of the marginal densities under $H_0$ at each items, each column corresponding to a p-value serie.
`f1Mat`	matrix containing the evaluation of the marginal densities under $H_1$ at each items, each column corresponding to a p-value serie.
`F0Mat`	matrix containing the evaluation of the marginal cdf under $H_0$ at each items, each column corresponding to a p-value serie.
`F1Mat`	matrix containing the evaluation of the marginal cdf under $H_1$ at each items, each column corresponding to a p-value serie.
`fHconfig_sum`	vector containing $(\sum_cw_c\psi_c(Z_i))$ for each items $i$ .

The elements of interest are the posterior probabilities matrix, posterior, the estimated proportion of observations belonging to each configuration, prior, and the estimated correlation matrix of the Gaussian copula, Rcopula. The remaining elements are returned primarily for use by other functions.

Examples

data(PvalSets_cor)
PvalMat <- as.matrix(PvalSets_cor[,-3])
## Build the Hconfig objects
Q <- 2
Hconfig <- GetHconfig(Q)

## Run the function
res.fit <- qch.fit(pValMat = PvalMat,Hconfig = Hconfig,copula="gaussian")

## Display the prior of each class of items
res.fit$prior

## Display the correlation estimate of the gaussian copula
res.fit$Rcopula

## Display the first posteriors
head(res.fit$posterior)
data(PvalSets_cor)
PvalMat <- as.matrix(PvalSets_cor[,-3])
## Build the Hconfig objects
Q <- 2
Hconfig <- GetHconfig(Q)

## Run the function
res.fit <- qch.fit(pValMat = PvalMat,Hconfig = Hconfig,copula="gaussian")

## Display the prior of each class of items
res.fit$prior

## Display the correlation estimate of the gaussian copula
res.fit$Rcopula

## Display the first posteriors
head(res.fit$posterior)

Perform composite hypothesis testing.

Description

Perform any composite hypothesis test by specifying the configurations 'Hconfig.H1' corresponding to the composite alternative hypothesis among all configurations 'Hconfig'.

By default, the function performs the composite hypothesis test of being associated with "at least $q$ " simple tests, for $q=1,..Q$ .

Usage

qch.test(res.qch.fit, Hconfig, Hconfig.H1 = NULL, Alpha = 0.05, threads_nb = 0)
qch.test(res.qch.fit, Hconfig, Hconfig.H1 = NULL, Alpha = 0.05, threads_nb = 0)

Arguments

`res.qch.fit`	The result provided by the `qch.fit()` function.
`Hconfig`	A list of all possible combination of $H_0$ and $H_1$ hypotheses generated by the `GetHconfig()` function.
`Hconfig.H1`	An integer vector (or a list of such vector) of the `Hconfig` index corresponding to the composite alternative hypothesis configuration(s). Can be generated by the `GetH1AtLeast()` or `GetH1Equal()` functions. If `NULL`, the composite hyporhesis tests of being associated with "at least $q$ " simple tests, for q=1,..Q are performed.
`Alpha`	the nominal Type I error rate for FDR control. Default is `0.05`.
`threads_nb`	The number of threads to use. The number of thread will set to the number of core available by default.

Value

A list with the following elements:

`Rejection`	a matrix providing for each item the result of the composite hypothesis test, after adaptive Benjamin-Höchberg multiple testing correction.
`lFDR`	a matrix providing for each item its local FDR estimate.
`Pvalues`	a matrix providing for each item its p-value of the composite hypothesis test.

Examples

data(PvalSets_cor)
PvalMat <- as.matrix(PvalSets_cor[,-3])
Truth <- PvalSets[,3]

## Build the Hconfig objects
Q <- 2
Hconfig <- GetHconfig(Q)

## Infer the posteriors
res.fit <- qch.fit(pValMat = PvalMat, Hconfig = Hconfig, copula="gaussian")

## Run the test procedure with FDR control
H1config <- GetH1AtLeast(Hconfig,2)
res.test <- qch.test(res.qch.fit = res.fit,Hconfig = Hconfig, Hconfig.H1 = H1config)
table(res.test$Rejection$AtLeast_2,Truth==4)


data(PvalSets_cor)
PvalMat <- as.matrix(PvalSets_cor[,-3])
Truth <- PvalSets[,3]

## Build the Hconfig objects
Q <- 2
Hconfig <- GetHconfig(Q)

## Infer the posteriors
res.fit <- qch.fit(pValMat = PvalMat, Hconfig = Hconfig, copula="gaussian")

## Run the test procedure with FDR control
H1config <- GetH1AtLeast(Hconfig,2)
res.test <- qch.test(res.qch.fit = res.fit,Hconfig = Hconfig, Hconfig.H1 = H1config)
table(res.test$Rejection$AtLeast_2,Truth==4)

Update the estimate of R correlation matrix of the gaussian copula, parallelized version

Description

Update the estimate of R correlation matrix of the gaussian copula, parallelized version

Usage

R_MLE_update_gaussian_copula_ptr_parallel(
  Hconfig,
  fHconfig_sum,
  OldPrior,
  Logf0Mat,
  Logf1Mat,
  zeta0,
  zeta1,
  OldR,
  OldRinv,
  RhoIndex,
  threads_nb = 0L
)
R_MLE_update_gaussian_copula_ptr_parallel(
  Hconfig,
  fHconfig_sum,
  OldPrior,
  Logf0Mat,
  Logf1Mat,
  zeta0,
  zeta1,
  OldR,
  OldRinv,
  RhoIndex,
  threads_nb = 0L
)

Arguments

`Hconfig`	list of vector of 0 and 1, corresponding to the configurations
`fHconfig_sum`	a double vector containing sum_c(w_c*psi_c), obtained by fHconfig_sum_update_ptr_parallel()
`OldPrior`	a double vector containing the prior w_c
`Logf0Mat`	a double matrix containing the log(f0(xi_q))
`Logf1Mat`	a double matrix containing the log(f1(xi_q))
`zeta0`	a double matrix containing the qnorm(F0(x_iq))
`zeta1`	a double matrix containing the qnorm(F1(x_iq))
`OldR`	a double matrix corresponding to the copula parameter
`OldRinv`	a double matrix corresponding to the inverse copula parameter
`RhoIndex`	a int matrix containing the index of lower triangular part of a matrix
`threads_nb`	an int the number of threads

Value

a double vector containing the lower triangular part of the MLE of R

Gaussian copula correlation matrix Maximum Likelihood estimator.

Description

Gaussian copula correlation matrix Maximum Likelihood estimator.

Usage

R.MLE(Hconfig, zeta0, zeta1, Tau)
R.MLE(Hconfig, zeta0, zeta1, Tau)

Arguments

`Hconfig`	A list of all possible combination of H0 and H1 hypotheses generated by the `GetHconfig()` function.
`zeta0`	a matrix containing the Phi(F_0(Z_iq)), each column corresponding to a p-value serie.
`zeta1`	a matrix containing the Phi(F_1(Z_iq)), each column corresponding to a p-value serie.
`Tau`	a matrix providing for each item (in row) its posterior probability to belong to each of the H-configurations (in columns).

Value

Estimate of the correlation matrix.

Check the Gaussian copula correlation matrix Maximum Likelihood estimator

Description

Check the Gaussian copula correlation matrix Maximum Likelihood estimator

Usage

R.MLE.check(R)
R.MLE.check(R)

Arguments

`R`	Estimate of the correlation matrix.

Value

Estimate of the correlation matrix.

Gaussian copula correlation matrix Maximum Likelihood estimator (memory handling)

Description

Gaussian copula correlation matrix Maximum Likelihood estimator (memory handling)

Usage

R.MLE.memory(
  Hconfig,
  fHconfig_sum,
  OldPrior,
  Logf0Mat,
  Logf1Mat,
  zeta0,
  zeta1,
  OldR,
  OldRinv
)
R.MLE.memory(
  Hconfig,
  fHconfig_sum,
  OldPrior,
  Logf0Mat,
  Logf1Mat,
  zeta0,
  zeta1,
  OldR,
  OldRinv
)

Arguments

`Hconfig`	A list of all possible combination of H0 and H1 hypotheses generated by the `GetHconfig()` function.
`fHconfig_sum`	a vector containing sum_c(w_c*psi_c) for each items.
`OldPrior`	a vector containing the prior probabilities for each of the H-configurations.
`Logf0Mat`	a matrix containing log(f0Mat), each column corresponding to a p-value serie.
`Logf1Mat`	a matrix containing log(f1Mat), each column corresponding to a p-value serie.
`zeta0`	a matrix containing qnorm(F0Mat), each column corresponding to a p-value serie.
`zeta1`	a matrix containing qnorm(F1Mat), each column corresponding to a p-value serie.
`OldR`	the copula correlation matrix.
`OldRinv`	the inverse of copula correlation matrix.

Value

Estimate of the correlation matrix.

Package 'qch'

Help Index

Gaussian copula density for each Hconfiguration.

Description

Usage

Arguments

Value

EM calibration in the case of the gaussian copula (unsigned)

Description

Usage

Arguments

Value

EM calibration in the case of the gaussian copula (unsigned) with memory management

Description

Usage

Arguments

Value

EM calibration in the case of conditional independence

Description

Usage

Arguments

Value

EM calibration in the case of conditional independence with memory management (unsigned)

Description

Usage

Arguments

Value

Signed case function: Separate f1 into f+ and f-

Description

Usage

Arguments

Value

FastKerFdr signed

Description

Usage

Arguments

Value

FastKerFdr unsigned

Description

Usage

Arguments

Value

Computation of the sum sum_c(w_c*psi_c) using Gaussian copula parallelized version

Description

Usage

Arguments

Value

Computation of the sum sum_c(w_c*psi_c) parallelized version

Description

Usage

Arguments

Value

Gaussian copula density

Description

Usage

Arguments

Value

Specify the configurations corresponding to the composite H1H_1H1​ test "AtLeast".

Description

Usage

Arguments

Value

See Also

Examples

Specify the configurations corresponding to the composite H1H_1H1​ test "Equal".

Description

Usage

Arguments

Value

See Also

Examples

Generate the H0H_0H0​/H1H_1H1​ configurations.

Description

Usage

Arguments

Value

Examples

Update of the prior estimate in EM algo parallelized version

Description

Usage

Specify the configurations corresponding to the composite $H_1$ test "AtLeast".

Specify the configurations corresponding to the composite $H_1$ test "Equal".

Generate the $H_0$ / $H_1$ configurations.

Infer posterior probabilities of $H_0$ / $H_1$ configurations.