"Building" exact confidence nets

Confidence nets, that is, collections of confidence intervals that fill out the parameter space and whose exact parameter coverage can be computed, are familiar in nonparametric statistics. Here, the distributional assumptions are based on invariance under the action of a finite reflection group. Exact confidence nets are exhibited for a single parameter, based on the root system of the group. The main result is a formula for the generating function of the coverage interval probabilities. The proof makes use of the theory of "buildings" and the Chevalley factorization theorem for the length distribution on Cayley graphs of finite reflection groups.Comment: 20 pages. To appear in Bernoull

Quantum state discrimination bounds for finite sample size

In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of two given and completely known states, rho or sigma. In general, it is not possible to decide the identity of the true state with certainty, and the optimal measurement strategy depends on whether the two possible errors (mistaking rho for sigma, or the other way around) are treated as of equal importance or not. Results on the quantum Chernoff and Hoeffding bounds and the quantum Stein's lemma show that, if several copies of the system are available then the optimal error probabilities decay exponentially in the number of copies, and the decay rate is given by a certain statistical distance between rho and sigma (the Chernoff distance, the Hoeffding distances, and the relative entropy, respectively). While these results provide a complete solution to the asymptotic problem, they are not completely satisfying from a practical point of view. Indeed, in realistic scenarios one has access only to finitely many copies of a system, and therefore it is desirable to have bounds on the error probabilities for finite sample size. In this paper we provide finite-size bounds on the so-called Stein errors, the Chernoff errors, the Hoeffding errors and the mixed error probabilities related to the Chernoff and the Hoeffding errors.Comment: 31 pages. v4: A few typos corrected. To appear in J.Math.Phy

Papillitis as the prominent ocular sign in Acquired Immune Deficiency Syndrome (AIDS)

A 29-year old homosexual presented with clinical symptoms and an immunological picture of AIDS syndrome. Ocular involvement started in August 1986 with reduction of visual acuity in the right eye rapidly progressing to amaurosis. The most prominent ophthalmoscopical sign was of papillitis which had, in the beginning, the characteristics of an ischaemic optic neuropathy. Besides this, cotton-wool spots, retinal haemorrhages and limited areas of Cytomegalovirus (CMV) retinitis were found. Choroid was also involved with secondary CMV retinitis. On the other hand, sheathing of retinal vessels and Roth’s spots were absent. Although papilloedema, haemorrhages, cotton-wool exudates and CMV retinitis completely disappeared by October 1986, the general condition aggravated and the patient finally succumbed.peer-reviewe

Efficient algorithms for conditional independence inference

The topic of the paper is computer testing of (probabilistic) conditional independence (CI) implications by an algebraic method of structural imsets. The basic idea is to transform (sets of) CI statements into certain integral vectors and to verify by a computer the corresponding algebraic relation between the vectors, called the independence implication. We interpret the previous methods for computer testing of this implication from the point of view of polyhedral geometry. However, the main contribution of the paper is a new method, based on linear programming (LP). The new method overcomes the limitation of former methods to the number of involved variables. We recall/describe the theoretical basis for all four methods involved in our computational experiments, whose aim was to compare the efficiency of the algorithms. The experiments show that the LP method is clearly the fastest one. As an example of possible application of such algorithms we show that testing inclusion of Bayesian network structures or whether a CI statement is encoded in an acyclic directed graph can be done by the algebraic method

Ocular manifestations in lepromatous and tuberculoid leprosy

Ocular manifestations of leprosy in 100 patients examined were reported on; -80% were suffering from the lepromatous type of the disease. The most frequent change was loss of eyebrows (40%) which was seen mainly in lepromatous patients. The sclera and cornea were rarely affected separately, but sclerokerato-iridocyclitis was found in 3%. On the other hand, the iris was involved rather more often -16% (atrophy of the iris -4, atrophy of the pupillary margin -3, miosis -1, posterior synechiae -6, keratic precipitates -1, and iris "pearls" -1). The iritis always had an insidious chronic evolution. The origin of the iritis is probably multifactorial: a) neuroparalytic due to involvement of the autonomic nerves supplying the iris muscles, primarily dilator; b) direct effect of Mycobacterium leprae on the iris tissue; and c) immune or auto-immune mechanisms. The posterior uvea was rarely affected (2%). No case of primary glaucoma was detected, but secondary glaucoma due to sclerokerato-iridocyclitis was found in 2 cases. Cataract seems to occur more frequently in leprosy patients (20%) than in the general population. The anterior segment was mostly affected (21%), and all these cases belonged to the lepromatous (16) or borderline lepromatous (5) type.peer-reviewe