Sufficiency beliefs

Bayesian statistics are applicable to analyzing uncertainty in all phases of a risk assessment. Bayesian or probabilistic induction provides a quantitative way to estimate the plausibility of a proposed causality model (Howson and Urbach 1989), including the causal (conceptual) models central to chemical risk assessment (Newman and Evans 2002). Bayesian inductive methods quantify the plausibility of a conceptual model based on existing data and can accommodate a process of data augmentation (or pooling) until sufficient belief (or disbelief) has been accumulated about the proposed cause-effect model. Once a plausible conceptual model is defined, Bayesian methods can quantify uncertainties in parameter estimation or model predictions (predictive inferences). Relevant methods can be found in numerous textbooks, e.g., Carlin and Louis (2000) and Gelman et al. (1997). 

The relationship between the main subsystems and other minor systems is illustrated schematically in Figure 12.4. This places management at the core of the quality system, with the other systems arranged as major and minor satellites that revolve around it. This perspective provides the basis for the Quality System Inspection Technique (QSIT), which the FDA uses for auditing medical device facilities. This is based on a top-down approach, which starts with management controls and then looks at three other key subsystems of Design Controls, Corrective and Preventative Actions (CAPA) and Production and Process Controls. The belief is that by focussing on just these four subsystems, you will actually touch on all the other subsystems and obtain a sufficiently satisfactory overview of the state of compliance of the facility. 

It has been well remarked of Ramsay that he stood to the outside world for an essentially British school of chemistry. To describe him as original would be like saying water is wet. He was of the essence of originality, and, during the time the writer knew him, entirely without any apparent sheet-anchor of fixed conviction or established belief in scientific doctrine, which at all times, in a science somewhat prone to let go sheet-anchors, made him a unique and almost incomprehensible personality. It is true that in his later years he suffered from the defects of these qualities, and he failed to criticize sufficiently his own ideas and experimental results before making them public. (Worthington 1916)... 

The improvements made in hydroaminomethylation technology suggest that certain variants of this reaction are sufficiently developed for the potential production of amines. The synthesis of linear tertiary and secondary amines from terminal alkenes shows promise in this regard. Belief s recent contributions towards hydroaminomethylation using ammonia to produce linear primary amines, which are of industrial significance due to their abundance, suggest a bright future for this reaction. Branched selective hydroaminomethylation remains relatively underdeveloped and needs further study. 

Based on this evidence, the odds that a toxic release caused the flshkill is a convincing 108 to 1. The level of belief is now sufficiently high for a reasonable person to take regulatory action. Bayes theorem allowed optimal use of evidence to define the belief warranted in the causal hypothesis that a toxic release caused the flshkill evidence changed our state of knowledge about the flshkill. 

Answers to why we strive for particular goals, or avoid particular outcomes, may lie in events that occurred in infancy or early childhood. Becoming aware of these unconscious influences, contrary to some popular belief, does not always require deep psychoanalysis. Many of our unconscious motives and forces are only unconscious because we have never taken the time to allow them to surface. Once we examine our behaviour and start the process of self-questioning, much will come into consciousness. You may not plumb the bottom of your psyche. But all you are seeking is sufficient awareness and understanding to provide a lever for change. 

There are also other elements that the first principle requires us to include in S. We must include O s premises, because S needs a reason for undertaking the task of producing the belief that p in O, and, though the belief that has the premises would be sufficient, it is hard to see why S should acquire this belief without the premises themselves. The performance of the task will then require further beliefs in... 

What is hard to explain is how a belief, or the perception that one has sufficient reasons for a belief, can sustain a contrary belief. Of course it cannot sustain it in the sense of giving it rational support sustain here must mean only cause. What we must do is find a point in the sequence of mental states where there is a cause that is not a reason something irrational according to the agent s own standards.6... 

It is shown in this paper that, contrary to previous common belief, under certain special, but still fully feasible experimental conditions rarefaction shock waves can exist. In particular, this situation should certainly occur in gases with a sufficiently large specific heat e near the critical point of fluid-vapor transition. In recent years the prediction made by Ya.B. has been conclusively confirmed by experiment.1 Later Ya.B. considered the peculiarities of the state near the critical point which may occur in a rapid, shock expansion. 

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