A two-phase method for extracting explanatory arguments from Bayesian networks

Errors in reasoning about probabilistic evidence can have severe consequences. In the legal domain a number of recent miscarriages of justice emphasises how severe these consequences can be. These cases, in which forensic evidence was misinterpreted, have ignited a scientific debate on how and when probabilistic reasoning can be incorporated in (legal) argumentation. One promising approach is to use Bayesian networks (BNs), which are well-known scientific models for probabilistic reasoning. For non-statistical experts, however, Bayesian networks may be hard to interpret. Especially since the inner workings of Bayesian networks are complicated, they may appear as black box models. Argumentation models, on the contrary, can be used to show how certain results are derived in a way that naturally corresponds to everyday reasoning. In this paper we propose to explain the inner workings of a BN in terms of arguments. We formalise a two-phase method for extracting probabilistically supported arguments from a Bayesian network. First, from a Bayesian network we construct a support graph, and, second, given a set of observations we build arguments from that support graph. Such arguments can facilitate the correct interpretation and explanation of the relation between hypotheses and evidence that is modelled in the Bayesian network

The Gravitational Wave Universe Toolbox: A software package to simulate observation of the Gravitational Wave Universe with different detectors

Context. As the importance of Gravitational Wave (GW) Astrophysics increases rapidly, astronomers in different fields and with different backgrounds can have the need to get a quick idea of which GW source populations can be detected by which detectors and with what measurement uncertainties. Aims. The GW-Toolbox is an easy-to-use, flexible tool to simulate observations on the GW universe with different detectors, including ground-based interferometers (advanced LIGO, advanced VIRGO, KAGRA, Einstein Telescope, and also customised designs), space-borne interferometers (LISA and a customised design), pulsar timing arrays mimicking the current working ones (EPTA, PPTA, NANOGrav, IPTA) and future ones. We include a broad range of sources such as mergers of stellar mass compact objects, namely black holes, neutron stars and black hole-neutron stars; and supermassive black hole binaries mergers and inspirals, Galactic double white dwarfs in ultra-compact orbit, extreme mass ratio inspirals and Stochastic GW backgrounds. Methods. We collect methods to simulate source populations and determine their detectability with the various detectors. The paper aims at giving a comprehensive description on the algorithm and functionality of the GW-Toolbox. Results. The GW-Toolbox produces results that are consistent with more detailed calculations of the different source classes and can be accessed with a website interface (gw-universe.org) or as a python package (https://bitbucket.org/radboudradiolab/gwtoolbox). In the future, it will be upgraded with more functionality.Comment: 21 pages, 26 figures, 4 tables. Submitted to Astronomy & Astrophysics; Website url: gw-universe.or

Exact algorithms for Kayles

In the game of Kayles, two players select alternatingly a vertex from a given graph G, but may never choose a vertex that is adjacent or equal to an already chosen vertex. The last player that can select a vertex wins the game. In this paper, we give an exact algorithm to determine which player has a winning strategy in this game. To analyze the running time of the algorithm, we introduce the notion of a K-set: a nonempty set of vertices W ⊆ V is a K-set in a graph G = ( V , E ) , if G [ W ] is connected and there exists an independent set X such that W = V − N [ X ]. The running time of the algorithm is bounded by a polynomial factor times the number of K-sets in G. We prove that the number of K-sets in a graph with n vertices is bounded by O(1.6052^n). A computer-generated case analysis improves this bound to O(1.6031^n) K-sets, and thus we have an upper bound of O(1.6031^n) on the running time of the algorithm for Kayles. We also show that the number of K-sets in a tree is bounded by n ⋅ 3 n / 3 and thus Kayles can be solved on trees in O(1.4423^n) time. We show that apart from a polynomial factor, the number of K-sets in a tree is sharp. As corollaries, we obtain that determining which player has a winning strategy in the games G_avoid ( POS DNF 2 ) and G_seek ( POSDNF_3 ) can also be determined in O(1.6031^n) time. In G_avoid(POSDNF_2) , we have a positive formula F on n Boolean variables in Disjunctive Normal Form with two variables per clause. Initially, all variables are false, and players alternately set a variable from false to true; the first player that makes F true loses the game. The game G_seek ( POSDNF 3 ) is similar, but now there are three variables per clause, and the first player that makes F true wins the game

Exact algorithms for Kayles

In the game of Kayles, two players select alternatingly a vertex from a given graph G, but may never choose a vertex that is adjacent or equal to an already chosen vertex. The last player that can select a vertex wins the game. In this paper, we give an exact algorithm to determine which player has a winning strategy in this game. To analyze the running time of the algorithm, we introduce the notion of a K-set: a nonempty set of vertices W ⊆ V is a K-set in a graph G = ( V , E ) , if G [ W ] is connected and there exists an independent set X such that W = V − N [ X ]. The running time of the algorithm is bounded by a polynomial factor times the number of K-sets in G. We prove that the number of K-sets in a graph with n vertices is bounded by O(1.6052^n). A computer-generated case analysis improves this bound to O(1.6031^n) K-sets, and thus we have an upper bound of O(1.6031^n) on the running time of the algorithm for Kayles. We also show that the number of K-sets in a tree is bounded by n ⋅ 3 n / 3 and thus Kayles can be solved on trees in O(1.4423^n) time. We show that apart from a polynomial factor, the number of K-sets in a tree is sharp. As corollaries, we obtain that determining which player has a winning strategy in the games G_avoid ( POS DNF 2 ) and G_seek ( POSDNF_3 ) can also be determined in O(1.6031^n) time. In G_avoid(POSDNF_2) , we have a positive formula F on n Boolean variables in Disjunctive Normal Form with two variables per clause. Initially, all variables are false, and players alternately set a variable from false to true; the first player that makes F true loses the game. The game G_seek ( POSDNF 3 ) is similar, but now there are three variables per clause, and the first player that makes F true wins the game

The Gravitational Wave Universe Toolbox

Context. As the importance of gravitational wave (GW) astrophysics increases rapidly, astronomers interested in GWs who are not experts in this field sometimes need to get a quick idea of what GW sources can be detected by certain detectors, and the accuracy of the measured parameters. Aims. The GW-Toolbox is a set of easy-to-use, flexible tools to simulate observations of the GW universe with different detectors, including ground-based interferometers (advanced LIGO, advanced VIRGO, KAGRA, Einstein Telescope, Cosmic Explorer, and also customised interferometers), space-borne interferometers (LISA and a customised design), and pulsar timing arrays mimicking the current working arrays (EPTA, PPTA, NANOGrav, IPTA) and future ones. We include a broad range of sources, such as mergers of stellar-mass compact objects, namely black holes, neutron stars, and black hole–neutron star binaries, supermassive black hole binary mergers and inspirals, Galactic double white dwarfs in ultra-compact orbit, extreme-mass-ratio inspirals, and stochastic GW backgrounds. Methods. We collected methods to simulate source populations and determine their detectability with various detectors. Our aim is to provide a comprehensive description of the methodology and functionality of the GW-Toolbox. Results. The GW-Toolbox produces results that are consistent with previous findings in the literature, and the tools can be accessed via a website interface or as a Python package. In the future, this package will be upgraded with more functions