EM_calibration_gaussian

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

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.(2025) <doi: 10.1093/nargab/lqaf118>. 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.

Tristan Mary-Huard

Query Composite Hypotheses

Annaig De Walsche

Franck Gauthier

EM_calibration_gaussian function

<dl><dt>Hconfig</dt>
<dd>A list of all possible combination of \(H_0\) and \(H_1\) hypotheses generated by the GetHconfig() function.</dd>
<dt>F0Mat</dt>
<dd>a matrix containing the evaluation of the marginal cdf under \(H_0\) at each items, each column corresponding to a p-value serie.</dd>
<dt>F1Mat</dt>
<dd>a matrix containing the evaluation of the marginal cdf under \(H_1\) at each items, each column corresponding to a p-value serie.</dd>
<dt>fHconfig</dt>
<dd>a matrix containing H-config densities evaluated at each items, each column corresponding to a configurations.</dd>
<dt>R.init</dt>
<dd>the initialization of the correlation matrix of the Gaussian copula parameter.</dd>
<dt>Prior.init</dt>
<dd>the initialization of prior probabilities for each of the H-configurations.</dd>
<dt>Precision</dt>
<dd>Precision for the stop criterion. (Default is 1e-6)</dd></dl>

Arguments

EM calibration in the case of the Gaussian copula (unsigned) — EM_calibration_gaussian

<dl>

<dt>Hconfig</dt>
<dd>A list of all possible combination of \(H_0\) and \(H_1\) hypotheses generated by the GetHconfig() function.</dd>


<dt>F0Mat</dt>
<dd>a matrix containing the evaluation of the marginal cdf under \(H_0\) at each items, each column corresponding to a p-value serie.</dd>


<dt>F1Mat</dt>
<dd>a matrix containing the evaluation of the marginal cdf under \(H_1\) at each items, each column corresponding to a p-value serie.</dd>


<dt>fHconfig</dt>
<dd>a matrix containing H-config densities evaluated at each items, each column corresponding to a configurations.</dd>


<dt>R.init</dt>
<dd>the initialization of the correlation matrix of the Gaussian copula parameter.</dd>


<dt>Prior.init</dt>
<dd>the initialization of prior probabilities for each of the H-configurations.</dd>


<dt>Precision</dt>
<dd>Precision for the stop criterion. (Default is 1e-6)</dd>

</dl>

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

EM_calibration_gaussian: EM calibration in the case of the Gaussian copula (unsigned)

Description

Usage

Value

Arguments