Next, the construction of a bayesian network from a fault tree lies in the estimation (quantification) of probabilities, it consists in this step to assign probabilities of occurrence of basic events (primaries) of fault tree to node roots as probabilities a priori, but in case of induced events (intermediate) and final events (dreaded) associated probabilities will be estimated on the basis of calculation of conditional probabilities
11) Henceforth, let it be understood that the examples involving higher conditional probabilities
compared to a baseline include the requisite relation of making the end more probable unless otherwise specified.
For that, the time-dependent probability of failure is computed using the joint up-crossing method , conditional probabilities
of failure and the total probability theorem.
As I present in Figure 2, students who were fully included in general education had higher conditional probabilities
for graduation in any year after high school entry.
However, consistency requires that conditional probabilities
express logical inferences not physical influences.
The statistically less "electable" candidates, whose conditional probabilities
of winning fall in the 25-35% range according to prediction markets, are Ted Cruz (35.
The conditional probabilities
of system failure in column 2 of the table are exact and the approximation is only in column 3, where the probability of the condition is approximated by the latency of B alone.
It is only the final computation of the conditional probabilities
for each individual goal that requires access to the complete set of explanations.
Independent and Conditional Probabilities
for Concept Structuring:
Tables 3-6 present the conditional probabilities
calculated for the manufacturing sectors covered by Pavitt's (1984) taxonomy.
This is done by use of the 'chain rule', which says in a BN the full joint probability distribution is the product of all conditional probabilities
specified in the BN :
It concerned conditional probabilities
or 'what if?
Although a move toward conditional probabilities
of audit is occasionally implied, even if unintentionally, theorists have yet to incorporate the concept fully into utility models of tax compliance.
The Directed Acyclic Graph (DAG) that results after the construction of a BN is quantified through a series of conditional probabilities
based on data or information available about the system or problem (Jensen, Nielsen 2007; Korb, Nicholson 2011) and defines a factorisation of a joint probability distribution over the variables represented in the DAG.
Subsequent chapters cover countable and uncountable sample spaces, continuous random variables, functions of one and two random variables, conditional probabilities
for countable sample spaces and continuous random variables, Bernoulli, geometric and Poisson processes, Brownian motion and white noise, and convergence of random variables.