Efficient computational strategies for doubly intractable problems with applications to Bayesian social networks

Powerful ideas recently appeared in the literature are adjusted and combined to design improved samplers for Bayesian exponential random graph models. Different forms of adaptive Metropolis-Hastings proposals (vertical, horizontal and rectangular) are tested and combined with the Delayed rejection (DR) strategy with the aim of reducing the variance of the resulting Markov chain Monte Carlo estimators for a given computational time. In the examples treated in this paper the best combination, namely horizontal adaptation with delayed rejection, leads to a variance reduction that varies between 92% and 144% relative to the adaptive direction sampling approximate exchange algorithm of Caimo and Friel (2011). These results correspond to an increased performance which varies from 10% to 94% if we take simulation time into account. The highest improvements are obtained when highly correlated posterior distributions are considered.Comment: 23 pages, 8 figures. Accepted to appear in Statistics and Computin

Participatory justice and mediation toward a new model of justice

This paper provides a brief description of the model of participatory justice that is emerging in Europe and in North and South American States. Participatory justice promotes new forms of conflict resolution, as does mediation, based on voluntariness and confidentiality, as well as the participation of all parties in the management of conflict. In 2010, Italian legislators introduced mediation as an alternative form of dispute resolution in civil and commercial matters in order to reduce the burden of the Courts. This reform has not been successful so far because Italian lawmakers have introduced mediation into the civil justice system without reforming the framework of its underlying principles.El presente artículo tiene como propósito realizar una breve descripción teórica sobre el modelo de justicia participativa que está surgiendo en Europa y en los Estados del continente americano. La justicia participativa promueve métodos alternativos de resolución de conflictos, como la mediación, caracterizados por la voluntariedad, la confidencialidad y la participación de todas las partes en la gestión de conflictos que las dividen. En 2010 los legisladores italianos introdujeron la mediación en asuntos civiles y mercantiles para reducir la carga de los tribunales. La reforma, sin embargo, no tuvo éxito debido a que los legisladores italianos establecieron la mediación sin armonizar sus principios con los del modelo tradicional de justicia

Branched covers of the sphere and the prime-degree conjecture

To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate surface cover" is an abstract branch datum, a priori not coming from a branched cover, but satisfying the Riemann-Hurwitz formula. The old Hurwitz problem asks which candidate surface covers are realizable by branched covers. It is now known that all candidate covers are realizable when the candidate covered surface has positive genus, but not all are when it is the 2-sphere. However a long-standing conjecture asserts that candidate covers with prime degree are realizable. To a candidate surface cover one can associate one Y -> X between 2-orbifolds, and in a previous paper we have completely analyzed the candidate surface covers such that either X is bad, spherical, or Euclidean, or both X and Y are rigid hyperbolic orbifolds, thus also providing strong supporting evidence for the prime-degree conjecture. In this paper, using a variety of different techniques, we continue this analysis, carrying it out completely for the case where X is hyperbolic and rigid and Y has a 2-dimensional Teichmueller space. We find many more realizable and non-realizable candidate covers, providing more support for the prime-degree conjecture.Comment: Some slips in the first version have been corrected, and a reference to the omitted proofs now fully available online has been added; 44 pages, 14 figure

An extension of Peskun ordering to continuous time Markov chains

Peskun ordering is a partial ordering defined on the space of transition matrices of discrete time Markov chains. If the Markov chains are reversible with respect to a common stationary distribution "greek Pi", Peskun ordering implies an ordering on the asymptotic variances of the resulting Markov chain Monte Carlo estimators of integrals with respect to "greek Pi". Peskun ordering is also relevant in the framework of time-invariance estimating equations in that it provides a necessary condition for ordering the asymptotic variances of the resulting estimators. In this paper Peskun ordering is extended from discrete time to continuous time Markov chains. Key words and phrases: Peskun ordering, Covariance ordering, Effciency ordering, MCMC, time-invariance estimating equations, asymptotic variance, continuous time Markov chains.

Efficient estimate of Bayes factors from Reversible Jump output

We exend Meng and Wong (1996) identity from a fixed to a varying dimentional setting. The identity is a very powerful tool to estimate ratios of normalizing constants and thus can be used to evaluate Bayes factors. The extention is driven by the reversibler jump algorithm so that the output from the semplar can be directly used to efficiently estimate the required Bayes factor. Two applications, involving linear and logistic regression models, illustrate the advantages of the suggested approach with respect to alternatives previously proposed in the literature.Bayes factor; Bayesian modeel choice; Marginal likelihood; Markov chain Monte Carlo; Reversible jump

Parallel hierarchical sampling:a general-purpose class of multiple-chains MCMC algorithms

This paper introduces the Parallel Hierarchical Sampler (PHS), a class of Markov chain Monte Carlo algorithms using several interacting chains having the same target distribution but different mixing properties. Unlike any single-chain MCMC algorithm, upon reaching stationarity one of the PHS chains, which we call the “mother” chain, attains exact Monte Carlo sampling of the target distribution of interest. We empirically show that this translates in a dramatic improvement in the sampler’s performance with respect to single-chain MCMC algorithms. Convergence of the PHS joint transition kernel is proved and its relationships with single-chain samplers, Parallel Tempering (PT) and variable augmentation algorithms are discussed. We then provide two illustrative examples comparing the accuracy of PHS with