## Score and Information for Recursive Exponential Models with Incomplete Data. (0)

Citations: | 10 - 2 self |

### BibTeX

@TECHREPORT{Thiesson_scoreand,

author = {Bo Thiesson},

title = {Score and Information for Recursive Exponential Models with Incomplete Data.},

institution = {},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

Recursive graphical models usually underlie the statistical modelling concerning probabilistic expert systems based on Bayesian networks. This paper defines a version of these models, denoted as recursive exponential models, which have evolved by the desire to impose sophisticated domain knowledge onto local fragments of a model. Besides the structural knowledge, as specified by a given model, the statistical modelling may also include expert opinion about the values of parameters in the model. It is shown how to translate imprecise expert knowledge into approximately conjugate prior distributions. Based on possibly incomplete data, the score and the observed information are derived for these models. This accounts for both the traditional score and observed information, derived as derivatives of the log-likelihood, and the posterior score and observed information, derived as derivatives of the log-posterior distribution. Throughout the paper the specialization int...

### Citations

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Citation Context ...k. Final preparation was done at Microsoft Research, Redmond, WA 98052-6399. of Wermuth and Lauritzen (1983), which usually underlie the statistical modelling concerning probabilistic expert systems (=-=Pearl 1988-=-; Andreassen et al. 1989; Spiegelhalter et al. 1993) based on Bayesian networks. For a recursive graphical model the structural relations between variables are represented by a directed acyclic graph,... |

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Citation Context ...of providing the first and second order derivatives of the log-likelihood and log-posterior distribution to be used for iterative estimation methods, and for interfacing a sequential updating method (=-=Spiegelhalter and Lauritzen 1990-=-a, 1990b) to follow up on a quantified model as new observations occur. An application of first order derivatives for estimation with incomplete data in REMs is demostrated in a companion paper (Thies... |

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Citation Context ...ariable, X v , and directed edges signify for each variable the existence of direct causal influence from variables represented by parent nodes, X pa(v) . Markov properties with respect to the graph (=-=Kiiveri et al. 1984-=-; Lauritzenset al. 1990) imply that any distribution, which is structurally defined by the model, can be represented by tables of conditional distributions, p(X v j X pa(v) ), which for each possible ... |

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Citation Context ...) = Y i ~ v 2I ~ v p(i ~ v js~ v ; ` ~ vj ~ v ) P v2~v n(iv ;v ) ; each defined by the exponential model (4). The natural local conjugate priors are therefore defined by conjugate exponential models (=-=Diaconis and Ylvisaker 1979-=-) p(` ~ vj ~ v ) / exp i ` 0 ~ vj ~ vs\Gamma fiOE(` ~ vj ~ v ) j ; wheresis a vector of same dimension as ` ~ vj ~ v and fi is a scalar. Let ` ~ vj ~ v denote the value which maximizes p(` ~ vj ~ v ).... |

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Citation Context ... 1990a, 1990b) to follow up on a quantified model as new observations occur. An application of first order derivatives for estimation with incomplete data in REMs is demostrated in a companion paper (=-=Thiesson 1995-=-). For recursive graphical models without local restrictions a similar derivation of first order derivatives was proposed in Spiegelhalter et al. (1993) and Lauritzen (1995) and given in Russell et al... |

17 | Mixed interaction models - Lauritzen, Wermuth - 1984 |