Default Bayes Factors for one-sided hypothesis testing

Bayesian hypothesis testing for non-nested hypotheses various "default" Bayes factors, such as the fractional Bayes factor, the median intrinsic Bayes factor and the encompassing and expected intrinsic Bayes factors. The different default methods are first compared with each other and with the p-value in normal one-sides testing, to illustrate the basic issues. General results for one-sides testing in location and scale models are then presented. The default Bayes factors are also studied for specific models involving multiple hypotheses. In most of the examples presented we also derive the intrinsic prior; this is the prior distribution which, if used directly, would yield answers (asymtotically) equivalent to those for the given default Bayes factor.Bayes factor, fractional Bayes factor, intrinsic Bayes factor, model comparison, one-sided hypothesis testing, multiple hypothesistesting

Capital process and optimality properties of a Bayesian Skeptic in coin-tossing games

We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of Reality's moves. From this it is proved that the Skeptic's Bayesian strategy weakly forces the strong law of large numbers (SLLN) with the convergence rate of O(\sqrt{\log n/n})$ and if Reality violates SLLN then the exponential growth rate of the capital process is very accurately described in terms of the Kullback divergence between the average of Reality's moves when she violates SLLN and the average when she observes SLLN. We also investigate optimality properties associated with Bayesian strategy

Small-scale solar magnetic fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.Comment: 43 pages, 18 figure

Bayesian approach and Naturalness in MSSM analyses for the LHC

The start of LHC has motivated an effort to determine the relative probability of the different regions of the MSSM parameter space, taking into account the present, theoretical and experimental, wisdom about the model. Since the present experimental data are not powerful enough to select a small region of the MSSM parameter space, the choice of a judicious prior probability for the parameters becomes most relevant. Previous studies have proposed theoretical priors that incorporate some (conventional) measure of the fine-tuning, to penalize unnatural possibilities. However, we show that such penalization arises from the Bayesian analysis itself (with no ad hoc assumptions), upon the marginalization of the mu-parameter. Furthermore the resulting effective prior contains precisely the Barbieri-Giudice measure, which is very satisfactory. On the other hand we carry on a rigorous treatment of the Yukawa couplings, showing in particular that the usual practice of taking the Yukawas "as required", approximately corresponds to taking logarithmically flat priors in the Yukawa couplings. Finally, we use an efficient set of variables to scan the MSSM parameter space, trading in particular B by tan beta, giving the effective prior in the new parameters. Beside the numerical results, we give accurate analytic expressions for the effective priors in all cases. Whatever experimental information one may use in the future, it is to be weighted by the Bayesian factors worked out here.Comment: LaTeX, 19 pages, 3 figure

Enhanced Quantum Estimation via Purification

We analyze the estimation of a finite ensemble of quantum bits which have been sent through a depolarizing channel. Instead of using the depolarized qubits directly, we first apply a purification step and show that this improves the fidelity of subsequent quantum estimation. Even though we lose some qubits of our finite ensemble the information is concentrated in the remaining purified ones.Comment: 6 pages, including 3 figure

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping delta away from half-filling, finite-size density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k_F and 4k_F for the currents and densities, where 2k_F = pi(1-delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities.Comment: 24 pages, 17 figures. Follow-up to cond-mat/0209444. (v2) Some revisions in text, improved presentation. Minor changes in title, abstract and reference

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

Peripheral T-cell lymphoma, not otherwise specified: a report of 340 cases from the International Peripheral T-cell Lymphoma Project

The International Peripheral T-cell Lymphoma Project is a collaborative effort to better understand peripheral T-cell lymphoma (PTCL). A total of 22 institutions submitted clinical and pathologic material on 1314 cases. One objective was to analyze the clinical and pathologic features of 340 cases of PTCL, not otherwise specified. The median age of the patients was 60 years, and the majority (69%) presented with advanced stage disease. Most patients (87%) presented with nodal disease, but extranodal disease was present in 62%. The 5-year overall survival was 32%, and the 5-year failure-free survival was only 20%. The majority of patients (80%) were treated with combination chemotherapy that included an anthracycline, but there was no survival advantage. The International Prognostic Index (IPI) was predictive of both overall survival and failure-free survival (P < .001). Multivariate analysis of clinical and pathologic prognostic factors, respectively, when controlling for the IPI, identified bulky disease ( 65 10 cm), thrombocytopenia (< 150 7 109/L), and a high number of transformed tumor cells (> 70%) as adverse predictors of survival, but only the latter was significant in final analysis. Thus, the IPI and a single pathologic feature could be used to stratify patients with PTCL-not otherwise specified for novel and risk-adapted therapies

Quantum Mechanics from Focusing and Symmetry

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables - inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a clear interpretation. The Born formula is proved from weak assumptions, and from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed.Comment: 26 page

Ethnocentrism in the Low Countries: A comparative perspective

Contains fulltext : 3361.pdf (publisher's version ) (Open Access)New Community, continued by: Journal of ethnic and migration studies [1369-183X