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Table 1: Means and variances of the marginal probability distributions of nodes, initially and after evidence.
2003
"... In PAGE 6: ... The first part of the code defines the mean vector and covariance matrix of the Bayesian network. Table1 shows the initial marginal probabilities of the nodes (no evidence) and the conditional probabilities of the nodes given each of the evidences {A = x1} and {A = x1, C = x3}. An examination of the results in Table 1 shows that the conditional means and variances are rational expressions, that is, ratios of polynomials in the parameters.... In PAGE 6: ... Table 1 shows the initial marginal probabilities of the nodes (no evidence) and the conditional probabilities of the nodes given each of the evidences {A = x1} and {A = x1, C = x3}. An examination of the results in Table1 shows that the conditional means and variances are rational expressions, that is, ratios of polynomials in the parameters. Note, for example, that for the case of evidence {A = x1, C = x3}, the polynomials are first- degree in p, q, a, b, x1, and x3, that is, in the mean and variance parameters and in the evidence variables, and second-degree in d, f, i.... ..."
Cited by 2
Tables 10.2 and 10.3 show the simulation results in terms of the minimum resulting margin at LT and NT node for noise models XA and XB, XC, XD respectively. The margin for the loop that have the minimum margin, for a given bitrate, are shown in bold. (They are the ones that determine the insertion loss.) Then among those marked margins, we have used italic (and blue) to indicate where more than 0.5dB margin exist.
Table 1.1 Marginal probabilities of states being true obtained in the chest clinic model (ASIA). First column: exact marginals. Second column: marginals computed using rst order approximation (mean eld). Third column: marginals computed using an approximation up to second order (TAP). Node Exact MF TAP
Table 2. Initial probabilities of nodes.
1997
"... In PAGE 4: ... program in C++ language. In fact the code in Fig. 2 has been generated by this computer program given the network in Example 1. Table2 shows that the initial marginal probabilities of the nodes are polynomials in the parameters.... In PAGE 10: ...an example, from Table2 the maximum and minimum values for the initial probabilities of node H = 0 are attained in the set f0:372; 0:36; 0:3704; 0:3596g. 9 Conclusions The symbolic structure of prior and posterior marginal probabilities of Bayesian networks have been characterized as polynomials or rational functions of the parameters, respectively, and the degrees of the polynomials have been shown to be dependent on the deterministic or random character of evidence.... ..."
Cited by 2
Table 10: Learning Dynamic 5-Node Test Case - Ordinate Coefficients (aR) and Slope Co- efficients (bR) for the Linear Marginal Cost Functions Reported to the ISO by the Five Generators on Day 422 in Each of the Twenty Runs, with Summary Statistics
2006
"... In PAGE 23: ... Tables 8 and 9 provide detailed numerical solution values (means and standard deviations) for real power production levels and LMPs, respectively, on day 422. Table10 gives the ordinate coefficient aR and slope coefficient bR for the (linear) marginal cost function reported to the ISO on Day 422 by each of the five Generators in each of the twenty runs. In the following discussion we highlight various aspects of these outcomes that differ significantly from the corresponding outcomes presented for the no-learning treatment in Section 4.... ..."
Cited by 5
Table 1: C4BD approximation error of single node marginals for the fully connected graph C3BL and the 4 nearest neighbour grid with 9 nodes, with varying potential and coupling strengths B4CSpotBN CScoupB5. Three different variational methods are compared: MF/Tree derives a lower bound with mean field approximation for A8BV and tree-reweighted belief propagation for A8; MF/SDP derives a lower bound with the SDP relaxation used for A8; Tree/MF derives an upper bound using tree- reweighted belief propagation for A8BV and mean field for A8. SDP denotes the heuristic use of the dual parameters in the SDP relaxation, with no provable upper or lower bounds.
2004
"... In PAGE 7: ... To assess the accuracy of each approximation, we use the C4BD error, defined as BD D2 D2 CG D7BPBD CYD4AIB4CG BE BVB5 A0 CQ D4AIB4CG BE BVB5CY (36) where CQ D4AI denotes the estimated marginal. The results are shown in Table1 for the single node case, and in Table 2... ..."
Cited by 6
Table 1. A procedure for computing marginal prices when the number of supply and demand points are large
"... In PAGE 5: ...etwork used for the analysis in the state (see Section 3.2 for more details.). This observation leads one to design an enumerative procedure that is computationally based more on the nodes of the transportation network rather than the pixels of the region. The core operations in the improved procedure are given in Table1 . The procedure was implemented in the C programming language and was loosely connected with the Arc/Info GIS software package for the convenience of analysis and display of the resulting marginal price surface.... In PAGE 5: ... The procedure was implemented in the C programming language and was loosely connected with the Arc/Info GIS software package for the convenience of analysis and display of the resulting marginal price surface. ( Table1 about here) 2. An Application in the Identification of Candidate Ethanol Conversion Plant Locations The methodology described in Section 2 was applied in a Regional Integrated Biomass Assessment (RIBA) project [13].... ..."
Table V also shows that the aggregate throughput under the ECS improves marginally in comparison to the IEEE 802.11. This can be explained as follows. Under the IEEE 802.11, whenever node B sends back the CTS frame to node A, node C will defer by the EIFS value. However, the Data frame transmitted by node A will be discarded by node B as node C will send out a frame after it has deferred by the EIFS duration. Therefore, the bandwidth during the EIFS deferment at node C is wasted, explaining why the aggregate throughput under IEEE 802.11 is smaller than that in the ECS. Again, the improvement of ECS in the aggregate throughput should be much higher if a high-rate physical layer is used.
Table II. Cost assignments of some event-based parsimony methods marginally touching (jungles) or falling outside (other methods) the space described in Table I. In modified BPA, n is the number of vertices (nodes) in H between the two host edges involved in the shift, plus one. Fitch optimisation cannot be used for tree fitting but is powerful in detecting duplication- switching patterns (Table III).
2002
Cited by 3
Table 3: Flight crew model variables
"... In PAGE 38: ....1.5 Model quantification Quantification of the model concerns quantification of the marginal distributions of the nodes in the model as well as of the dependencies between the nodes. Table3 lists the nodes, their definition and how the marginal distribution will be derived, either based on data or on expert judgement. All relations between nodes will be quantified based on expert judgment.... ..."
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