Specific items of nonfinancial COIs in research [n (%)].

Specific items of nonfinancial COIs in research [n (%)].</p

COI subjects involved in research [n (%)].

COI subjects involved in research [n (%)].</p

Specific items of financial COIs in research [n (%)].

Specific items of financial COIs in research [n (%)].</p

Characteristics of COI disclosure policies among journals [n (%)].

Characteristics of COI disclosure policies among journals [n (%)].</p

Contents of COI policies among journals [n (%)].

Contents of COI policies among journals [n (%)].</p

Intramolecular Electron Transfer in Tetraammine(L)ruthenium(III)-Modified Manganocytochromes <i>c</i>

Intramolecular Electron Transfer in Tetraammine(L)ruthenium(III)-Modified Manganocytochromes c</i

The empirical Bayes estimators of the parameter of the uniform distribution with an inverse gamma prior under Stein’s loss function

For the hierarchical uniform and inverse gamma model, we calculate the Bayes posterior estimator of the parameter of the uniform distribution under Stein’s loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein’s Loss (PESL). We also obtain the Bayes posterior estimator of the parameter under the squared error loss function and the corresponding PESL. Moreover, we obtain empirical Bayes estimators of the parameter of the uniform distribution by two methods. Note that the estimators of the hyperparameters of the model by the Maximum Likelihood Estimation (MLE) method are summarized in a theorem, whose proof involves the upper incomplete gamma function and a special case of the Meijer G-function. In numerical simulations, we address from four perspectives. First, we exemplify the two inequalities of the Bayes posterior estimators and the PESLs. Second, we illustrate that the moment estimators and the Maximum Likelihood Estimators (MLEs) are consistent estimators of the hyperparameters. Third, we calculate the goodness-of-fit of the model for the simulated data. Fourth, we plot the marginal densities of the model for various hyperparameters. Finally, we utilize the current prices of the 300 component stocks of Shenzhen 300 Index to illustrate our theoretical studies.</p

Top 10 mutations with the highest causal effect on DNA replication in 10 cancers.

The figure shows the ATE value and the mutation rate of each predicted key mutation.</p

The Mann-Whitney U test (M.W.) analysis reflects the significant differences between mutated groups and non-mutated groups of mutated genes with high ATE values in the activity of DNA replication (DR) for 10 cancers.

The Mann-Whitney U test (M.W.) analysis reflects the significant differences between mutated groups and non-mutated groups of mutated genes with high ATE values in the activity of DNA replication (DR) for 10 cancers.</p

An illustration of the proposed framework.

The biological process activity of each sample is obtained by core genes regression and used as the outcome of the casual model. The casual model consists of an inference network to calculate the mean and variance of P(Z|X,y,m) and a model network to recover P(Z,X,y,m).</p