A posteriori

The a posteriori probability P[A G] for having the spectral density A(uj), given the simulation data G, is... 

Apokamphersaure, /. apocamphoric acid. Apokodein, n. apocodeine. aposteriorisch, a. a posteriori. 

Thus, if we know a priori the probability of the occurrence of bu we can compute the a posteriori probability that if a occurred then 6, was the cause of it, thus going from effects to causes. The problem here is to determine P(bt), which most of the time are not known and are sometimes (inadequately) assumed to be equally likely when nothing is known about them. 

Since a heterodyne receiver is an amplitude and phase detector, it could nicely be used to correlate optical signals received at various remote sites. The local oscillator can be a single laser distributed by optical fiber to the various sites or local lasers that can be synchronized "a posteriori" by reference to a common source (e.g. a bright star). 

This approach is equivalent to the maximum a posteriori (MAP) approach derived by Wallner (Wallner, 1983). The position of the maximum is unchanged by a monotonic transformation and hence further simplification can be achieved by taking the logarithm of Eq. 8... 

Leboissetier, A., N. Okong o, and J. Bellan, Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Rart 2. A posteriori modelling. /. Fluid Mech., 2005. 523 37-78. 

The theoretical results provided by the large basis sets II-V are much smaller than those from previous references [15-18] the present findings confirm that the second-hyperpolarizability is largely affected by the basis set characteristics. It is very difficult to assess the accuracy of a given CHF calculation of 2(ap iS, and it may well happen that smaller basis sets provide theoretical values of apparently better quality. Whereas the diagonal eomponents of the eleetrie dipole polarizability are quadratic properties for which the Hartree-Fock limit can be estimated with relative accuracy a posteriori, e.g., via extended calculations [38], it does not seem possible to establish a variational principle for, and/or upper and lower bounds to, either and atris-... 

Vahron, P., Vibok, A., Mayer, I., 1993, Comparision of a Posteriori and a Priori BSSE Correction Schemes for SCF Intermolecular Energies , J. Comput. Chem., 14, 401. 

To assure consistency and speed in multidisciplinary structure analysis of low-MW compounds involving various techniques (IR, NMR, MS, etc.) most industrial laboratories use a Standard Operating Procedure (SOP). In such schemes IR analysis is frequently used as a cheap filter for a quick starting control and as a means for verification. As IR detects only structural units identification of an unknown compound on the basis of IR is difficult. Mass spectrometry is used as the prime identification tool and is especially important in the determination of the exact mass and gross formulae. While structural prognostication on the basis of MS is difficult for the non-expert, a posteriori interpretation is quite feasible. H NMR is both easy and cheap, however requires greater sample quantities than either... 

In brief, the Bayesian approach uses PDFs of pattern classes to establish class membership. As shown in Fig. 22, feature extraction corresponds to calculation of the a posteriori conditional probability or joint probability using the Bayes formula that expresses the probability that a particular pattern label can be associated with a particular pattern. 

The calculations discussed in the previous section fit the noise-free amplitudes exactly. When the structure factor amplitudes are noisy, it is necessary to deal with the random error in the observations we want the probability distribution of random scatterers that is the most probable a posteriori, in view of the available observations and of the associated experimental error variances. 

Another recent tool has been developed within the ORCHESTRA project. The tool keeps into account both the chemometric information and the toxicity predictions done by the model, and in particular what kind of errors have been done by the model. It applies to the CAESAR QSAR models. Furthermore, this tool is based not only on the a priori data and information, as the other approaches, but also on the a posteriori result of the model. The user knows if the model can or cannot be used for a certain compound. In some cases a warning is given, recommending expert opinion. In all cases the reasons for the reliability is given, and it can be evaluated in a transparent way. 

---