A structural Markov property for decomposable graph laws that allows control of clique intersections

We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques, so is capable of encoding some interesting structure. We prove the equivalence of this property to an exponential family assumption, and discuss identifiability, modelling, inferential and computational implications.Comment: 10 pages, 3 figures; updated from V1 following journal review, new more explicit title and added section on inferenc

Sampling decomposable graphs using a Markov chain on junction trees

Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology for such inference, by making two contributions to the computational geometry of decomposable graphs. The first of these provides sufficient conditions under which it is possible to completely connect two disconnected complete subsets of vertices, or perform the reverse procedure, yet maintain decomposability of the graph. The second is a new Markov chain Monte Carlo sampler for arbitrary positive distributions on decomposable graphs, taking a junction tree representing the graph as its state variable. The resulting methodology is illustrated with numerical experiments on three specific models.Comment: 22 pages, 7 figures, 1 table. V2 as V1 except that Fig 1 was corrected. V3 has significant edits, dropping some figures and including additional examples and a discussion of the non-decomposable case. V4 is further edited following review, and includes additional reference

Living Originalism

Originalists routinely argue that originalism is the only coherent and legitimate theory of constitutional interpretation. This Article endeavors to undermine those claims by demonstrating that, despite the suggestion of originalist rhetoric, originalism is not a single, coherent, unified theory of constitutional interpretation, but is rather a disparate collection of distinct constitutional theories that share little more than a misleading reliance on a common label. Originalists generally agree only on certain very broad precepts that serve as the fundamental underlying principles of constitutional interpretation: specifically, that the writtenness of the Constitution necessitates a fixed constitutional meaning, and that courts that see themselves as empowered to give the Constitution some avowedly different meaning are behaving contrary to law. Originalists have been able to achieve agreement on these broad underlying principles, but they have often viewed as unduly narrow and mistaken the understanding held by the original originalists-the framers of originalism, if you will-as to how those principles must be put into action. And originalists disagree so profoundly amongst themselves about how to effectuate those underlying principles that over time they have articulated-and continue to articulate-a wide array of strikingly disparate, and mutually exclusive, constitutional theories. In this regard, originalists have followed a living, evolving approach to constitutional interpretation. Our account of originalism\u27s evolution-and of the extensive disagreement among originalists today-undermines originalists\u27 normative claims about the superiority of their approach. Originalists\u27 claims about the unique and exclusive legitimacy of their theory-that originalism self-evidently represents the correct method of constitutional interpretation-founder when one considers that originalists themselves cannot even begin to agree on what their correct approach actually entails. And their claims that originalism has a unique ability to produce determinate and fixed constitutional meaning, and thus that only originalism properly treats the Constitution as law and properly constrains judges from reading their own values into the Constitution, stumble when one considers the rapid evolution and dizzying array of versions of originalism; because each version has the potential to produce a different constitutional meaning, the constitutional meaning that a committed originalist judge would find turns out to be anything but fixed. As originalism evolves, the constitutional meanings that it produces evolve along with it. Today\u27s originalists not only reach results markedly different from those originalists reached thirty years ago, but also produce widely divergent results amongst themselves. Judges committed to the originalist enterprise thus have significant discretion to choose (consciously or subconsciously) the version of originalism that is most likely to dictate results consistent with their own preferences. As such, originalism suffers from the very flaws that its proponents have identified in its alternatives

Capacity of a Simple Intercellular Signal Transduction Channel

We model the ligand-receptor molecular communication channel with a discrete-time Markov model, and show how to obtain the capacity of this channel. We show that the capacity-achieving input distribution is iid; further, unusually for a channel with memory, we show that feedback does not increase the capacity of this channel.Comment: 5 pages, 1 figure. To appear in the 2013 IEEE International Symposium on Information Theor