Parametric Approach

In contrast to traditional ambient fixed station "parametric approaches to river quality evaluation for trends determination and water quality standards attainment, data from the Willamette River, Oregon, USA were used to demonstrate the value of quantitative, semi-quantitative and qualitative approaches to mechanistic assessment of river water quality. 

Wahrendorf, J., Mahon, G.A.T. and Schumacher, M. (1985). Anon-parametric approach to the statistical analysis of mutagenicity data. Mutation Res. 147 5-13. 

There is often a particular concern for the effects of outliers or heavy-tailed distributions when using standard statistical techniques. To address this type of a situation, a parametric approach would be to use ML estimation assuming a heavy-tailed distribution (perhaps a Student t distribution with few degrees of freedom). However, simple ad hoc methods such as trimmed means may be useful. There is a large statistical literature on robust and outlier-resistant methods, (e.g., Hoaglin et al. 1983 Barnett and Lewis 1994). 

For these reasons non-parametric methods are used infrequently within the context of clinical trials and they tend only to be considered if it is clear that a corresponding parametric approach, either directly or following a data transformation, is unsuitable. 

More robust deconvolution methods can be derived by a parametric approach. For example, let us seek h(t) in the form of a polyexponential... 

Another non - parametric approach is deconvolution by discrete Fourier transformation with built - in windowing. The samples obtained in pharmacokinetic applications are, however, usually short with non - equidistant sample time points. Therefore, a variety of parametric deconvolution methods have been proposed (refs. 20, 21, 26, 28). In these methods an input of known form depending on unknown parameters is assumed, and the model response predicted by the convolution integral (5.66) is fitted to the data. 

The parametric approach, which is not strictly needed for a single Gray-Scott reaction, works very well for an arbitrary number of parallel reactions and for continuous mixtures. Figure 16 shows a case of two parallel reactions for which an isola and a mushroom coexist. Because the notions of continuous mixtures and reactions will be treated in Chapter 8, G H and in the group of papers listed in the Index of Subjects in Publications under the heading Continuous mixtures, we can be very brief and start with the nondimensional equations. Let x be the index of the mixture whose species are /4(x). The steady-state concentration of the material with index in (x, x + dx) is V(x)dx, the feed concentration a(x)dx and the conversion U(x) = 1 - V/(x)/a(x), the last being defined only for values of x for which a(x) is not zero. B, the autocatalytic agent, forms itself as an undifferentiated product whose concentration is W. The rate of the first reaction, and hence p,(x), depends on the... 

Thus, the parametric approach works well for continuous mixtures and we have only to calculate integrals, which, except in particular cases, we may have to calculate using finite sums. 

The parametric approach lends itself to a spreadsheet type of calculation. The first column can contain a large number of values of SI spaced logarithmically, i.e., if there are N values between a and b, the nth is a(bla)n/N. Actually, it is best to have three contiguous intervals (a,b), (b,c), and (c,d) each with, for example, 100 values each. Then a and d can be chosen to get a convincing... 

O Donoghue and Nilges, 1997), but these are neither more accurate, nor do they have the computational simplicity and elegance of the parametric approach. 

Refinery profit as measured by the LP objective function increased as the incremental crude was charged to the refinery. At a point equal to about 50% of the available incremental crude, however, the profit function began to decline. The profit at maximum incremental crude rate actually ended up at a lower value than the initial LP case value using this parametric approach. 

Finally, we may consider a parametric analysis of the relative differences (Figure 14-14 and Table 14-9). A goodness-of-fit test (Anderson-Darling test, P greater than 0.5) showed that the relative differences did not depart significantly from a normal distribution, which in this case supports the parametric approach (Figure 14-15). The parametric 2.5 and 97.5... 

In all types of data analysis there are assumptions made. In a parametric approach, like the one in NONMEM, many assumptions concern the handling of the residual error (9,12) and, in a sense, the validity of the whole analysis rests on the degree to which we have accounted for the residual variability appropriately. The two most important assumptions in this respect are (a) that the residual variability is homoscedastic and (b) that the residuals are symmetrically distributed. 

Escalate on the basis of an exposure-response relationship and not a simple dose-response relationship and using mCRM or likelihood CRM or a non-parametric approach depending on the statistical tools that are available to the team. The response should be based on both toxicity and efficacy separately parameterized according to continuous or at least ordinal variables. 

A set of observed data points is assumed to be available as samples from an unknown probability density function. Density estimation is the construction of an estimate of the density function from the observed data. In parametric approaches, one assumes that the data belong to one of a known family of distributions and the required function parameters are estimated. This approach becomes inadequate when one wants to approximate a multi-model function, or for cases where the process variables exhibit nonlinear correlations [127]. Moreover, for most processes, the underlying distribution of the data is not known and most likely does not follow a particular class of density function. Therefore, one has to estimate the density function using a nonparametric (unstructured) approach. 

A Negiz and A Cinar. A parametric approach to statistical monitoring of processes with autocorrelated observations. In AIChE Annual Meeting, Miami, FL, 1995. 

A parametric approach of the r-process referred to as the multi-event r-process (MER) has been developed recently (see [24] for details). It drops some of the basic assumptions of the canonical model, but keeps the... 

A fundamental issue in the description of even the simplest, isolated autoionising resonance in the parametric approach followed by Fano [391] - and further pursued in K-matrix theory - is that the atom cannot be deperturbed, that is one cannot access the so-called prediagonalised states which are imagined to exist prior to autoionisation being included as a perturbative interaction, since the effect is anyway internal to the atom and cannot truly be turned off. This has the disadvantage that the parameters, once they have been obtained, must still be calculated from an ab initio model of the atom for a full comparison with theory. It might seem that the parametric theory cannot really be checked independently of ab initio calculations whose accuracy is hard to ascertain. 

In the comparison of calibration methods, the results show that the non-parametric techniques decreased the regression error by approximately 50% over the parametric approaches. The sensor array used in these examples was... 

Acion L, Peterson JJ, Temple S, Arndt S (2006) Probabilistic index an intuitive non-parametric approach to measuring the size of treatment effects. Statistics in Medicine 25 591-602. 

Concorde D, Toutain PL, The withdrawal time estimation of veterinary drugs A non-parametric approach, J. Vet. Pharmacol. Ther. 1997 20 374-379. 

Martinez M, Friedlander L, Condon R, Meneses J, O Rangers J, Weber N, Miller M, Response to criticisms of the US FDA parametric approach for withdrawal time estimation Rebuttal and comparison to the nonparametric method proposed by Concorde and Toutain, J. Vet. Pharmacol. Ther. 2000 23 21-35. 

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