The coefficient estimates from the Lasso procedure can also be interpreted in a Bayesian framework as posterior mode estimates using a Laplace (double exponential) prior on the coefficients [Tibshirani, 1996].
In addition, from a Bayesian perspective the posterior mode of the distribution of SNP effects (i.e., the mode of the distribution conditional on a training set) can also be used as point estimator.
For a medium-shift size, δ=+6, around one-and-a-half standard deviation, the posterior mode concentrates on the 100th sample whereas the c-chart signals with 38 samples delay.
Figure 1 Square root of the relative mean squared error (RMSE), as a function of p, of posterior mode (black lines) and posterior median (blue lines) of p and σ based on the reference priors π r 1 (solid lines), π r 2 (dashed lines), π r 3 (long-dashed lines) and the noninformative prior π U (dotted lines).
They were obtained from the posterior mode of a previous Bayesian analysis.
They have shown that the posterior mode of a Bayesian model, similar to that proposed by Meuwissen et al. [ 2], and the regression coefficients estimated using LASSO are equal.
The likelihood function is defined on Ω, and the relationship R in Ω that produces the maximum value of the likelihood is the maximum likelihood estimate of the true relationship, corresponding to the posterior mode with a uniform prior.
More sceptical priors (reflecting more certainty the cases in the cluster do not have a common cause) shrink the posterior mode more towards 1.0 and make it more likely that the 95% credible interval will include the null value of SIR = 1.0.
For every pseudo-observed (simulated) data set, an estimate is obtained from the posterior mode.
In iASeq, we used an EM algorithm to find the posterior mode of parameters and carried out statistical inference accordingly.
