On predictive probability matching priors

We revisit the question of priors that achieve approximate matching of Bayesian and frequentist predictive probabilities. Such priors may be thought of as providing frequentist calibration of Bayesian prediction or simply as devices for producing frequentist prediction regions. Here we analyse the $O(n^{-1})$ term in the expansion of the coverage probability of a Bayesian prediction region, as derived in [Ann. Statist. 28 (2000) 1414--1426]. Unlike the situation for parametric matching, asymptotic predictive matching priors may depend on the level $\alpha$. We investigate uniformly predictive matching priors (UPMPs); that is, priors for which this $O(n^{-1})$ term is zero for all $\alpha$. It was shown in [Ann. Statist. 28 (2000) 1414--1426] that, in the case of quantile matching and a scalar parameter, if such a prior exists then it must be Jeffreys' prior. In the present article we investigate UPMPs in the multiparameter case and present some general results about the form, and uniqueness or otherwise, of UPMPs for both quantile and highest predictive density matching.Comment: Published in at http://dx.doi.org/10.1214/074921708000000048 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Strict Property Tax Caps: A Case Study of Massachusetts\u27s Proposition 2 1/2, its Shortcomings, and the Path Forward

Strict property tax caps are statutory measures that limit municipalities from raising property taxes by more than a certain percentage each fiscal year. In addition, they place a ceiling on the total amount of real and personal property tax revenue a municipality can raise annually. Often spearheaded by voter initiative, strict property tax caps are championed by proponents as a way to limit taxes and increase civic participation. Conversely, detractors frame caps as artificial barriers that improperly constrain local governments in their taxing powers. Massachusetts voters approved a strict property tax cap, Proposition 2 1⁄2, in 1980. Proposition 2 1⁄2 provides that communities may increase taxes on real and personal property annually by no more than 2.5% of the total fair cash value of such property. Further, it states that the total annual property tax revenue raised by municipalities cannot surpass 2.5% of the assessed value of all taxable property in each community. In the three-and-a-half decades since Proposition 2 1⁄2 was adopted, many cities and towns have found that they cannot raise sufficient revenue to meet their communities’ needs because of the restrictions imposed by the cap. However, the statute does contain a side-step maneuver: a community can override its levy limit with a majority vote. This Note examines the total number of override votes—attempted and successful—from 1980 through 2010. In doing so, it assesses the impact Proposition 2 1⁄2 has had and is continuing to have on municipalities, namely the services local governments provide to their residents. The data indicates that the number of proposed override votes has increased over time, as communities have found that they are unable to meet their needs under the 2.5% increase limit. Further, the vote totals make clear that successful override votes happen more frequently in wealthier communities versus poorer communities. Based on this data, this Note argues that Proposition 2 1⁄2’s 2.5% levy cap is an unrealistic and artificial barrier. Strict property tax caps place arbitrary limits on the amounts municipalities can raise taxes, without regard to changes in inflation, the cost of providing services, or community needs. The Note concludes by suggesting potential alternatives moving forward

XMM-Newton observations of Abell 2255 : a test case of a merger after `core-crossing'

It has been known that Abell 2255 is not a relaxed cluster, but it is undergoing a merger. Here, we report on the analysis of the XMM-Newton observations of this cluster. The X-ray data give us the opportunity to reveal the complexity of the cluster, especially its temperature distribution. The integrated spectrum is well fitted by a single temperature thermal model, indicating a mean temperature of ~7 keV. However, the cluster is not isothermal at this temperature: its eastern regions are significantly cooler, at ~5.5 keV, whilst towards the West the temperature reaches ~8.5 keV. These temperature asymmetries can be explained if Abell 2255 has been assembled recently by the merging of smaller subunits. It is now in the phase after the cores of these subunits have collided (the `core-crossing' phase) some 0.1-0.2 Gyr ago. A comparison with numerical simulations suggests that it will settle down into a single relaxed cluster in ~(2-3) Gyr.Comment: 9 pages, 6 figures, accepted by MNRA

XMM-Newton observations of the binary cluster system Abell 399/401

Abell 399 and Abell 401 are both rich clusters of galaxies, at temperatures 7.2keV and 8.5keV respectively. They lie at a projected separation of ~3Mpc, forming a close pair. We have observed the system with the XMM-Newton satellite. The data of each cluster show significant departures from our idealised picture of relaxed rich clusters. There is also evidence for enhanced X-ray flux in the region between the two, where the temperature is higher than our expectations. Although tidal or compression effects might affect the large scale structure of the two clusters, we show that these cannot account for the distortions seen in the inner regions. We argue that the reasonably relaxed morphology of the clusters, and the absence of major temperature anomalies, argues against models in which the two have already experienced a close encounter. The properties of the intermediate region suggests that they are at an early stage of merging, and are currently interacting mildly, because their separation is still too large for more dramatic effects. The substructure we find in their inner regions seems to point to their individual merging histories. It seems likely that in the Abell 399/401 system, we are witnessing two merger remnants, just before they merge together to form a single rich cluster. This picture is consistent with recent numerical simulations of cluster formation. (abridged)Comment: 20 pages, 14 figures, to be published in MNRA

Recent Saccadic Eye Movement Research Uncovers Patterns of Cognitive Dysfunction in Schizophrenia.

The frontal cortex and the subcortical areas of the brain play a major role in the control of thought and action. Eye movements are increasingly used in neuropsychological research to explore the executive and sensorimotor functions of such neural networks. This interface links the control of action, at the fundamental levels of neurophysiological and neurochemical processes, with the high-level cognitive operations that underlie visual orienting. Patients with schizophrenia have neurocognitive impairments that can be readily investigated with novel saccadic eye movement paradigms. Animal, human lesion, and neuroimaging studies have identified the cerebral centers that underlie saccadic eye movements. The areas of the prefrontal cortex include the dorsolateral prefrontal cortex, the frontal eye fields, the supplementary eye fields, and the anterior cingulate gyrus. Pathology of saccadic eye movements therefore provides information on the functional status of the underlying neural circuitry in brain disorders such as schizophrenia

The Chandra Deep Group Survey -- cool core evolution in groups and clusters of galaxies

We report the results of a study which assembles deep observations with the ACIS-I instrument on the Chandra Observatory to study the evolution in the core properties of a sample of galaxy groups and clusters out to redshifts $z\approx 1.3$. A search for extended objects within these fields yields a total of 62 systems for which redshifts are available, and we added a further 24 non-X-ray-selected clusters, to investigate the impact of selection effects and improve our statistics at high redshift. Six different estimators of cool core strength are applied to these data: the entropy (K) and cooling time ($t_{cool}$) within the cluster core, the cooling time as a fraction of the age of the Universe ($t_{cool}/t_{Uni}$), and three estimators based on the cuspiness of the X-ray surface brightness profile. A variety of statistical tests are used to quantify evolutionary trends in these cool core indicators. In agreement with some previous studies, we find that there is significant evolution in $t_{cool}/t_{Uni}$, but little evolution in $t_{cool}$, suggesting that gas is accumulating within the core, but that the cooling time deep in the core is controlled by AGN feedback. We show that this result extends down to the group regime and appears to be robust against a variety of selection biases (detection bias, archival biases and biases due to the presence of central X-ray AGN) which we consider.Comment: Accepted by MNRAS, 24 pages, 11 figure