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Rational hazard forecasts should fully recognize the large, indeed dominant role of uncertainties in volcanic processes, and be therefore expressed through probabilities.
For volcanic risk assessment, the functions account for uncertainties (through probabilities) in the link between hazard intensity and damage (loss) upon which risk mitigation and management decisions are based.
It's bad enough that the quantum field is invisible, without location, and only measured through probabilities.
For simplicity, uncertainty is handled through probabilities and their calculus.
For qualitative researchers, a case analysis may, for instance, be an adequate knowledge form, while many quantitative researchers primarily express their knowledge through probabilities.
The area-level exposure distribution in our setting is characterized through probabilities of exposure at low, medium, and high level rather than through area-level mean values.
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Guidelines for microdroplet experiments are established through probability analysis of variables basic to specimen design.
This fascinating layman's trek through probability theory, from its roots in dice games in the seventeenth century to its role in modern-day thermodynamics, tackles humanity's innate need to seek order in even the most chaotic phenomena.
Then the weakest failure modes, i.e. the representative failure modes that have significant impact on the system, are located through Probability Network Evaluation Technique.
The comparative study is carried out by analyzing the statistics of the waves and through probability of exceedance of the wave peaks.
The characteristics of distribution of collision in configuration and velocity spaces are investigated in detail through probability density functions (PDFs) in the generalized coordinates.
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