Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra.There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

Child Welfare as Child Protection Then and Now: What Social Workers Did and Continue to Do

The research reported here builds on the work of one of the authors who, some thirteen years ago, in a similar study, examined the potential for social workers to shift from a child protection to a child welfare practice orientation. As with the original research study, this present project seeks to examine the everyday practices of social workers with children and families as revealed by file analysis, vignette questionnaires (reported here) and interviews with families and social workers (to be reported). A twenty-item vignette questionnaire was completed by fifty-five social workers (65.5 per cent response rate). It was found that there was little agreement on coding decisions with regard to which cases should be designated child protection or child welfare. Further analysis revealed that, regardless of such coding decisions, families tended to receive similar responses by social workers. The results demonstrate that, whilst there has been a reduction in the headline numbers of child protection investigations undertaken across Health and Social Care Trusts in Northern Ireland, the everyday patterns of practice with families and children where parenting concerns remain evident reflect child protection risk management priorities and practices. 

Sequence Effects in the Valuation of Multiple Environmental Programs Using the Contingent Valuation Method

In contingent valuation, the willingness to pay for hypothetical programs may be affected by the order in which programs are presented to respondents. With inclusive lists, economic theory suggests that sequence effects should be expected. However, when policy makers allocate public budgets to several environmental programs, they may be interested in assessing the value of the programs without the valuations being affected by the order in which the programs are presented. Using single-bounded dichotomous choice contingent valuation questions, we show that if respondents have the possibility to revise their willingness-to-pay answers, sequence effects are mitigated. (JEL Q51, Q54)