Fusion, propagation, and structuring in belief networks
Artificial Intelligence
Probabilistic reasoning using graphs
Processing and Management of Uncertainty in Knowledge-Based Systems on Uncertainty in knowledge-based systems. International Conference on Information
Investigation of variances in belief networks
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Belief network induction
Expert Systems and Probabiistic Network Models
Expert Systems and Probabiistic Network Models
Expert Systems: Uncertainty and Learning
Expert Systems: Uncertainty and Learning
Parametric Structure of Probabilities in Bayesian Networks
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
An empirical comparison of three inference methods
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
A characterization of the dirichlet distribution with application to learning Bayesian networks
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Bayesian network classifiers. an application to remote sensing image classification
NN'05 Proceedings of the 6th WSEAS international conference on Neural networks
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
Expert Systems with Applications: An International Journal
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In this paper we analyze the problem of learning and updating of uncertainty in Dirichlet models, where updating refers to determining the conditional distribution of a single variable when some evidence is known.We first obtain the most general family of prior-posterior distributions which is conjugate to a Dirichlet likelihood and we identify those hyperparameters that are influenced by data values. Next, we describe some methods to assess the prior hyperparameters and we give a numerical method to estimate the Dirichlet parameters in a Bayesian context, based on the posterior mode. We also give formulas for updating uncertainty by determining the conditional probabilities of single variables when the values of other variables are known. A time series approach is presented for dealing with the cases in which samples are not identically distributed, that is, the Dirichlet parameters change from sample to sample. This typically occurs when the population is observed at different times. Finally, two examples are given that illustrate the learning and updating processes and the time series approach.