Relative likelihood, defined

Models Part of the foundation of statistics consists of the mathematical models which characterize an experiment. The models themselves are mathematical ways of describing the probabihty, or relative likelihood, of observing specified values of random variables. For example, in tossing a coin once, a random variable x could be defined by assigning to x the value I for a head and 0 for a tail. Given a fair coin, the probabihty of obsei ving a head on a toss would be a. 5, and similarly for a tail. Therefore, the mathematical model governing this experiment can be written as... 

The final combination represented in the third statement is performed using Bayes theorem, which essentially weights the likelihood from the trial with the relative plausibilities defined by the prior distribution (Spiegelhalter et al., 2004). 

Urbanization as a factor in the relative likelihood of U.S. housing units having LBP was presented and quantified in this survey, as summarized in Table 6.14. Urbanization referred to (1) presence in or outside an MSA as defined by the U.S. Bureau of the Census and/or (2) presence in one of two MSA categories differing in population size as also defined by the U.S. Bureau of the Census. Those U.S. MSAs with a population of 2,000,000 or higher had 24,967,000 residential units, of which 8,963,000 or 36%... 

The key descriptors used to predict the likelihood of a CYP inhibition are incredibly vast. Descriptors can, for example, be defined as spatial, electronic or conformational. Some of the key structural properties include lipophilicity, pKa and PSA and are relatively easy to interpret, while others are more complex. For further information on descriptors used in DDI modeling, please refer to De Groot et al. [6]. 

The longer the neurological deficit lasts and the later in the course of the stroke symptoms CT or DWI are performed, the higher the likelihood of a positive finding. Moderate decreases of cerebral perfusion as defined by increased relative mean transit times (rMTT), decreased relative cerebral blood flow (rCBF) but normal relative cerebral blood volume (rCBV) are typically found in DWI negative TIA or stroke patients (Ay et al. 1999b). 

If, however, rirz = 1, then P[i and Pzi defined above are equal. That is to say, the likelihood that an Mi unit follows an M unit equals the likelihood that it follows an Mz unit in the product. The absolute value of this probability depends on the relative coneentrations of monomers in the feed, but the equivalence of probabilities is independent of the feed and copolymer compositions. A similar equality for Pz2 tnd Piz can be shown by analogous reasoning, and this equivalence of probabilities is a necessary condition for a random distribution of monomer residues in the copolymer. 

The entropy of an image is defined as 5 = -" filogfi where fi is the intensity in pixel i relative to a default or model value. The statistic used is the Poisson log-likelihood L=log Prob(data model) = e x /n The... 

While it is relatively easy to identify hazards at system conception, performing a hazard or risk assessment before a design is available is more problematic. At best, only a very rough estimate is possible. Risk is usually defined as a combination of severity and likelihood. Because these two different qualities (severity and likelihood) cannot be combined mathematically, they are commonly qualitatively combined using a risk matrix. Figure 10.4 shows a fairly standard form for such a matrix. 

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