A comparison of two approaches for solving unconstrained influence diagrams

AbstractInfluence diagrams and decision trees represent the two most common frameworks for specifying and solving decision problems. As modeling languages, both of these frameworks require that the decision analyst specifies all possible sequences of observations and decisions (in influence diagrams, this requirement corresponds to the constraint that the decisions should be temporarily linearly ordered). Recently, the unconstrained influence diagram was proposed to address this drawback. In this framework, we may have a partial ordering of the decisions, and a solution to the decision problem therefore consists not only of a decision policy for the various decisions, but also of a conditional specification of what to do next. Relative to the complexity of solving an influence diagram, finding a solution to an unconstrained influence diagram may be computationally very demanding w.r.t. both time and space. Hence, there is a need for efficient algorithms that can deal with (and take advantage of) the idiosyncrasies of the language. In this paper we propose two such solution algorithms. One resembles the variable elimination technique from influence diagrams, whereas the other is based on conditioning and supports any-space inference. Finally, we present an empirical comparison of the proposed methods

Sequential influence diagrams: A unified asymmetry framework

We describe a new graphical language for specifying asymmetric decision problems. The language is based on a filtered merge of several existing languages including sequential valuation networks, asymmetric influence diagrams, and unconstrained influence diagrams. Asymmetry is encoded using a structure resembling a clustered decision tree, whereas the representation of the uncertainty model is based on the (unconstrained) influence diagram framework. We illustrate the proposed language by modeling several highly asymmetric decision problems, and we describe an efficient solution procedure

Sequential Influence Diagrams: A Unified Asymmetry Framework

We describe a new graphical language for specifying asymmetric decision problems. The language is based on a filtered merge of several existing languages including sequential valuation networks, asymmetric influence diagrams, and unconstrained influence diagrams. Asymmetry is encoded using a structure resembling a clustered decision tree, whereas the representation of the uncertainty model is based on the (unconstrained) influence diagram framework. We illustrate the proposed language by modeling several highly asymmetric decision problems, and we outline an efficient solution procedure

Muons and emissivities of neutrinos in neutron star cores

In this work we consider the role of muons in various URCA processes relevant for neutrino emissions in the core region of neutron stars. The calculations are done for $\beta$--stable nuclear matter with and without muons. We find muons to appear at densities $\rho = 0.15$ fm$^{-3}$, slightly around the saturation density for nuclear matter $\rho_0 =0.16$ fm$^{-3}$. The direct URCA processes for nucleons are forbidden for densities below $\rho = 0.5$ fm$^{-3}$, however the modified URCA processes with muons $(n+N\rightarrow p+N +\mu +\overline{\nu}_{\mu}, p+N+\mu \rightarrow n+N+\nu_{\mu}$), where $N$ is a nucleon, result in neutrino emissivities comparable to those from $(n+N\rightarrow p+N +e +\overline{\nu}_e, p+N+e \rightarrow n+N+\nu_e$). This opens up for further possibilities to explain the rapid cooling of neutrons stars. Superconducting protons reduce however these emissivities at densities below $0.4$ fm$^{-3}$.Comment: 14 pages, Revtex style, 3 uuencoded figs include