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Deterministic vs. probabilistic (stochastic). A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions.
The systems studied in chaos theory are deterministic. If the initial state were known exactly, then the future state of such a system could theoretically be predicted. However, in practice, knowledge about the future state is limited by the precision with which the initial state can be measured, and chaotic systems are characterized by a strong dependence on the initial condit
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
The probability function P is defined in such a way that, if the experiment were to be repeated an infinite number of times, the relative frequencies of occurrence of each of the events would approach agreement with the values P assigns them.
Tasks are affected by external events, which transform an activity from one state to another. One of the important properties of an event is the moment when an event occurs during the course of an activity. This moment, when an event occurs, in most cases is probabilistic and can be defined using statistical distribution. The original state is ...
Probabilistic forecasting summarizes what is known about, or opinions about, future events. In contrast to single-valued forecasts (such as forecasting that the maximum temperature at a given site on a given day will be 23 degrees Celsius, or that the result in a given football match will be a no-score draw), probabilistic forecasts assign a probability to each of a number of different ...
deterministic actions, which can be taken only one at a time, and a single agent. Since the initial state is known unambiguously, and all actions are deterministic, the state of the world after any sequence of actions can be accurately predicted, and the question of observability is irrelevant for classical planning.
As a result, many turn to a notion of probabilistic causation. Informally, A probabilistically causes B if A's occurrence increases the probability of B. This is sometimes interpreted to reflect imperfect knowledge of a deterministic system but other times interpreted to mean that the causal system under study has an inherently indeterministic ...