Mathematically, a spatially stationary field is represented by the parameter vector A defined by A = b a 1 σ 1 x 01 y 01 … a B σ B x 0 B y 0 B k T (1).
Based on Eq. (12) which is derived by MSA, the approximate result of the output vector change ∆Y caused by the parameter vector change (Delta {varvec{upalpha}}) and input vector change Δu can be obtained after the PSM Sα and ISM Su are taken into Eq. (12).
Moreover, s k (θ,ψ k,t) is the angular signal distribution of the kth source that is parameterized by the parameter vector, (boldsymbol {psi }_{k}=left [bar {theta }_{k},sigma _{k}right ]^{T}), containing its central DOA, (bar {theta }_{k}), and angular spread, σ k.
The first stage for the user is to place both models in approximately the same position and orientation, see Figure 5, and then the anatomy of the Candide-3 model (given by the parameter vector σ) is manually adapted to the target head model using 10 sliders.
Here, we assume that the mRNA degradation rate for a gene across the experiments comes from the same distribution, which is characterized by the parameter vector.
We considered a set of models M1,..., M B, where each model M k consists of a family of distributions p(D| θ k, M k ) indexed by the parameter vector θ k, where D = (X, Y) is the observed data.
After building an augmented system state by concatenating the parameter vector and the state vector, the joint estimation of states and parameters reduces to filtering of the augmented state vector which makes SMC methods directly applicable to the problem.
end{aligned} All the above distributions depend on the spike history up to time t, denoted by (mathcal{H}_{t}), the parameter vector θ and the stimulus (S t)).
The identification criterion is to minimize the least squares error (12) by optimization over the parameter vector a, that consists of the unknown parameters in (5).
The parameter size column in Table 1 approximates the memory size which is needed to store the parameter vector by multiplying the number of parameters by 8. Since the parameter vector is not sparse, we store it as a dense vector which include continuous real values.
Above we used θ* to denote the 'true' parameter vector, for which (1) describes reality with sufficient accuracy, and by θ ^ we denote the parameter vector which minimizes (2).
