Bayesian: being, relating to, or involving statistical methods that assign probabilities or distributions to events (as rain tomorrow) or parameters (as a population mean) based on experience or best guesses before experimentation and data collection and that apply Bayes' theorem to revise the probabilities and distributions after obtaining experimental data.
This is Bayes Theorem. In the context of Bayes, probability speaks the the degree of belief. We believe that the cost of our project will come in under $10M if all the work goes as planned.
Bayes' theorem links the degree of belief in a proposition before and after accounting for evidence. For Bayes to be used in project work, we need evidence of what happened in the past. Were there any projects of a similar nature that came in under $10M.
This approach, while possibly counter intuitive, is distinctly different from taking a guess about what the project would cost. It says that to have any credible estimate, we need to know something about what happened in the past.
In project work, a Bayesian network is formed as a probabilistic graph - a directed graph. This less than definitive data about the project represented in the directed graph (the sequence of work activities), can apply Bayesian statistics to determine probabilities in the presence of uncertainty.
From Bayes An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, in a Letter to John Canton, A. M. F. R. S. Philosophical Transactions (1683-1775)