Probability models for

Lancet D, Sadovsky E and Seidemann E 1993 Probability model for molecular recognition in biological receptor repertoires significance to the olfactory system Proc. Natl Acad. Sci. USA 90 3715-19... 

Setting up the probability model for the data and parameters of the system under smdy. This entails defining prior distributions for all relevant parameters and a likelihood function for the data given the parameters. 

Figure 9.3. Concept of using a state estimator to Figure 9.4. A probable model for a state estimator,...

Statistical studies of MALDI MS applied to bacterial samples show that some biomarker peaks are highly reproducible and appear very consistently, while others appear much less reliably.1719 In Jarman et al.20 and Wahl et al.21 a probability model for MALDI signatures is proposed that takes into account the variability in appearance of biomarker peaks. This method constructs MALDI reference signatures from the set of peak locations for reproducible biomarker peaks, along with a measure of the reproducibility of each peak. 

Hierarchical model A model consisting of multiple parameters that can be regarded as related or connected in some way by the structure of the problem, implying that a joint probability model for these parameters should reflect the dependence among them. 

A whole series of known anomalies in. the static and mnetie properties of the proton in aqueous solution may he explained by the assumption that it is present as the hydrated hydroninm ion. Earlier considerations [1 j have already resulted in the following most probable model for the hydration shell of the proton (Pig. I). H3(F as centre is strongly... 

Figure 10. Pairing of two disclination lines of opposite signs (lamellar details are not featured) (top) a less probable model for the core of a dislocation (middle) and focal line appearing on the dislocation in order to release locally deformation energy (bottom)...

The Bayesian approach to subset selection is outlined in Sections 2 to 4. Section 2 gives the mathematical ingredients of the analysis a probability model for the data, prior distributions for the parameters (J3, a, 5) of the model, and the resultant posterior distribution. 

A general and precise description of stereoisomerism in polymers is suggested on the basis of the repetition theory which describes the distinct patterns along a line that can be obtained from a three-dimensional motif. The probability models for describing the" stero-sequence length in various possible cases of interest in stereoregular polymers are discussed. It is shown that for describing the stereosequence structure, the simplest probability model must involve a Markov chain with four probability parameters. 

Fig. 2. The motif model for 7-proteobactcrial lexA orthologous promoters. (A) The probability model for the frequency solution shown in B. The optimal MAP model in C contains 14 sites from seven sequences. Several of these sites have low sampling probabilities and may represent false-positives.

The bounds of a cumulative distribution might be or if those bounds are mathematically meaningful to the probability model. For a lower bound a = -o°, the cumulative distribution is interpreted as the probability of observing a value smaller than b. The positive infinity bound is exactly opposite. 

Harlow, D. G., and Wei, R. P., A Mechanistically Based Approach to Probability Modeling for Corrosion Fatigue Crack Growth, Engr. Frac. Mech., 45, 1 (1993), 79-88. 

It is now possible to maximize the posterior probability P M DC) to give the most probable model for the two-dimensional spectrum S Fi,F2). There are many methods available for such a computation, including the Markov chain Monte-Carlo algorithm. 

Lancet, D., Sadovsky, E., Seidemann, E. Probability models for molecular recognitionin biological receptor repertoires Significance to the olfactory system. PNAS 90, 3715-3719 (1993)... 

An energy based packing analysis was performed(40) for this polysaccharide by considering two independent chains, which implies the possibility of having parallel or antiparallel chains. Results based on these calculations show that the antiparallel structure seems to be the more probable model for this compound, although an x-ray refinement has not yet been performed. Interchain hydrogen bonds are readily formed between the chains and are probably responsible for the water insolubility of the compound. 

The other dominant approach for estimation is known as Bayesian estimation. We do not attempt to give a detailed exposition of the topic here much greater detail can be found in Gehnan et al. (2004) and Carhn and Louis (2000). In this approach, the parameters are treated as random variables themselves. This is in contrast to the maximum-likehhood estimation procedure, in which the parameters are treated as unknown constants that only take one possible value. In the Bayesian framework, the goal is to make inference about the parameters. This is done in the following way. The parameters themselves have a certain probabUistic model that we call a prior distribution. We then construct a posterior probability model for the parameters by the use of Bayes s mle ... 

This prior PDF is based on choosing a Gaussian PDF as a probability model for the eigen equation errors, where the prior covariance matrix Y,eq controls the size of these equation errors. The uncertainty in the equation errors for each mode are modeled as independent and identically distributed, so ... 

This work is a step towards building a full initiation probability model for explosive storage. Further work is required to understand the likelihood of unit response to triggers. The empirical Bayes methods... 

It is well established that collision speed is the most important predictor for injury severity [3-7]. However, for constructing probability models for advanced applications, several additional research questions arise ... 

Plausibility Check and Indications for Implementation 5.4.1 Probability Models for ISS and Fatalities... 

A main focus of the thesis was the construction of injury probability models for the pedestrian in frontal vehicle crashes (Chap. 5). The literature review conducted... 

---