Aleatory uncertainties are associated with physical variability (e.g., material properties, operating condition manufacturing, and tolerance) in the system and environment which are typically handled using probabilistic methods.
Because the cumulative distribution functions for many common probability distributions are sigmoidal, these curves are typically the result of a probabilistic mechanism.
These probabilistic associations are typically rather weak and the contributions of these genetic variations to disease are often greatly overshadowed by environmental (lifestyle) factors that contribute more significantly to increasing the risk of diseases such as lung cancer or type II diabetes.
Probabilistic sampling designs are typically used for site assessment, waste management, remedial investigation/feasibility studies, remedial action projects, and risk-assessment studies.
A multivariate probability class is introduced given the first- and second-moment information and the condition on log-concavity of the JPDF, which is versatile enough to cover the majority of multivariate probabilistic models that are typically used in reliability applications.
Probabilistic graphical models are typically trained to maximize the likelihood of the training data and evaluated on some measure of accuracy on the test data.
Probabilistic hazard datasets are typically quite robust in that they often include a range of data types (e.g., volcanic ash thickness, ash grain size) at multiple levels of uncertainty (e.g., 90th percentile, average) over a number of different time frames (e.g., in the event of an eruption, in the next 10 years).
Moreover, most of the above methods are based on probabilistic models, which are typically very computation intensive.
Secondly, many empirical studies have investigated potential FIE in maturation schedules and probabilistic reaction norms (Dieckmann and Heino 2007), whereas changes in growth are typically assumed to be plastic and empirical studies looking at FIE in growth remain rare.
Probabilistic or stochastic models use probability in the formulation of the model and are typically used for a population of only few cells or for molecular events with only small number of molecules, e.g., transcription.
