Many arguments have been given for regarding the probability laws as coherence conditions on degrees of belief and for taking some principle of conditionalization to be a rule of probabilistic inference.
The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization.
This is not because Figure 5 is conclusively ruled out by the distribution, but rather because it is gratuitously complex: it postulates more causal connections (and hence more probabilistic parameters) than are necessary to explain the underlying pattern of probabilistic dependencies.
As physics stands, we can safely conclude that the universe is gushing out of the quantum vacuum right this moment with mathematical precision as described by the probabilistic rules of quantum field theory and, ultimately, the probabilistic rules of superstring theory and quantum gravity.
Mostly only footprints are known, so that buildings had to be extruded with extensive use of probabilistic rules.
We therefore used a stochastic model to extract a succinct set of probabilistic rules that capture this diversity.
The derivation of probabilistic rules based on the transition probabilities between individual prototypes is the stringent extension of the presented approach for describing complex sequences (Geurten et. al. submitted).
The shape of the cell is evolved by updating each pixel based on a set of probabilistic rules.
