Harold Jeffreys's Theory of Probability Revisited

Published exactly seventy years ago, Jeffreys's Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the derivation of noninformative priors as well as on the scaling of Bayes factors have had a lasting impact on the field. However, the book reflects the characteristics of the time, especially in terms of mathematical rigor. In this paper we point out the fundamental aspects of this reference work, especially the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based on functional divergences. Our major aim here is to help modern readers in navigating in this difficult text and in concentrating on passages that are still relevant today.Comment: This paper commented in: [arXiv:1001.2967], [arXiv:1001.2968], [arXiv:1001.2970], [arXiv:1001.2975], [arXiv:1001.2985], [arXiv:1001.3073]. Rejoinder in [arXiv:0909.1008]. Published in at http://dx.doi.org/10.1214/09-STS284 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Subduction Duration and Slab Dip

The dip angles of slabs are among the clearest characteristics of subduction zones, but the factors that control them remain obscure. Here, slab dip angles and subduction parameters, including subduction duration, the nature of the overriding plate, slab age, and convergence rate, are determined for 153 transects along subduction zones for the present day. We present a comprehensive tabulation of subduction duration based on isotopic ages of arc initiation and stratigraphic, structural, plate tectonic and seismic indicators of subduction initiation. We present two ages for subduction zones, a long‐term age and a reinitiation age. Using cross correlation and multivariate regression, we find that (1) subduction duration is the primary parameter controlling slab dips with slabs tending to have shallower dips at subduction zones that have been in existence longer; (2) the long‐term age of subduction duration better explains variation of shallow dip than reinitiation age; (3) overriding plate nature could influence shallow dip angle, where slabs below continents tend to have shallower dips; (4) slab age contributes to slab dip, with younger slabs having steeper shallow dips; and (5) the relations between slab dip and subduction parameters are depth dependent, where the ability of subduction duration and overriding plate nature to explain observed variation decreases with depth. The analysis emphasizes the importance of subduction history and the long‐term regional state of a subduction zone in determining slab dip and is consistent with mechanical models of subduction

Urban particulate pollution reduction by four species of green roof vegetation in a UK city

AbstractUrban particulate pollution in the UK remains at levels which have the potential to cause negative impacts on human health. There is a need, therefore, for mitigation strategies within cities, especially with regards to vehicular sources. The use of vegetation as a passive filter of urban air has been previously investigated, however green roof vegetation has not been specifically considered. The present study aims to quantify the effectiveness of four green roof species – creeping bentgrass (Agrostis stolonifera), red fescue (Festuca rubra), ribwort plantain (Plantago lanceolata) and sedum (Sedum album) – at capturing particulate matter smaller than 10 μm (PM10). Plants were grown in a location away from major road sources of PM10 and transplanted onto two roofs in Manchester city centre. One roof is adjacent to a major traffic source and one roof is characterised more by urban background inputs. Significant differences in metal containing PM10 capture were found between sites and between species. Site differences were explained by proximity to major sources. Species differences arise from differences in macro and micro morphology of the above surface biomass. The study finds that the grasses, A. stolonifera and F. rubra, are more effective than P. lanceolata and S. album at PM10 capture. Quantification of the annual PM10 removal potential was calculated under a maximum sedum green roof installation scenario for an area of the city centre, which totals 325 ha. Remediation of 2.3% (±0.1%) of 9.18 tonnes PM10 inputs for this area could be achieved under this scenario

Children with Special Health Care Needs: Impact of Health Care Expenditures on Family Financial Burden

We investigated the relationship between health care expenditures for Special Health Care Needs (SHCN) children and family perception of financial burden. Using 2005/2006 National Survey of Children with Special Health Care Needs data, a multivariate logistic regression model was used to estimate the relationship between the SHCN child’s health care expenditure and perceived financial burden, while controlling for family and child characteristics. Our analysis suggests that health care expenditures for a SHCN child of $250 and more are associated with family perception of financial burden. In addition, families with lower socioeconomic status also perceived financial burden at lower level of expenditures. Members of the health care team who treat children with SHCN have an important role in understanding and assessing family financial burden as part of the care delivery to the child and the family. Our study reinforces the need to treat the whole family as the unit of care, especially when caring for children with special health care needs

Minimum Decision Cost for Quantum Ensembles

For a given ensemble of $N$ independent and identically prepared particles, we calculate the binary decision costs of different strategies for measurement of polarised spin 1/2 particles. The result proves that, for any given values of the prior probabilities and any number of constituent particles, the cost for a combined measurement is always less than or equal to that for any combination of separate measurements upon sub-ensembles. The Bayes cost, which is that associated with the optimal strategy (i.e., a combined measurement) is obtained in a simple closed form.Comment: 11 pages, uses RevTe

The power of Bayesian evidence in astronomy

We discuss the use of the Bayesian evidence ratio, or Bayes factor, for model selection in astronomy. We treat the evidence ratio as a statistic and investigate its distribution over an ensemble of experiments, considering both simple analytical examples and some more realistic cases, which require numerical simulation. We find that the evidence ratio is a noisy statistic, and thus it may not be sensible to decide to accept or reject a model based solely on whether the evidence ratio reaches some threshold value. The odds suggested by the evidence ratio bear no obvious relationship to the power or Type I error rate of a test based on the evidence ratio. The general performance of such tests is strongly affected by the signal to noise ratio in the data, the assumed priors, and the threshold in the evidence ratio that is taken as `decisive'. The comprehensiveness of the model suite under consideration is also very important. The usefulness of the evidence ratio approach in a given problem can be assessed in advance of the experiment, using simple models and numerical approximations. In many cases, this approach can be as informative as a much more costly full-scale Bayesian analysis of a complex problem.Comment: 11 pages; MNRAS in pres

Data-in-Place: Thinking through the Relations Between Data and Community

We present findings from a year-long engagement with a street and its community . The work is targeted at exploring how the production and use of data is bound up with place, both in terms of physical and social geography. We detail three strands of the project. First, we consider how residents have sought to curate existing data about the street in the form of an archive with physical and digital components. Second, we report endeavours to capture data about the street’s environment, especially of traffic moving through it. Third, we draw on the possibilities afforded by technologies for polling opinion. We reflect on how these engagements have: materialised distinctive relations between the community and their data; surfaced flows and contours of data , and spatial, temporal and social boundaries ;and enacted a multiplicity of ‘small worlds’. We consider how such a conceptualisation of data-in-place is relevant to the design of data technologies