Probabilistic statements

A probabilistic statement of the likelihood of human-error events presents each error in the task analysis as the right limb in a binary branch of the HRA event tree. These binary branches form the chronological limbs of the HRA event tree, with the first potential error siai ting from the highest point on the tree. (Figure 4.5-4). Any given [ask appears as a two-limb branch the left limb represents the probability of success the right limb represents the probability of failure. 

By the time this realization arose, it was well recognized that random phenomena were describable only by probabilistic statements by definition it is not possible to state a priori what the outcome of any given random event will be. 

Like the word significance, the concept of probability is used in everyday language as well as in the discipline of Statistics. As Turner (2007) noted, the statement "I ll probably be there on Saturday" involves a probabilistic statement, but there is no degree of quantification (if you know the individual making this statement, past experience may lead you to have an informed opinion concerning the relative meaning of "probably," but this is a subjective judgment). 

If instead we consider that we wish to make probabilistic statements about patients in general, including those from centres we did not include, we then have to move to regarding the centres themselves as some realization of a random process. The true difference in treatment effects from centre to centre now becomes a further source of random variation because, although, if we restrict inference to these centres only, this variability is frozen (the differences are what they are and that is an end of it), if we talk about future centres then these might also vary and there is no reason why these other differences should be exactly the same which now apply. If we take account of this further source of variation, not only in forming estimators but also in calculating confidence intervals, then we have a random-effects model. 

For example, if a patient has a PET scan with F-18 FDG because of the finding of a nodule in the lung revealed by a chest x-ray, the interpretation should involve quantification of the rate of accumulation of the tracer by the lesion, together with a probabilistic statement of the degree of its malignancy and the presence of lesions elsewhere in the lungs or whole body. In view of the uncertainty in medicine, statements should whenever possible involve probability of certainty statements. 

As already mentioned the fault tree represents the logical relations between the primary events (in what follows often denoted by component failures for the sake of simplicity) and the undesired (unwanted or top) event (in what follows often denoted by system failure for the sake of simplicity). The relations represented by the fault tree are deterministic. We arrive at probabilistic statements only if probabilities are assigned to the component failures. 

In the usual probabilistic terminology this gap between statements (II) and (III) is hardly noticeable, because the term relative probability is used in a variable meaning. First it is an abbreviation for the ratio of certain T-volumes, as in the following formulation of Theorem... 

This is again a synthesis of a collection of remarks which are dispersed over all the quoted works of Boltzmann. They show clearly how many purely intuitive statements are hidden behind the usual probabilistic terminology. 

Neurotransmitter release is not assured in response to synaptic stimulation. Rather, the process of vesicle fusion for individual release-competent vesicles is probabilistic. This process confers a discrete probability (between 0 and 1) that a given synapse will release neurotransmitter after an action potential (the synaptic release probability). For the majority of synapses in the central nervous system, the release probability at a deflned synaptic contact is below 0.3, which leads to the often-quoted statement that the release process is reliably unreliable (1). Despite this fact, it has been demonstrated that some central nervous system synapses (in a variety of brain regions) do exhibit release probabilities as high as 0.9 (2-4). This higher synaptic release... 

The dominant theme of quantum theory is that its causal statements about a system are probabilistic. In other words, the epistemic rule of correspondence, which relates experience to quantum-theoretical states, involves probabilistic concepts in an essential way. In particular, an essential premise of quantum theory is that the physical condition or state of a system at a given time cannot be fully disclosed experimentally unless many measurements are made on replicas of the system prepared in a specified manner. Conversely, an inherent prerequisite of quantum theory is that a preparation of a system be specified and uniquely associated with a state prior to any attempt to reveal experimentally the characteristics of the state. It is this prerequisite that clearly distinguishes quantum mechanics from classical mechanics. It has been discussed extensively in the literature. 

In much of statistics, the notion of a population is stressed and the subject is sometimes even defined as the science of making statements about populations using samples. However, the notion of a population can be extremely elusive. In survey work, for example, we often have a definite population of units in mind and a sample is taken from this population, sometimes according to some well-specified probabilistic rule. If this rule is used as the basis for calculation of parameter estimates and their standard errors, then this is referred to as design-based inference (Lehtonen and Pahkinen, 2004). Because there is a form of design-based inference which applies to experiments also, we shall refer to it when used for samples as sampling-based inference. 

Before presenting our results on structural implications of the observed and predicted levels of activity in the MB and of the requirement of lossless information transmission, some explanation of our probabilistic approach seems warranted. The probability Ppn of activity in a given PN mainly reflects properties of the input space (odor space) and different patterns of PN activity are diced out for every LFP cycle. The connection probabilities pn->kc and kc bkc, on the other hand, refer to the random connectivity of each locust, i.e., the connectivity is determined only once for each animal. In building distributions (and taking averages) with respect to both probability spaces, we are making statements about the distribution of (and the typical value of) properties for all locusts in response to all possible odors, in a sense. 

Certification is also strictly based on what the SUBSAFE program defines as Objective Quality Evidence (OQE). OQE is defined as any statement of fact, either quantitative or qualitative, pertaining to the quality of a product or service, based on observations, measurements, or tests that can be verified. Probabilistic risk assessment, which usually cannot be verified, is not used. 

USNRC s policy for implementing risk-informed regulation was expressed in the 1995 policy statement on the use of probabilistic risk assessment (PRA) methods in nuclear regulatory activities. The policy statement says The use of PRA technology should be increased in all regulatory matters to the extent supported by the state-of-the-art in PRA methods and data and in a manner that complements the NRC s deterministic approach and supports the NRC s traditional defence-in-depth philosophy. 

Lupton (1999, p.7), in her broad discussion of the concept of risk, cites John Maynard Keynes in a similar statement on investor s behaviour by reference to Reddy (1996), stating that investor s behaviours should be classified as subject to imcertainty rather than the laws of risk, because they are driven by "animal spirits " which by their very nature are not subject to probabilistic or risk analysis (Reddy, 1996 229). 

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