## Bayesian Networks and Decision GraphsBayesian networks and decision graphs are formal graphical languages for representation and communication of decision scenarios requiring reasoning under uncertainty. Their strengths are two-sided. It is easy for humans to construct and to understand them, and when communicated to a computer, they can easily be compiled. Furthermore, handy algorithms are developed for analyses of the models and for providing responses to a wide range of requests such as belief updating, determining optimal strategies, conflict analyses of evidence, and most probable explanation. The book emphasizes both the human and the computer side. Part I gives a thorough introduction to Bayesian networks as well as decision trees and infulence diagrams, and through examples and exercises, the reader is instructed in building graphical models from domain knowledge. This part is self-contained and it does not require other background than standard secondary school mathematics. Part II is devoted to the presentation of algorithms and complexity issues. This part is also self-contained, but it requires that the reader is familiar with working with texts in the mathematical language. The author also: *Provides a well-founded practical introduction to Bayesian networks, decision trees and influence diagrams *Gives several examples and exercises exploiting the computer systems for Bayesian netowrks and influence diagrams *Gives practical advice on constructiong Bayesian networks and influence diagrams from domain knowledge. *Embeds decision making into the framework of Bayesian networks *Presents in detail the currently most efficient algorithms for probability updating in Bayesian networks *Discusses a wide range of analyes tools and model requests together with algorithms for calculation of responses. *Gives a detailed presentation of the currently most efficient algorithm for solving influence diagrams.Finn V. Jensen is professor of computer science at the University of Aalborg. |

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### Contents

III | 3 |

IV | 4 |

V | 6 |

VI | 10 |

VII | 11 |

IX | 12 |

X | 13 |

XII | 15 |

LXXVII | 109 |

LXXVIII | 110 |

LXXIX | 113 |

LXXX | 114 |

LXXXII | 116 |

LXXXIV | 118 |

LXXXV | 119 |

LXXXVI | 120 |

XIII | 17 |

XIV | 18 |

XV | 20 |

XVI | 21 |

XVII | 22 |

XVIII | 23 |

XIX | 24 |

XX | 25 |

XXI | 27 |

XXII | 28 |

XXIII | 30 |

XXV | 35 |

XXVI | 36 |

XXVII | 38 |

XXVIII | 39 |

XXIX | 40 |

XXX | 41 |

XXXI | 43 |

XXXII | 44 |

XXXIV | 46 |

XXXV | 50 |

XXXVI | 52 |

XXXVII | 54 |

XXXVIII | 55 |

XXXIX | 57 |

XLI | 59 |

XLII | 61 |

XLIII | 62 |

XLIV | 64 |

XLV | 66 |

XLVI | 68 |

XLVII | 69 |

XLVIII | 70 |

L | 71 |

LII | 72 |

LIII | 73 |

LIV | 74 |

LVI | 79 |

LVII | 80 |

LVIII | 81 |

LIX | 82 |

LX | 83 |

LXI | 84 |

LXII | 87 |

LXIII | 88 |

LXIV | 89 |

LXV | 90 |

LXVI | 91 |

LXVII | 92 |

LXVIII | 93 |

LXIX | 95 |

LXX | 97 |

LXXI | 98 |

LXXII | 101 |

LXXIV | 102 |

LXXV | 104 |

LXXVI | 105 |

LXXXVII | 122 |

LXXXIX | 125 |

XC | 128 |

XCIII | 133 |

XCIV | 135 |

XCV | 136 |

XCVI | 137 |

XCIX | 140 |

C | 142 |

CI | 145 |

CII | 147 |

CIII | 151 |

CV | 157 |

CVI | 159 |

CVII | 162 |

CVIII | 165 |

CIX | 166 |

CXI | 169 |

CXII | 172 |

CXIII | 174 |

CXIV | 177 |

CXV | 179 |

CXVI | 180 |

CXVIII | 182 |

CXIX | 184 |

CXX | 187 |

CXXI | 189 |

CXXII | 192 |

CXXIII | 193 |

CXXIV | 201 |

CXXV | 202 |

CXXVI | 203 |

CXXVIII | 205 |

CXXIX | 208 |

CXXXI | 209 |

CXXXIII | 210 |

CXXXIV | 211 |

CXXXV | 213 |

CXXXVII | 216 |

CXXXVIII | 219 |

CXXXIX | 222 |

CXLI | 223 |

CXLIII | 225 |

CXLIV | 227 |

CXLV | 228 |

CXLVI | 235 |

CXLVII | 236 |

CXLVIII | 238 |

CXLIX | 241 |

CLI | 245 |

CLII | 246 |

CLIII | 251 |

CLV | 253 |

CLVI | 255 |

263 | |

### Common terms and phrases

action algorithm Angina Artificial Intelligence assume Bayes Bayesian network calculate called causal network certainty chain rule chance node chance variable clique Cold conditional independencies conditional probabilities configuration conflict Construct d-separated decision nodes decision tree determine direction domain graph elimination order evidence example Exercise expected utility Fever fill-ins fractional updating give graph in Figure graphical hidden Markov model hypothesis variable impact infected influence diagram initial instantiated Jensen join tree joint probability table Lauritzen Let BN marginalizing Markov maximal messages method milk model in Figure moral graph network in Figure observed optimal P(Angina pa(A parameters parents perfect elimination sequence perform policy network posterior probabilities prior probabilities propagation Proposition represented Section set of potentials set of variables simplicial nodes slice solving sore throat spark plugs strategy strong junction tree structure subset task Theorem triangulated graph troubleshooting undirected graph utility nodes yields