Sentence examples for prior equation from inspiring English sources
As the prior equation shows, the rhs does not depend on any asset specific parameter.
Substituting that into the prior equation I obtain: begin{aligned} {mathbf {p}}^{*tau }=frac{1-tau }{1-tau /R_mathrm{f}^{*tau }}E[m_i^*mathbf {X}].
The prior (Equation 7) was the same as that for the basic model, but the likelihood included independent spatial uncertainty terms, σs1 and σs2, representing the standard deviations of the Gaussian likelihoods evoked by the first and second stimuli, respectively.
FABIA: our new method with sparse prior Equation (4).
We compare the following 13 biclustering methods: FABIA : our new method with sparse prior Equation (4 ).
BPP uses gamma priors G on the population size parameters and on the age of the root in the species tree (τ 0 ), with prior mean α/ β and prior variance α/ β 2. The other divergence time parameters were assigned the Dirichlet prior (equation 2 in [ 15]).
The results of the simulations are compared on a qualitative manner with our prior equation-based host response models as shown in Figure 4 and Figure 5 (dashed lines).
By writing,, and, for a well-defined design matrix Z and a (possibly high-dimensional) vector of regression parameters β, all different priors (equations 4 and 5) can be expressed in a general Gaussian form 6 with an appropriate penalty matrix.
A component's weight (wi) would correspond to the number of functional channels of that type (in the formalism used here, weights would be negative for inputs contributing prior information (equation 3) and positive for inputs contributing current information (equation 4)).
With the proposed source prior in Equation (11), we derive a new learning algorithm to find a set of linear transformation matrices that make the components as statistically independent as possible, such that { W b * } = arg max { W b } L ( { W b } ), (13).
Plots (a) – (d) in Figure 3 are based on the Bayesian analysis which combines the two studies via the power prior in equation (2).
