Two approaches will be investigated including the posterior mixture method (a Bayesian approach) and the empirical variance method (a frequentist approach).
For estimating the correlation range (also called "decorrelation length") and the variance of the field, two simple estimating functions based on the so-called "conditional Gaussian Gibbs-energy mean" (CGEM) and the empirical variance (EV) were recently introduced.
We will show that despite stable regularities in aggregate diffusion patterns, it remains surprisingly difficult to predict the success of any particular individual or piece of content in an online social network, with our best performing models explaining only half of the empirical variance in outcomes.
Through Monte Carlo simulation we show that both variance estimators are approximately unbiased, but that the new estimator is more stable (i.e., has lower empirical variance) and provides empirical confidence interval coverage rates that coincide more closely with the nominal coverage rates.
However, the empirical variance was significantly larger than the mean.
In addition, Fig. 2 displays the empirical variance of the estimation for each algorithm.
In fact, this way is somehow like a way of computing an approximated empirical variance of a dataset.
However in many applications, the empirical variance is found to be higher than the value assumed by the Poisson distribution.
In two publicly available data sets and one new data set, our approach identified subset(s) of reference genes with smaller empirical variance of the normalizing factor than in subsets identified using previously published methods.
We have verified that the bias of the centralised estimator (y_{t}^{K}) is lesser than the bias of the estimator (y_{t}^{Mtimes N}), as predicted by the theoretical analysis, while (y_{t}^{Mtimes N}) attains a smaller empirical variance than (y_{t}^{K}) (at least for N<1600 and 40≤J≤100).
Due to the fact that we only need μ ̃ and Σ ̃ j j, we propose the following approximation: μ ̃ is computed through the optimization of J ( f ) = τ ε ∥ g - H f ∥ 2 + 1 2 Σ j τ j f j 2 with respect to f and Σ ̃ j j which is the variance of f j is approximated by the empirical variance of f j during the iterations of the optimization algorithm.
