Jeffreys priors for mixture estimation: properties and alternatives

While Jeffreys priors usually are well-defined for the parameters of mixtures of distributions, they are not available in closed form. Furthermore, they often are improper priors. Hence, they have never been used to draw inference on the mixture parameters. The implementation and the properties of Jeffreys priors in several mixture settings are studied. It is shown that the associated posterior distributions most often are improper. Nevertheless, the Jeffreys prior for the mixture weights conditionally on the parameters of the mixture components will be shown to have the property of conservativeness with respect to the number of components, in case of overfitted mixture and it can be therefore used as a default priors in this context.Comment: arXiv admin note: substantial text overlap with arXiv:1511.0314

Accelerating Metropolis-Hastings algorithms: Delayed acceptance with prefetching

MCMC algorithms such as Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions as exemplified by huge datasets. We offer in this paper an approach to reduce the computational costs of such algorithms by a simple and universal divide-and-conquer strategy. The idea behind the generic acceleration is to divide the acceptance step into several parts, aiming at a major reduction in computing time that outranks the corresponding reduction in acceptance probability. The division decomposes the "prior x likelihood" term into a product such that some of its components are much cheaper to compute than others. Each of the components can be sequentially compared with a uniform variate, the first rejection signalling that the proposed value is considered no further, This approach can in turn be accelerated as part of a prefetching algorithm taking advantage of the parallel abilities of the computer at hand. We illustrate those accelerating features on a series of toy and realistic examples.Comment: 20 pages, 12 figures, 2 tables, submitte

Hospital production in a national health service: the physician's dilemma

There is a paucity of literature concerning the relation between the resource utilization decisions of the salaried hospital based physician and patient outcomes in a national health service. The purpose of our study is to model and test hospital production where the major decision makers are physicians. We view the output of the hospital as a distribution function over final health states of the patient. Our model contains a utility function for physicians whose arguments include the expected final health status of the patient and a pressure function which reflects the resource allocation and hospital financing policy of the Portuguese Health Ministry. Two sets of first order conditions derived from the theoretical model are estimated within a simultaneous equations framework using data consisting of inpatient discharges for the most frequent non-obstetric DRG during the 1992-1999 time period. We find evidence that budget setting methods and the possession of a third party payer outside of the NHS are important predictors for use of the resource in question. Moreover, we find that use of the resource is important in predicting the final health status of the patient.

Meteorite cloudy zone formation as a quantitative indicator of paleomagnetic field intensities and cooling rates on planetesimals

Metallic microstructures in slowly-cooled iron-rich meteorites reflect the thermal and magnetic histories of their parent planetesimals. Of particular interest is the cloudy zone, a nanoscale intergrowth of Ni-rich islands within a Ni-poor matrix that forms below 350{\deg}C by spinodal decomposition. The sizes of the islands have long been recognized as reflecting the low-temperature cooling rates of meteorite parent bodies. However, a model capable of providing quantitative cooling rate estimates from island sizes has been lacking. Moreover, these islands are also capable of preserving a record of the ambient magnetic field as they grew, but some of the key physical parameters required for recovering reliable paleointensity estimates from magnetic measurements of these islands have been poorly constrained. To address both of these issues, we present a numerical model of the structural and compositional evolution of the cloudy zone as a function of cooling rate and local composition. Our model produces island sizes that are consistent with present-day measured sizes. This model enables a substantial improvement in the calibration of paleointensity estimates and associated uncertainties. In particular, we can now accurately quantify the statistical uncertainty associated with the finite number of islands and the uncertainty on their size at the time of the record. We use this new understanding to revisit paleointensities from previous pioneering paleomagnetic studies of cloudy zones. We show that these could have been overestimated but nevertheless still require substantial magnetic fields to have been present on their parent bodies. Our model also allows us to estimate absolute cooling rates for meteorites that cooled slower than 10000{\deg}C My-1. We demonstrate how these cooling rate estimates can uniquely constrain the low-temperature thermal history of meteorite parent bodies.Comment: Manuscript resubmitted after revision

Naturalness in testable type II seesaw scenarios

New physics coupling to the Higgs sector of the Standard Model can lead to dangerously large corrections to the Higgs mass. We investigate this problem in the type II seesaw model for neutrino mass, where a weak scalar triplet is introduced. The interplay of direct and indirect constraints on the type II seesaw model with its contribution to the Higgs mass is analyzed. The focus lies on testable triplet masses and (sub) eV-scale triplet vacuum expectation values. We identify scenarios that are testable in collider and/or lepton flavor violation experiments, while satisfying the Higgs naturalness criterion.Comment: 18 pages, 8 figures, 2 table