Batch means and spectral variance estimators in Markov chain Monte Carlo

Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the asymptotic normal distribution. We consider spectral and batch means methods for estimating this variance. In particular, we establish conditions which guarantee that these estimators are strongly consistent as the simulation effort increases. In addition, for the batch means and overlapping batch means methods we establish conditions ensuring consistency in the mean-square sense which in turn allows us to calculate the optimal batch size up to a constant of proportionality. Finally, we examine the empirical finite-sample properties of spectral variance and batch means estimators and provide recommendations for practitioners.Comment: Published in at http://dx.doi.org/10.1214/09-AOS735 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

COMPTEL solar flare measurements

We review some of the highlights of the COMPTEL measurements of solar flares. These include images of the Sun in γ rays and neutrons. One of the important features of the COMPTEL instrument is its capability to measure weak fluxes of γ rays and neutrons in the extended phase of flares. These data complement the spectra taken with the COMPTEL burst spectrometer and the telescope during the impulsive phase of flares. We focus our attention on some of these general capabilities of the instrument and the latest results of two long‐duration γ‐ray flares, i.e., 11 and 15 June 199

Ecosystem (dis)benefits arising from formal and informal land-use in Manchester (UK); a case study of urban soil characteristics associated with local green space management

Urban soils are subject to anthropogenic influences and, reciprocally, provide benefits and dis-benefits to human wellbeing; for example carbon storage, nutrient cycling and the regulation trace element and contaminant mobility. Collective stewardship of urban green commons provides contemporary examples of the diversity of uses and management of green space in cities and represents a growing movement in user participation in, and awareness of, the importance of urban ecological health. Exploring the range of social-ecological benefits exemplified in the urban environment has generally focused on above-ground processes, with few studies examining the potential for (dis)benefits arising from edaphic characteristics of collectively-managed spaces. An investigation into the influence of formal and informal green space management on carbon fluxes and heavy metal concentrations in urban soils was carried out in Manchester (UK) finding that carbon storage in soils of collectively managed urban green commons (7.15 ±1.42 kg C m⁻²) was significantly greater than at formally managed sites (for example city parks: 5.08 ±0.69 kg C m⁻²), though the latter exhibited reduced losses through CO2 emission. Variation in heavy metal concentrations and mobility were likewise observed, exemplified by the acidification of surface soils by leaf litter at orchard sites, and the resultant increase in the mobility of lead (Pb) and zinc (Zn). The results of this study indicate the importance of small-scale contemporary urban green space management on selected ecosystem services provided by the limited soil resource of cities. Thus, a greater consideration of the effects of horticultural and amenity activities with regards to soil quality/functionality is required to ensure available urban green commons retain or increase their ecological quality over time

CASK regulates CaMKII autophosphorylation in neuronal growth, calcium signaling, and learning

Calcium (Ca2+)/calmodulin (CaM)-dependent kinase II (CaMKII) activity plays a fundamental role in learning and memory. A key feature of CaMKII in memory formation is its ability to be regulated by autophosphorylation, which switches its activity on and off during synaptic plasticity. The synaptic scaffolding protein CASK (calcium (Ca2+)/calmodulin (CaM) associated serine kinase) is also important for learning and memory, as mutations in CASK result in intellectual disability and neurological defects in humans. We show that in Drosophila larvae, CASK interacts with CaMKII to control neuronal growth and calcium signalling. Furthermore, deletion of the CaMK-like and L27 domains of CASK (CASK β null) or expression of overactive CaMKII (T287D) produced similar effects on synaptic growth and Ca2+ signalling. CASK overexpression rescues the effects of CaMKII overactivity, consistent with the notion that CASK and CaMKII act in a common pathway that controls these neuronal processes. The reduction in Ca2+ signalling observed in the CASK β null mutant caused a decrease in vesicle trafficking at synapses. In addition, the decrease in Ca2+ signalling in CASK mutants was associated with an increase in Ether-à-go-go (EAG) potassium (K+) channel localisation to synapses. Reducing EAG restored the decrease in Ca2+ signalling observed in CASK mutants to the level of wildtype, suggesting that CASK regulates Ca2+ signalling via EAG. CASK knockdown reduced both appetitive associative learning and odour evoked Ca2+ responses in Drosophila mushroom bodies, which are the learning centres of Drosophila. Expression of human CASK in Drosophila rescued the effect of CASK deletion on the activity state of CaMKII, suggesting that human CASK may also regulate CaMKII autophosphorylation

Orientation of Demagnetized Bees

The orientation of honey bee dances is affected by the earth's magnetic field. Honey bees possess localized, well-oriented, stable and superparamagnetic domains of magnetite. Four lines of evidence suggest that the superparamagnetic domains of bees are more likely to be involved in magnetic field detectors than the stable domains. (1) Although the stable domains vary widely in size and number between bees, approximately 2×10^8 superparamagnetic domains are found reliably in all bees, and are restricted to there latively narrow size range of 300–350 Å. This suggests that the superparamagnetic domains are more likely to have a biological function. (2) Behavioural observations of dances in null fields are difficult to reconcile with astable-domain detector but are clearly predicted by many superparamagnetic detector models. (3) When honey bees are demagnetized, their ability to orient to the earth's field is unaffected. This suggests that the detector either utilizes the super paramagnetic domains or depends on aligned anisotropic stable domains processed without regard to magneticpolarity. (4) Bees that have only superparamagnetic domains are able nevertheless to orient to the earth's magnetic field, a phenomenon which indicates that permanent domains may not be required for detection

Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?

Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the quality of the reported estimates. We address this issue in that we discuss why Monte Carlo standard errors are important, how they can be easily calculated in Markov chain Monte Carlo and how they can be used to decide when to stop the simulation. We compare their use to a popular alternative in the context of two examples.Comment: Published in at http://dx.doi.org/10.1214/08-STS257 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org