A wrapper function estimating posterior expectations of the \(\gamma\) variables using an empirical Bayesian technqiue.
e_step_func(beta_t, beta_var, df, adj = 5, lambda = 0.1, monotone = TRUE)A list including
delta estimated posterior expectations of the \(\gamma\).
pi0 estimated proportion of null hypothesis
Expectation of the posterior mean (assuming \(\gamma=1\))
Current posterior variance (assuming \(\gamma=1\))
Degrees of freedom for the t-distribution (use to calculate p-values).
Bandwidth multiplier to Silverman's `rule of thumb' for calculating the marginal density of the test-statistics (default = 5).
Value of the \(\lambda\) parameter for estimating the proportion of null hypothesis using Storey et al. (2004) (default = 0.1).
Logical - Should the estimated marginal density of the test-statistics be monotone non-increasing from zero (default = TRUE).
Storey, J. D., Taylor, J. E., and Siegmund, D. (2004), “Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: A unified approach,” J. R. Stat. Soc. Ser. B. Stat. Methodol., 66, 187–205. McLain, A. C., Zgodic, A., & Bondell, H. (2022). Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm. arXiv preprint arXiv:2209.08139.