Package 'qch'

Gaussian copula density for each H-configuration.

Description

Gaussian copula density for each H-configuration.

Usage

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

Arguments

Hconfig	A list of all possible combination of $H_0$ and $H_1$ hypotheses generated by the GetHconfig() function.
F0Mat	a matrix containing the evaluation of the marginal cdf under $H_0$ at each items, each column corresponding to a p-value serie.
F1Mat	a matrix containing the evaluation of the marginal cdf under $H_1$ 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 H-configuration 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,
  max_iter = 10000
)

Arguments

Hconfig	A list of all possible combination of $H_0$ and $H_1$ hypotheses generated by the GetHconfig() function.
F0Mat	a matrix containing the evaluation of the marginal cdf under $H_0$ at each items, each column corresponding to a p-value serie.
F1Mat	a matrix containing the evaluation of the marginal cdf under $H_1$ at each items, each column corresponding to a p-value serie.
fHconfig	a matrix containing H-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)
max_iter	the maximum number of iterations allowed for the algorithm to converge or complete its process.(Default is 1e4.)

Value

A list with the following elements:

priorHconfig	vector of estimated prior probabilities for each of the H-configurations.
Rcopula	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,
  max_iter = 10000
)

Arguments

Logf0Mat	a matrix containing the $\log(f_0(x^i_q))$
Logf1Mat	a matrix containing the $\log(f_1(x^i_q))$
F0Mat	a matrix containing the evaluation of the marginal cdf under $H_0$ at each items, each column corresponding to a p-value serie.
F1Mat	a matrix containing the evaluation of the marginal cdf under $H_1$ 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 $H_0$ and $H_1$ hypotheses generated by the GetHconfig() function.
Precision	Precision for the stop criterion. (Default is 1e-6)
threads_nb	The number of threads to use.
max_iter	the maximum number of iterations allowed for the algorithm to converge or complete its process.(Default is 1e4.)

Value

A list with the following elements:

priorHconfig	vector of estimated prior probabilities for each of the H-configurations.
Rcopula	the estimated correlation matrix of the Gaussian copula.

---

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, max_iter = 10000)

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)
max_iter	the maximum number of iterations allowed for the algorithm to converge or complete its process.(Default is 1e4.)

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,
  max_iter = 10000
)

Arguments

Logf0Mat	a matrix containing the $\log(f_0(x^i_q))$
Logf1Mat	a matrix containing the $\log(f_1(x^i_q))$
Prior.init	the initialization of prior probabilities for each of the H-configurations.
Hconfig	A list of all possible combination of $H_0$ and $H_1$ hypotheses generated by the GetHconfig() function.
Precision	Precision for the stop criterion. (Default is 1e-6)
threads_nb	The number of threads to use.
max_iter	the maximum number of iterations allowed for the algorithm to converge or complete its process.(Default is 1e4.)

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)

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 $H_0$ at each items, each column corresponding to a p-value serie.
f1Mat	a matrix containing the evaluation of the marginal density functions under $H_1$ at each items, each column corresponding to a p-value serie.
p0	the proportions of $H_0$ items for each series.
plotting	boolean, should some diagnostic graphs be plotted. (Default is FALSE.)

Value

A list with the following elements:

f1plusMat	a matrix containing the evaluation of the marginal density functions under $H_1^+$ at each items, each column corresponding to a p-value serie.
f1minusMat	a matrix containing the evaluation of the marginal density functions under $H_1^-$ at each items, each column corresponding to a p-value serie.
p1plus	an estimate of the proportions of $H_1^+$ items for each series.
p1minus	an estimate of the proportions of $H_1^-$ items for each series.

---

FastKerFdr signed

Description

Kernel estimation of the density in a two-components mixture model where one component are a standard Gaussian density.

Usage

FastKerFdr_signed(
  X,
  p0 = NULL,
  plotting = FALSE,
  NbKnot = 1e+05,
  tol = 1e-05,
  max_iter = 10000
)

Arguments

X	a vector of probit-transformed p-values (corresponding to a p-value serie).
p0	a priori proportion of $H_0$ 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.)
max_iter	the maximum number of iterations allowed for the algorithm to converge or complete its process.(Default is 1e4.)

Value

A list with the following elements:

p0	vector of the estimated proportions of $H_0$ hypotheses for each of p-value serie.
tau	the vector of $H_1$ posteriors.
f1	a numeric vector, each coordinate $i$ corresponding to the evaluation of the $H_1$ density at point $x_i$, where $x_i$ is the $i$th item in X.
F1	a numeric vector, each coordinate $i$ corresponding to the evaluation of the $H_1$ cdf at point $x_i$, where $x_i$ is the $i$th item in X.

---

FastKerFdr unsigned

Description

Kernel estimation of the density in a two-components mixture model where one component are a standard Gaussian density. Here we suppose that the density to estimate lives in $R^+$.

Usage

FastKerFdr_unsigned(
  X,
  p0 = NULL,
  plotting = FALSE,
  NbKnot = 1e+05,
  tol = 1e-05,
  max_iter = 10000
)

Arguments

X	a vector of probit-transformed p-values (corresponding to a p-value serie)
p0	a priori proportion of $H_0$ 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.)
max_iter	the maximum number of iterations allowed for the algorithm to converge or complete its process.(Default is 1e4.)

Value

A list with the following elements:

p0	vector of the estimated proportions of $H_0$ hypotheses for each of p-value serie.
tau	the vector of $H_1$ posteriors.
f1	a numeric vector, each coordinate $i$ corresponding to the evaluation of the $H_1$ density at point $x_i$, where $x_i$ is the $i$th item in X.
F1	a numeric vector, each coordinate $i$ corresponding to the evaluation of the $H_1$ cdf at point $x_i$, where $x_i$ is the $i$th item in X.

---

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
)

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
)

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)

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 $\code{zeta}_i$.

---

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)

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.

See Also

GetH1Equal()

Examples

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 :{Exactly "Equal" $H_1$ hypotheses are of interest }

Usage

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.

See Also

GetH1AtLeast()

Examples

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)

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)

---

This function is a re-implementation of the initial R loop computing last incomplete trapezoid. See R function integral.kde_adapted().

Description

This function is a re-implementation of the initial R loop computing last incomplete trapezoid. See R function integral.kde_adapted().

Usage

last_incomplete_trapezoid_arma(
  q_prob,
  q_ind,
  q,
  eval,
  est,
  simp_rule,
  density = TRUE
)

Arguments

q_prob	reference of the vector q_prob containing the probability of each quantile q
q_ind	reference of the vector q_ind
q	reference of the vector q containing the quantiles
eval	reference of the vector eval
est	reference of the vector est
simp_rule	reference of the vector simp_rule
density	logical

Value

void. Its first argument q_prob is passed as a reference and modified in place.

---

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
)

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
)

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

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 $H_0$ hypothesis is true for the 2 tests, if item $i$ belongs to class 2 (resp. 3) then the $H_0$ 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

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",
  memory_efficient_EM = FALSE,
  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.
memory_efficient_EM	Logical. If TRUE, use the memory-efficient implementation of the EM algorithm. This option is recommended for large datasets, as it reduces memory usage at the cost of additional computation time. The memory-efficient implementation is automatically used when the size of the posterior matrix exceeds 2 GB.
threads_nb	Integer. Number of threads to use for parallel computation. This parameter is only used when memory_efficient_EM = TRUE. By default, the number of threads is set to the number of available CPU cores.
plotting	Logical. 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.
null_prop	the estimation of items under the null for each test series.

• If the memory efficient version of EM algorithm is not used, 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)

---

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'.

Usage

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 hypothesis 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 cores available by default.

Details

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

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.

See Also

qch.fit(), GetH1AtLeast(), GetH1Equal()

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)

---

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
)

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)

Arguments

Hconfig	A list of all possible combination of $H_0$ and $H_1$ 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)

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
)

Arguments

Hconfig	A list of all possible combination of $H_0$ and $H_1$ 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 $\log(f_0Mat)$, each column corresponding to a p-value serie.
Logf1Mat	a matrix containing $\log(f_1Mat)$, 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.

---

Same as function above but does not handle the index ordering of the vector q. Therefore, the 2nd argument order_q has to be an index ordered version of the vector q. Indeed, the R base function: order() is twice as fast as the arma::sort_index(q) This is therefore the recommended function to use.

Description

Same as function above but does not handle the index ordering of the vector q. Therefore, the 2nd argument order_q has to be an index ordered version of the vector q. Indeed, the R base function: order() is twice as fast as the arma::sort_index(q) This is therefore the recommended function to use.

Usage

remove_decreasing_values_cpp(q_prob, order_q, tol = 1e-10)

Arguments

q_prob	reference of the vector q_prob
order_q	reference of the vector q
tol	By default 1e-10

Value

void. Its first argument q_prob is passed as a reference and modified in place.

---

This function is a re-implementation of the initial R side while loop. See the end of R function integral.kde_adapted(). As shown in the commentary below, it is twice as slow to handle the index ordering of the vector q (2nd argument) here with the function arma::sort_index(). Consequently, it is recommended to use the function remove_decreasing_values_cpp() instead.

Description

This function is a re-implementation of the initial R side while loop. See the end of R function integral.kde_adapted(). As shown in the commentary below, it is twice as slow to handle the index ordering of the vector q (2nd argument) here with the function arma::sort_index(). Consequently, it is recommended to use the function remove_decreasing_values_cpp() instead.

Usage

remove_decreasing_values_cpp_slow_ordering(q_prob, q, tol = 1e-10)

Arguments

q_prob	reference of the vector q_prob
q	reference of the vector q
tol	By default 1e-10

Value

void. Its first argument q_prob is passed as a reference and modified in place.

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