Parameter weights

ErrF (parameters) = weight (reference value - calculated value)"... 

Drilling parameters (weight on bit, rotary speed, nozzle size, flowrate)... 

Transition matrix estimators have received less attention than the multicanonical and Wang-Landau methods, but have been applied to a small collection of informative examples. Smith and Bruce [111, 112] applied the transition probability approach to the determination of solid-solid phase coexistence in a square-well model of colloids. Erring ton and coworkers [113, 114] have also used the method to determine liquid-vapor and solid-liquid [115] equilibria in the Lennard-Jones system. Transition matrices have also been used to generate high-quality data for the evaluation of surface tension [114, 116] and for the estimation of order parameter weights in phase-switch simulations [117]. 

COAL STRUCTURE PARAMETERS (weight fraction DMMF)... 

Figure 7-5 The result of traditional minimum norm inversion without model parameter weights. The bottom panel shows the density distribution obtained after 32 iterations. The top panel presents the normalized misfit functional versus iteration number...

Now we introduce model parameter weights, using the approach outlined in Chapter -3, sections 3.5.4 ... 

Figure 7-6 Results of the minimum norm inversion with the model parameter weights.

In the derivation of Eq. (17) it is assumed that the "instrument parameters" Lo, L, and E are known exactly. In reality these quantities can be determined only according to some probability distribution P(L0, L, 6, E ), which determines the instrument resolution. The measured count rate Cm(t) is an average over the possible values of these parameters, weighted by their probability of occurrence... 

Filters are given by pulse sequences which, in most cases, generate longitudinal magnetization which differs from the thermodynamic equilibrium state in some specific way [99, 100]. Many different filters can be conceived and combined to produce parameter weights of spin density images. Basically, any pulse sequence can be considered a magnetization filter, but particularly useful ones are... 

The first term is a measure of the average log-goodness of fit of the model class Cj. It accounts for the log-goodness of fit for different combinations of the parameters, weighted by the posterior PDF, instead of the optimal parameters alone. An ideal model class should fit the data well even with a reasonably small perturbation of the parameters from their optimal values. In the special case if the likelihood function is of the Gaussian type and the prior PDF is relatively flat, the posterior PDF is approximately Gaussian and the log-likelihood function takes the following form ... 

The main design feature of Ihe IFF is that it assumes the features operate independently. This ensures that the munber of parameters (weights) to be determined is very low, and hence easy to learn from data or set by hand. The formulation doesn t in general suffer from sparse data problems, as there are nearly always enough examples of each feature present in the data. 

For m input variables the pseudo-dimension for prediction by a multilayer perceptron neural network requires that at least m+1 independent samples are available per node for building a model (Sontag, 1998 Schmitt, 2001). It therefore appears that a larger set of data points is required to fit nonlinear models, such as neural networks that generally have a large number of parameters (weights) to fit. 

---