Preface |
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v | |
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1 | (4) |
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1 | (1) |
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2 | (1) |
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What is not in this book? |
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3 | (1) |
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How should this book be used? |
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4 | (1) |
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Logic, Uncertainty, and Probability |
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5 | (20) |
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What is an expert system? |
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5 | (1) |
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Diagnostic decision trees |
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6 | (1) |
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7 | (1) |
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8 | (2) |
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The naive probabilistic approach |
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10 | (1) |
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Interpretations of probability |
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11 | (2) |
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13 | (1) |
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14 | (3) |
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Bayesian reasoning in expert systems |
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17 | (4) |
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A broader context for probabilistic expert systems |
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21 | (4) |
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Building and Using Probabilistic Networks |
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25 | (18) |
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Graphical modelling of the domain |
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26 | (5) |
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27 | (1) |
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28 | (1) |
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29 | (1) |
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Further background to the elicitation process |
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29 | (2) |
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From specification to inference engine |
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31 | (3) |
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31 | (2) |
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From moral graph to junction tree |
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33 | (1) |
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34 | (3) |
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The clique-marginal representation |
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36 | (1) |
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Incorporation of evidence |
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36 | (1) |
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Bayesian networks as expert systems |
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37 | (3) |
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Background references and further reading |
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40 | (3) |
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40 | (1) |
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Specifying the probability distribution |
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40 | (3) |
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43 | (20) |
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43 | (6) |
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Chordal and decomposable graphs |
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49 | (3) |
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52 | (3) |
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From chain graph to junction tree |
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55 | (6) |
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57 | (2) |
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59 | (2) |
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Background references and further reading |
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61 | (2) |
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Markov Properties on Graphs |
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63 | (20) |
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63 | (3) |
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Markov fields over undirected graphs |
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66 | (4) |
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Markov properties on directed acyclic graphs |
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70 | (5) |
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Markov properties on chain graphs |
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75 | (4) |
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Current research directions |
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79 | (1) |
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79 | (1) |
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Other graphical representations |
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80 | (1) |
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Background references and further reading |
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80 | (3) |
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83 | (42) |
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An illustration of local computation |
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84 | (1) |
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85 | (2) |
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86 | (1) |
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Local computation on the junction tree |
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87 | (8) |
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87 | (1) |
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Numerical specification and initialization |
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87 | (1) |
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88 | (1) |
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Flow of information between adjacent cliques |
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88 | (1) |
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89 | (1) |
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90 | (2) |
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92 | (1) |
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92 | (1) |
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Entering and propagating evidence |
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93 | (2) |
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95 | (1) |
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Generalized marginalization operations |
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95 | (14) |
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97 | (2) |
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Degeneracy of the most probable configuration |
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99 | (1) |
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99 | (2) |
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Finding the M most probable configurations |
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101 | (2) |
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Sampling without replacement |
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103 | (1) |
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104 | (2) |
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106 | (3) |
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109 | (11) |
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109 | (1) |
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109 | (1) |
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109 | (3) |
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112 | (2) |
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Propagation without evidence |
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114 | (1) |
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Propagation with evidence |
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114 | (5) |
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119 | (1) |
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Dealing with large cliques |
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120 | (3) |
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121 | (1) |
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122 | (1) |
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Current research directions and further reading |
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123 | (2) |
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Gaussian and Mixed Discrete-Gaussian Networks |
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125 | (30) |
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126 | (1) |
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Basic operations on CG potentials |
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127 | (4) |
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Marked graphs and their junction trees |
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131 | (4) |
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Decomposition of marked graphs |
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131 | (2) |
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Junction trees with strong roots |
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133 | (2) |
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135 | (2) |
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Operating in the junction tree |
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137 | (6) |
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Initializing the junction tree |
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138 | (1) |
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138 | (1) |
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139 | (1) |
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Flow of information between adjacent cliques |
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139 | (2) |
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141 | (2) |
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A simple Gaussian example |
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143 | (1) |
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144 | (6) |
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145 | (1) |
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146 | (1) |
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147 | (1) |
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Forming the junction tree |
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148 | (1) |
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Initializing the junction tree |
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148 | (1) |
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149 | (1) |
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Complexity considerations |
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150 | (1) |
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Numerical instability problems |
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151 | (1) |
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152 | (1) |
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Current research directions |
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152 | (1) |
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Background references and further reading |
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153 | (2) |
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Discrete Multistage Decision Networks |
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155 | (34) |
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The nature of multistage decision problems |
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156 | (1) |
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Solving the decision problem |
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157 | (2) |
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159 | (4) |
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Network specification and solution |
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163 | (9) |
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Structural and numerical specification |
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163 | (2) |
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165 | (1) |
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Making the elimination tree |
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166 | (1) |
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Initializing the elimination tree |
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167 | (1) |
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Message passing in the elimination tree |
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168 | (1) |
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Proof of elimination tree solution |
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169 | (3) |
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172 | (5) |
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172 | (3) |
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Making the elimination tree |
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175 | (1) |
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Initializing the elimination tree |
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176 | (1) |
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177 | (1) |
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177 | (6) |
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183 | (1) |
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184 | (3) |
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Background references and further reading |
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187 | (2) |
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Learning About Probabilities |
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189 | (36) |
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Statistical modelling and parameter learning |
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189 | (1) |
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Parametrizing a directed Markov model |
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190 | (2) |
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Maximum likelihood with complete data |
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192 | (1) |
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Bayesian updating with complete data |
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193 | (7) |
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193 | (4) |
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Specifying priors: An example |
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197 | (2) |
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Updating priors with complete data: An example |
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199 | (1) |
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200 | (2) |
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Sequential and batch methods |
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201 | (1) |
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Maximum likelihood with incomplete data |
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202 | (2) |
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202 | (2) |
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204 | (1) |
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Bayesian updating with incomplete data |
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204 | (12) |
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206 | (1) |
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Retaining global independence |
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207 | (2) |
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Retaining local independence |
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209 | (2) |
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211 | (2) |
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Simulation results: full mixture reduction |
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213 | (1) |
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Simulation results: partial mixture reduction |
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214 | (2) |
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Using Gibbs sampling for learning |
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216 | (5) |
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Hyper Markov laws for undirected models |
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221 | (1) |
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Current research directions and further reading |
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222 | (3) |
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Checking Models Against Data |
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225 | (18) |
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226 | (3) |
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227 | (2) |
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229 | (5) |
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232 | (1) |
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233 | (1) |
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234 | (1) |
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235 | (3) |
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236 | (2) |
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238 | (3) |
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241 | (2) |
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243 | (22) |
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244 | (1) |
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244 | (1) |
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Criteria for comparing models |
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245 | (6) |
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246 | (1) |
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247 | (1) |
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248 | (1) |
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249 | (1) |
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Model selection and model averaging |
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250 | (1) |
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Graphical models and conditional independence |
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251 | (2) |
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253 | (3) |
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Models containing only observed quantities |
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253 | (1) |
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Models with latent or hidden variables |
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254 | (1) |
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255 | (1) |
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256 | (9) |
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256 | (2) |
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Probability specification |
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258 | (2) |
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Prior information on parameters |
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260 | (1) |
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261 | (4) |
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265 | (16) |
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Conjugate Analysis for Discrete Data |
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267 | (4) |
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267 | (2) |
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269 | (2) |
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271 | (6) |
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271 | (2) |
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Sampling from the moral graph |
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273 | (1) |
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General probability densities |
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274 | (1) |
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275 | (2) |
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Information and Software on the World Wide Web |
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277 | (4) |
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Information about probabilistic networks |
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277 | (2) |
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Software for probabilistic networks |
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279 | (1) |
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Markov chain Monte Carlo methods |
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280 | (1) |
Bibliography |
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281 | (26) |
Author Index |
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307 | (6) |
Subject Index |
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313 | |