J. M. Bernardo and A. F. M. Smith. Bayesian Theory. Wiley Series in Probability and Mathematical Statistics. John Wiley and Sons, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....implementation could simply manipulate the data. The Haskell code for the revised model type becomes: lpr : theta x Double, ss : x] s, ll : s theta Double, addSs : s [x] s, removeSs : s [x] s For a large class of distributions (e.g. the Exponential Family [2]) the addSs and removeSs functions will be trivial, only involving addition and subtraction. 6 Parallelism In probabilistic machine learning algorithms the likelihood function is the major (if not the only) link to the data. Through use of su#cient statistics we replace the high dimensional data ....

J. M. Bernardo and A. F. M. Smith. Bayesian Theory. Wiley Series in Probability and Mathematical Statistics. John Wiley and Sons, Chichester, 1994.

....the different random variables [9, 20] Each node is associated to a table giving the distribution of probabilities of the corresponding random variable according to the values of the random variables of which it depends on. The influence diagrams introduce decision nodes into Bayesian networks [15, 17]. These networks are possible solutions to limit the combinatorial and information explosions in decision trees with probabilities. However, both approaches, Bayesian networks and influence diagrams, necessitate, to be handled, some information about the probabilistic dependence between the ....

....directives to do an action, and the contextual nodes, which select a branch depending on the knowledge about the current context. Figure 2 shows the decision tree representation of the official procedure for train lack of power solving (the meaning of the boxes is not important, see Annex 1 and [17]) it suffices to say that the rectangular boxes are actions and the circles, contextual nodes. In summary, our representation is inspired by decision trees, but mainly differs on two points. Firstly, our trees have no chance nodes but contextual nodes. Secondly, there are no probabilities. This ....

Oliver R. and Smith J., Influence Diagrams, Belief Nets and Decision analysis. Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York, 1990.

.... of freedom is desirable as examples show that in many typical cases non informative priors are discrete (see the examples at the end of this paper, and [Ber89] and [Zha94] on one hand, whereas Bernardo s reference priors, e.g. Jeffreys prior, typically have Lebesgue densities (see [Ber79] and [BS93]) Definition 2: For a compact, dominated and uniformly integrable experiment ( X; X ) P; Theta) with P : fP : 2 Thetag having densities ff : 2 Thetag the quantity I( Gamma Z X p (x) log p (x) dx) Z Theta Z X f (x) log f (x) dx) d ) H(P ) Gamma Z ....

J.M. Bernardo and A.F.M. Smith. Bayesian Theory. Wiley Series in Probability and Mathematical Statistics, Chichester, 1993.

....performances of the network given every possible combination of input variables is therefore only feasible when the number of input variables is rather small. Alternatives, but approximations, for this brute force method are backward elimination, forward selection, and stepwise selection (see e.g. [3,7]) Backward elimination starts with all input variables and removes the least relevant variables one at the time. Backward elimination stops if the performance of network drops below a given threshold by removal of any of the remaining input variables. Forward selection starts without any input ....

N. R. Draper and H. Smith. Applied Regression Analysis. Wiley Series in Probability and Mathematical Statistics. Wiley, New York, second edition, 1981.

....in our endeavors. This Section details some basic ideas and formalism used throughout the remainder of the dissertation. Also it lays the groundwork for some of the ideas presented in the Postscript. 1.3. 1 What Is a Probability In this document, we hold fast to the Bayesian view of probability [13, 14]. This is that a probability assignment summarizes what one does and does not know about a particular situation. A probability represents a state of knowledge; its numerical value quanti es the plausibility one is willing to give a hypothesis given some background information. This point of view ....

J. M. Bernardo and A. F. Smith, Bayesian Theory. Wiley Series in Probability and Mathematical Statistics, Chichester: Wiley, 1994. 155

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J. M. Bernardo and A. F. M. Smith. Bayesian Theory. Wiley Series in Probability and Mathematical Statistics. John Wiley and Sons, 1994.

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