Compatible Weighted Proper Scoring Rules

Many proper scoring rules such as the Brier and log scoring rules implicitly reward a probability forecaster relative to a uniform baseline distribution. Recent work has motivated weighted proper scoring rules, which have an additional baseline parameter. To date two families of weighted proper scoring rules have been introduced, the weighted power and pseudospherical scoring families. These families are compatible with the log scoring rule: when the baseline maximizes the log scoring rule over some set of distributions, the baseline also maximizes the weighted power and pseudospherical scoring rules over the same set. We characterize all weighted proper scoring families and prove a general property: every proper scoring rule is compatible with some weighted scoring family, and every weighted scoring family is compatible with some proper scoring rule

Linear Estimating Equations for Exponential Families with Application to Gaussian Linear Concentration Models

In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator of Hyv\"arinen (2005) provides an alternative where this normalization constant is not required. The corresponding estimating equations become linear for an exponential family. The score matching estimator is shown to be consistent and asymptotically normally distributed for such models, although not necessarily efficient. Gaussian linear concentration models are examples of such families. For linear concentration models that are also linear in the covariance we show that the score matching estimator is identical to the maximum likelihood estimator, hence in such cases it is also efficient. Gaussian graphical models and graphical models with symmetries form particularly interesting subclasses of linear concentration models and we investigate the potential use of the score matching estimator for this case

A Fast Algorithm for Sampling from the Posterior of a von Mises distribution

Motivated by molecular biology, there has been an upsurge of research activities in directional statistics in general and its Bayesian aspect in particular. The central distribution for the circular case is von Mises distribution which has two parameters (mean and concentration) akin to the univariate normal distribution. However, there has been a challenge to sample efficiently from the posterior distribution of the concentration parameter. We describe a novel, highly efficient algorithm to sample from the posterior distribution and fill this long-standing gap

Fingerprint Analysis with Marked Point Processes

We present a framework for fingerprint matching based on marked point process models. An efficient Monte Carlo algorithm is developed to calculate the marginal likelihood ratio for the hypothesis that two observed prints originate from the same finger against the hypothesis that they originate from different fingers. Our model achieves good performance on an NIST-FBI fingerprint database of 258 matched fingerprint pairs

Modelling the advection of vertically migrating shrimp larvae

The role of larval advection in determining the complex, large-scale patterns of immigration of penaeid postlarvae in the Gulf of Carpentaria is investigated by modelling the interaction between diurnal vertical migration of larvae with wind-forced and tidal currents. Eight vertical migration schemes are modelled in which both the timing of the migration and the position of the larvae in the water column are varied. These schemes are then coupled with both two-dimensional and three-dimensional models of the currents of the Gulf, to examine horizontal advection of larvae. When the larvae migrate vertically with a diurnal period, their horizontal advection is enhanced. The largest horizontal advection distances occur when the larvae move diurnally from the water column into the bottom boundary layer. Advection distances of up to 165 km are possible during the two to three week planktonic larval period. This distance corresponds to, and may determine, the offshore extent of the adult distribution. The onshore advection pattern of larvae varies in both space and time (on a seasonal scale) and is consistent with the observed spatial and temporal recruitment patterns seen by sampling postlarval immigation into nursery areas. During the period of highest reproductive activity (March) in the southeastern corner of the Gulf, the area of the largest fishery, the advection of larvae is offshore and little recruitment of postlarvae to the nursery grounds is accomplished. Six months later, during the next period of reproductive activity (October), when the number of spawning female shrimp is much lower, the phase of the tidal currents, relative to the day-night cycle, has progressed 180° and the larvae are moved onshore allowing postlarvae access to their estuarine nursery grounds several months prior to the main fishing season (March)

FUSE Measurements of Far Ultraviolet Extinction. I. Galactic Sight Lines

We present extinction curves that include data down to far ultraviolet wavelengths (FUV; 1050 - 1200 A) for nine Galactic sight lines. The FUV extinction was measured using data from the Far Ultraviolet Spectroscopic Explorer. The sight lines were chosen for their unusual extinction properties in the infrared through the ultraviolet; that they probe a wide range of dust environments is evidenced by the large spread in their measured ratios of total-to-selective extinction, R_V = 2.43 - 3.81. We find that extrapolation of the Fitzpatrick & Massa relationship from the ultraviolet appears to be a good predictor of the FUV extinction behavior. We find that predictions of the FUV extinction based upon the Cardelli, Clayton & Mathis (CCM) dependence on R_V give mixed results. For the seven extinction curves well represented by CCM in the infrared through ultraviolet, the FUV extinction is well predicted in three sight lines, over-predicted in two sight lines, and under-predicted in 2 sight lines. A Maximum Entropy Method analysis using a simple three component grain model shows that seven of the nine sight lines in the study require a larger fraction of grain materials to be in dust when FUV extinction is included in the models. Most of the added grain material is in the form of small (radii < 200 A) grains.Comment: Accepted for publication in the Astrophysical Journal. 31 pages with 7 figure

RPGR-associated retinal degeneration in human X-linked RP and a murine model

PURPOSE. We investigated the retinal disease due to mutations in the retinitis pigmentosa GTPase regulator (RPGR) gene in human patients and in an Rpgr conditional knockout (cko) mouse model. METHODS. XLRP patients with RPGR-ORF15 mutations (n = 35, ages at first visit 5–72 years) had clinical examinations, and rod and cone perimetry. Rpgr-cko mice, in which the proximal promoter and first exon were deleted ubiquitously, were back-crossed onto a BALB/c background, and studied with optical coherence tomography and electroretinography (ERG). Retinal histopathology was performed on a subset. RESULTS. Different patterns of rod and cone dysfunction were present in patients. Frequently, there were midperipheral losses with residual rod and cone function in central and peripheral retina. Longitudinal data indicated that central rod loss preceded peripheral rod losses. Central cone-only vision with no peripheral function was a late stage. Less commonly, patients had central rod and cone dysfunction, but preserved, albeit abnormal, midperipheral rod and cone vision. Rpgr-cko mice had progressive retinal degeneration detectable in the first months of life. ERGs indicated relatively equal rod and cone disease. At late stages, there was greater inferior versus superior retinal degeneration. CONCLUSIONS. RPGR mutations lead to progressive loss of rod and cone vision, but show different patterns of residual photoreceptor disease expression. Knowledge of the patterns should guide treatment strategies. Rpgr-cko mice had onset of degeneration at relatively young ages and progressive photoreceptor disease. The natural history in this model will permit preclinical proof-of-concept studies to be designed and such studies should advance progress toward human therapy

Chronic exposure to outdoor air pollution and diagnosed cardiovascular disease: meta-analysis of three large cross-sectional surveys

BACKGROUND: Higher exposure to outdoor air pollution is associated with increased cardiopulmonary deaths, but there is limited evidence about the association between outdoor air pollution and diagnosed cardiovascular disease. Our study aimed to estimate the size of the association between long term exposure to outdoor air pollution and prevalent cardiovascular disease. METHODS: We carried out a cross-sectional analysis of data on more than 19,000 white adults aged 45 and older who participated in three representative surveys of the English population in 1994, 1998 and 2003, examining the relationship between self-reported doctor-diagnosed cardiovascular disease and exposure to outdoor air pollutants using multilevel regression techniques and meta-analysis. RESULTS: The combined estimates suggested that an increase of 1 microg m-3 in concentration of particulate matter less than 10 microns in diameter was associated with an increase of 2.9% (95% CI -0.6% to 6.5%) in prevalence of cardiovascular disease in men, and an increase of 1.6% (95%CI -2.1% to 5.5%) in women. The year-specific analyses showed strongly positive associations in 2003 between odds of cardiovascular disease in both men and women and exposure to particulate matter but not in 1994 or 1998. We found no consistent associations between exposure to gaseous air pollutants and doctor-diagnosed cardiovascular disease. CONCLUSION: The associations of prevalent cardiovascular disease with concentration of particulate matter less than 10 microns in diameter, while only weakly positive, were consistent with the effects reported in cohort studies. The results provide evidence of the size of the association between particulate air pollution and the prevalence of cardiovascular disease but no evidence for an association with gaseous pollutants. We found strongly positive associations between particulate matter and cardiovascular disease in 2003 only, which highlights the importance of replicating findings in more than one population