Objective Bayes Factors for Gaussian Directed Acyclic Graphical Models

We propose an objective Bayesian method for the comparison of all Gaussian directed acyclic graphical models defined on a given set of variables. The method, which is based on the notion of fractional Bayes factor, requires a single default (typically improper) prior on the space of unconstrained covariance matrices, together with a prior sample size hyper-parameter, which can be set to its minimal value. We show that our approach produces genuine Bayes factors. The implied prior on the concentration matrix of any complete graph is a data-dependent Wishart distribution, and this in turn guarantees that Markov equivalent graphs are scored with the same marginal likelihood. We specialize our results to the smaller class of Gaussian decomposable undirected graphical models, and show that in this case they coincide with those recently obtained using limiting versions of hyper-inverse Wishart distributions as priors on the graph-constrained covariance matrices.Bayes factor; Bayesian model selection; Directed acyclic graph; Exponential family; Fractional Bayes factor; Gaussian graphical model; Objective Bayes;Standard conjugate prior; Structural learning. network; Stochastic search; Structural learning.

Moment Priors for Bayesian Model Choice with Applications to Directed Acyclic Graphs

We propose a new method for the objective comparison of two nested models based on non-local priors. More specifically, starting with a default prior under each of the two models, we construct a moment prior under the larger model, and then use the fractional Bayes factor for a comparison. Non-local priors have been recently introduced to obtain a better separation between nested models, thus accelerating the learning behaviour, relative to currently used local priors, when the smaller model holds. Although the argument showing the superior performance of non-local priors is asymptotic, the improvement they produce is already apparent for small to moderate samples sizes, which makes them a useful and practical tool. As a by-product, it turns out that routinely used objective methods, such as ordinary fractional Bayes factors, are alarmingly slow in learning that the smaller model holds. On the downside, when the larger model holds, non-local priors exhibit a weaker discriminatory power against sampling distributions close to the smaller model. However, this drawback becomes rapidly negligible as the sample size grows, because the learning rate of the Bayes factor under the larger model is exponentially fast, whether one uses local or non-local priors. We apply our methodology to directed acyclic graph models having a Gaussian distribution. Because of the recursive nature of the joint density, and the assumption of global parameter independence embodied in our prior, calculations need only be performed for individual vertices admitting a distinct parent structure under the two graphs; additionally we obtain closed-form expressions as in the ordinary conjugate case. We provide illustrations of our method for a simple three-variable case, as well as for a more elaborate seven-variable situation. Although we concentrate on pairwise comparisons of nested models, our procedure can be implemented to carry-out a search over the space of all models.Fractional Bayes factor; Gaussian graphical model; Non-local prior; Objective Bayes network; Stochastic search; Structural learning.

EVALUATION OF THE EFFECTIVENESS OF NATURAL ALTERNATIVE COPPER PRODUCTS AND LOW RATE COPPER FORMULATIONS AGAINST GRAPE DOWNY MILDEW IN ORGANIC VITICULTURE

The control of pathogenic fungi, especially downy mildew, represents the main problem in organic viticulture as only few fungicides, above all copper salts, can be used. As the copper causes problems of environmental impact, the Regulation EC n. 473/2002 fixed a ceiling on the use of copper compounds. Two years field trials were carried out in organic vineyeards to test the effectiveness, against Plasmopara viticola (Berk. et Curt.) Berl. et De Toni, of alternative copper products and low rate copper formulations, able to take place or to reduce copper quantities used. Amoung the alternative substances, in the first year of activity we examinated phito-stimulant and cuprics, while in the second year we examinated natural extracts, both vegetables and animals, and natural compound associates to the copper. The achieved results have underlined that, using the low rate copper formulations examinated, the total copper quantities were always less than 6 Kg copper per hectare, in accordance with the provisions of Regulation EC. The alternative products investigated have not guaranteed, instead, an adequate protection with high pressure od downy mildew. The trials confirm that the copper is indispensable for plant protection in organic farming, as it is not possible to replace it. We can only reduce the copper quantities used, at this point of time, but further studies are necessary to find appropriate alternative solutions able to control pathogenic agents in organic farming

Objective Bayesian Search of Gaussian DAG Models with Non-local Priors

Directed Acyclic Graphical (DAG) models are increasingly employed in the study of physical and biological systems, where directed edges between vertices are used to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more reasonably tackled if the variables are assumed to satisfy a given ordering; in this case, we simply have to estimate the presence or absence of each possible edge, whose direction is established by the ordering of the variables. We propose an objective Bayesian methodology for model search over the space of Gaussian DAG models, which only requires default non-local priors as inputs. Priors of this kind are especially suited to learn sparse graphs, because they allow a faster learning rate, relative to ordinary local priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables. We apply our method to a variety of simulated and real data sets.Fractional Bayes factor; High-dimensional sparse graph; Moment prior; Non-local prior; Objective Bayes; Pathway based prior; Regulatory network; Stochastic search; Structural learning.

Il cloud computing. Alla ricerca del diritto perduto nel web 3.0

Il presente saggio intende mettere a fuoco il fenomeno del cloud computing, tentando di setacciare i frammenti normativi dispersi in un fiume di norme difficilmente componibili a sistema, al fine di ricostruire il quadro giuridico vigente in materia. La certezza e la conoscibilità del diritto sono esigenze che si fanno viepiù pressanti in un terreno, come quello in esame, ancora tutto da dissodare e l’ignoranza del quale può a ragione far temere, con la prozia Léonie nella Recherche, che « la journée ne se passera pas sans pluie ». Ed è alla luce dell’attuale incertezza che si spiega il singolare fenomeno per cui, secondo una ricerca del 2014, gran parte delle imprese italiane hanno familiarità con la nuvola informatica, laddove solo una sparuta minoranza ha già iscritto in bilancio una posta per la transizione verso il nuovo paradigma. Non ci si limiterà a porre nel buratto il diritto positivo tradizionalmente inteso (sovrastatale, nazionale e regionale), ma, altresì, strumenti di soft law interni ed europei, nonché i contributi di autorità amministrative indipendenti e le riflessioni della più attenta dottrina anche extra-giuridica. Ciò nella convinzione che l’interdisciplinarità in questo campo non sia una scelta rimessa alla discrezionalità del singolo, ma un imperativo epistemologico. Chiudendo quante alle premesse metodologiche, si precisa che, dopo aver descritto il funzionamento della nuvola informatica e aver dato conto di alcuni documenti normativi a carattere generale, si procederà a una ricostruzione di tipo tematico, in modo tale da fornire, tanto al teorico, quanto al pratico, un agile strumento di lavoro, che allevî dalla faticosa lettura della congerie di atti riguardanti il cloud, potendosi concentrare anche solo sugli aspetti di contingente interesse

IPRexit. Intellectual property after the EU referendum

The Government is deciding how and when to trigger Article 50 of the Treaty on the Functioning of the European Union. In the meantime, some “remainers” are pointing out the allegedly tragic consequences of Brexit, whereas a more cautious approach would be wise. There is much uncertainty on the future of intellectual property (IP) in the UK after the referendum and one could foresee that there will be more cons than pros. However, some opportunities may as well arise. This poster aims to assess the impact of Brexit on IP by distinguishing between areas that do not need significant intervention, areas where no real intervention will be allowed and areas where there is need for an update. In the near future, the Government and the Parliament will be likely focused on the negotiations with the European Union and there is the risk that IP issues will be overlooked. Therefore, it will be up to the judiciary to modernise intellectual property and ensure that the UK does not depart radically from the IP systems of the Member States. Thus, by ensuring a substantial, albeit not full, harmonisation of the relevant rules, fragmented IP regimes will not constitute trade barriers and the UK will retain its appeal as a thriving marketplace for investors. In order to do so, some “IP regimes shopping” will be useful, although this will mean a partial departure from the EU rules. A takeaway is that since English judges will not be entitled to preliminary references to the Court of Justice, they will become eventually European judges

In light of the ends. Copyright hysteresis and private copy exception after the British Academy of Songwriters, Composers and Authors (BASCA) and others v Secretary of State for Business, Innovation and Skills case

In British Academy of Songwriters, Composers and Authors (BASCA) and others v Secretary of State for Business, Innovation and Skills, the High Court of Justice in matter of private copy exception provides the twofold prime opportunity to shed light on the state of the art of copyright in the UK and to flesh out the idea of 'legal hysteresis’. I support the reintroduction of the private copy exception, possibly in a less narrow fashion, and I explain the reasons why I am confident that my expectations will be fulfilled

On porn censorship and liberal ethics in the UK. Brief notes on the Audiovisual Media Services Regulations 2014

This article deals with the highly criticised Audiovisual Media Services Regulations 2014, which provides that now the British Board of Film Classification (BBFC) regulations apply also to the videos-on-demand (and not only to DVDs)