The effects and side-effects of statistics education: Psychology students’ (mis-)conceptions of probability

In three studies we looked at two typical misconceptions of probability: the representativeness heuristic, and the equiprobability bias. The literature on statistics education predicts that some typical errors and biases (e.g., the equiprobability bias) increase with education, whereas others decrease. This is in contrast with reasoning theorists’ prediction who propose that education reduces misconceptions in general. They also predict that students with higher cognitive ability and higher need for cognition are less susceptible to biases. In Experiments 1 and 2 we found that the equiprobability bias increased with statistics education, and it was negatively correlated with students’ cognitive abilities. The representativeness heuristic was mostly unaffected by education, and it was also unrelated to cognitive abilities. In Experiment 3 we demonstrated through an instruction manipulation (by asking participants to think logically vs. rely on their intuitions) that the reason for these differences was that these biases originated in different cognitive processes.

GIANT LOBES OF CENTAURUS A RADIO GALAXY OBSERVED WITH THE SUZAKU X-RAY SATELLITE

We report on Suzaku observations of selected regions within the southern giant lobe of the radio galaxy Centaurus A. In our analysis we focus on distinct X-ray features detected with the X-ray Imaging Spectrometer within the range 0.5-10 keV, some of which are likely associated with fine structure of the lobe revealed by recent high-quality radio intensity and polarization maps. With the available photon statistics, we find that the spectral properties of the detected X-ray features are equally consistent with thermal emission from hot gas with temperatures kT > 1 keV, or with a power-law radiation continuum characterized by photon indices Gamma similar to 2.0 +/- 0.5. However, the plasma parameters implied by these different models favor a synchrotron origin for the analyzed X-ray spots, indicating that a very efficient acceleration of electrons up to greater than or similar to 10 TeV energies is taking place within the giant structure of Centaurus A, albeit only in isolated and compact regions associated with extended and highly polarized radio filaments. We also present a detailed analysis of the diffuse X-ray emission filling the whole field of view of the instrument, resulting in a tentative detection of a soft excess component best fitted by a thermal model with a temperature of kT similar to 0.5 keV. The exact origin of the observed excess remains uncertain, although energetic considerations point to thermal gas filling the bulk of the volume of the lobe and mixed with the non-thermal plasma, rather than to the alternative scenario involving a condensation of the hot intergalactic medium around the edges of the expanding radio structure. If correct, this would be the first detection of the thermal content of the extended lobes of a radio galaxy in X-rays. The corresponding number density of the thermal gas in such a case is n(g) similar to 10(-4) cm(-3), while its pressure appears to be in almost exact equipartition with the volume-averaged non-thermal pressure provided by the radio-emitting electrons and the lobes' magnetic field. A prominent large-scale fluctuation of the Galactic foreground emission, resulting in excess foreground X-ray emission aligned with the lobe, cannot be ruled out. Although tentative, our findings potentially imply that the structure of the extended lobes in active galaxies is likely to be highly inhomogeneous and non-uniform, with magnetic reconnection and turbulent acceleration processes continuously converting magnetic energy to internal energy of the plasma particles, leading to possibly significant spatial and temporal variations in the plasma beta parameter around the volume-averaged equilibrium condition beta similar to 1.

Stochastic particle acceleration in the lobes of giant radio galaxies

We investigate the acceleration of particles by Alfven waves via the second-order Fermi process in the lobes of giant radio galaxies. Such sites are candidates for the accelerators of ultra-high-energy cosmic rays (UHECR). We focus on the nearby Fanaroff-Riley type I radio galaxy Centaurus A. This is motivated by the coincidence of its position with the arrival direction of several of the highest energy Auger events. The conditions necessary for consistency with the acceleration time-scales predicted by quasi-linear theory are reviewed. Test particle calculations are performed in fields which guarantee electric fields with no component parallel to the local magnetic field. The results of quasi-linear theory are, to an order of magnitude, found to be accurate at low turbulence levels for non-relativistic Alfven waves and at both low and high turbulence levels in the mildly relativistic case. We conclude that for pure stochastic acceleration via Alfven waves to be plausible as the generator of UHECR in Cen A, the baryon number density would need to be several orders of magnitude below currently held upper limits.

Statistics sunspots and settlement: Influences on sum of probability curves

Large data sets of radiocarbon dates are becoming a more common feature of archaeological research. The sheer numbers of radiocarbon dates produced, however, raise issues of representation and interpretation. This paper presents a methodology which both reduces the visible impact of dating fluctuations, but also takes into consideration the influence of the underlying radiocarbon calibration curve. By doing so, it may be possible to distinguish between periods of human activity in early medieval Ireland and the statistical tails produced by radiocarbon calibration.

Spatial statistics to estimate peat thickness using airborne radiometric data

Soil carbon stores are a major component of the annual returns required by EU governments to the Intergovernmental Panel on Climate Change. Peat has a high proportion of soil carbon due to the relatively high carbon density of peat and organic-rich soils. For this reason it has become increasingly important to measure and model soil carbon stores and changes in peat stocks to facilitate the management of carbon changes over time. The approach investigated in this research evaluates the use of airborne geophysical (radiometric) data to estimate peat thickness using the attenuation of bedrock geology radioactivity by superficial peat cover. Remotely sensed radiometric data are validated with ground peat depth measurements combined with non-invasive geophysical surveys. Two field-based case studies exemplify and validate the results. Variography and kriging are used to predict peat thickness from point measurements of peat depth and airborne radiometric data and provide an estimate of uncertainty in the predictions. Cokriging, by assessing the degree of spatial correlation between recent remote sensed geophysical monitoring and previous peat depth models, is used to examine changes in peat stocks over time. The significance of the coregionalisation is that the spatial cross correlation between the remote and ground based data can be used to update the model of peat depth. The result is that by integrating remotely sensed data with ground geophysics, the need is reduced for extensive ground-based monitoring and invasive peat depth measurements. The overall goal is to provide robust estimates of peat thickness to improve estimates of carbon stocks. The implications from the research have a broader significance that promotes a reduction in the need for damaging onsite peat thickness measurement and an increase in the use of remote sensed data for carbon stock estimations.

Dyslexia in higher education: Implications for maths anxiety, statistics anxiety and psychological well-being

This study examined levels of mathematics and statistics anxiety, as well as general mental health amongst undergraduate students with dyslexia (n = 28) and those without dyslexia (n = 71). Students with dyslexia had higher levels of mathematics anxiety relative to those without dyslexia, while statistics anxiety and general mental health were comparable for both reading ability groups. In terms of coping strategies, undergraduates with dyslexia tended to use planning-based strategies and seek instrumental support more frequently than those without dyslexia. Higher mathematics anxiety was associated with having a dyslexia diagnosis, as well as greater levels of worrying, denial, seeking instrumental support and less use of the positive reinterpretation coping strategy. By contrast, statistics anxiety was not predicted by dyslexia diagnosis, but was instead predicted by overall worrying and the use of denial and emotion focused coping strategies. The results suggest that disability practitioners should be aware that university students with dyslexia are at risk of high mathematics anxiety. Additionally, effective anxiety reduction strategies such as positive reframing and thought challenging would form a useful addition to the support package delivered to many students with dyslexia.

Integrating Multiple Point Statistics with Aerial Geophysical Data to assist Groundwater Flow Models

The process of accounting for heterogeneity has made significant advances in statistical research, primarily in the framework of stochastic analysis and the development of multiple-point statistics (MPS). Among MPS techniques, the direct sampling (DS) method is tested to determine its ability to delineate heterogeneity from aerial magnetics data in a regional sandstone aquifer intruded by low-permeability volcanic dykes in Northern Ireland, UK. The use of two two-dimensional bivariate training images aids in creating spatial probability distributions of heterogeneities of hydrogeological interest, despite relatively ‘noisy’ magnetics data (i.e. including hydrogeologically irrelevant urban noise and regional geologic effects). These distributions are incorporated into a hierarchy system where previously published density function and upscaling methods are applied to derive regional distributions of equivalent hydraulic conductivity tensor K. Several K models, as determined by several stochastic realisations of MPS dyke locations, are computed within groundwater flow models and evaluated by comparing modelled heads with field observations. Results show a significant improvement in model calibration when compared to a simplistic homogeneous and isotropic aquifer model that does not account for the dyke occurrence evidenced by airborne magnetic data. The best model is obtained when normal and reverse polarity dykes are computed separately within MPS simulations and when a probability threshold of 0.7 is applied. The presented stochastic approach also provides improvement when compared to a previously published deterministic anisotropic model based on the unprocessed (i.e. noisy) airborne magnetics. This demonstrates the potential of coupling MPS to airborne geophysical data for regional groundwater modelling.

Detecting the work statistics through Ramsey-like interferometry

Out-of-equilibrium statistical mechanics is attracting considerable interest due to the recent advances in the control and manipulations of systems at the quantum level. Recently, an interferometric scheme for the detection of the characteristic function of the work distribution following a time-dependent process has been proposed [L. Mazzola et al., Phys. Rev. Lett. 110 (2013) 230602]. There, it was demonstrated that the work statistics of a quantum system undergoing a process can be reconstructed by effectively mapping the characteristic function of work on the state of an ancillary qubit. Here, we expand that work in two important directions. We first apply the protocol to an interesting specific physical example consisting of a superconducting qubit dispersively coupled to the field of a microwave resonator, thus enlarging the class of situations for which our scheme would be key in the task highlighted above. We then account for the interaction of the system with an additional one (which might embody an environment), and generalize the protocol accordingly.

Line-driven radiative outflows in luminous quasars

An analysis of ≃19 500 narrow (≲200 km s^-1) CIV λλ1548.2,1550.8 absorbers in ≃34 000 Sloan Digital Sky Survey quasar spectra is presented. The statistics of the number of absorbers as a function of outflow velocity shows that in approximately two-thirds of outflows, with multiple C IV absorbers present, absorbers are line-locked at the 500 km s^-1 velocity separation of the C IV absorber doublet; appearing as 'triplets' in the quasar spectra. Line-locking is an observational signature of radiative line-driving in outflowing material, where the successive shielding of 'clouds' of material in the outflow locks the clouds together in outflow velocity. Line-locked absorbers are seen in both broad absorption line (BAL) quasars and non-BAL quasars with comparable frequencies and with velocities out to at least 20 000 km s^-1. There are no detectable differences in the absorber properties and the dust content of single C IV doublets and line-locked C IV doublets. The gas associated with both single and line-locked CIV absorption systems includes material with a wide range of ionization potential (14-138 eV). Both single and line-locked CIV absorber systems show strong systematic trends in their ionization as a function of outflow velocity, with ionization decreasing rapidly with increasing outflow velocity. Initial simulations, employing CLOUDY, demonstrate that a rich spectrum of line-locked signals at various velocities may be expected due to significant opacities from resonance lines of Li-, He- and H-like ions of O, C and N, along with contributions from He II and HI resonance lines. The simulations confirm that line-driving can be the dominant acceleration mechanism for clouds with N(H I) ≃ 10¹⁹ cm^-2.

Selecting superluminous supernovae in faint galaxies from the first year of the Pan-STARRS1 Medium Deep Survey

The Pan-STARRS1 (PS1) survey has obtained imaging in five bands (grizyP1) over 10 Medium Deep Survey (MDS) fields covering a total of 70 square degrees. This paper describes the search for apparently hostless supernovae (SNe) within the first year of PS1 MDS data with an aim of discovering superluminous supernovae (SLSNe). A total of 249 hostless transients were discovered down to a limiting magnitude of MAB ∼ 23.5, of which 76 were classified as Type Ia supernovae (SNe Ia). There were 57 SNe with complete light curves that are likely core-collapse SNe (CCSNe) or type Ic SLSNe and 12 of these have had spectra taken. Of these 12 hostless, non-Type Ia SNe, 7 were SLSNe of type Ic at redshifts between 0.5 and 1.4. This illustrates that the discovery rate of type Ic SLSNe can be maximized by concentrating on hostless transients and removing normal SNe Ia. We present data for two possible SLSNe; PS1-10pm (z = 1.206) and PS1-10ahf (z = 1.1), and estimate the rate of type Ic SLSNe to be between 3+3−2×10−53+3−2×10−53+3−2×10−5 and 8+2−1×10−58+2−1×10−58+2−1×10−5 that of the CCSN rate within 0.3 ≤ z ≤ 1.4 by applying a Monte Carlo technique. The rate of slowly evolving, type Ic SLSNe (such as SN2007bi) is estimated as a factor of 10 lower than this range.

Selection of burst-like transients and stochastic variables using multi-brand image differencing in the Pan-STARRS1 Medium Deep Survey

We present a novel method for the light-curve characterization of Pan-STARRS1 Medium Deep Survey (PS1 MDS) extragalactic sources into stochastic variables (SVs) and burst-like (BL) transients, using multi-band image-differencing time-series data. We select detections in difference images associated with galaxy hosts using a star/galaxy catalog extracted from the deep PS1 MDS stacked images, and adopt a maximum a posteriori formulation to model their difference-flux time-series in four Pan-STARRS1 photometric bands gP1, rP1, iP1, and zP1. We use three deterministic light-curve models to fit BL transients; a Gaussian, a Gamma distribution, and an analytic supernova (SN) model, and one stochastic light-curve model, the Ornstein-Uhlenbeck process, in order to fit variability that is characteristic of active galactic nuclei (AGNs). We assess the quality of fit of the models band-wise and source-wise, using their estimated leave-out-one cross-validation likelihoods and corrected Akaike information criteria. We then apply a K-means clustering algorithm on these statistics, to determine the source classification in each band. The final source classification is derived as a combination of the individual filter classifications, resulting in two measures of classification quality, from the averages across the photometric filters of (1) the classifications determined from the closest K-means cluster centers, and (2) the square distances from the clustering centers in the K-means clustering spaces. For a verification set of AGNs and SNe, we show that SV and BL occupy distinct regions in the plane constituted by these measures. We use our clustering method to characterize 4361 extragalactic image difference detected sources, in the first 2.5 yr of the PS1 MDS, into 1529 BL, and 2262 SV, with a purity of 95.00% for AGNs, and 90.97% for SN based on our verification sets. We combine our light-curve classifications with their nuclear or off-nuclear host galaxy offsets, to define a robust photometric sample of 1233 AGNs and 812 SNe. With these two samples, we characterize their variability and host galaxy properties, and identify simple photometric priors that would enable their real-time identification in future wide-field synoptic surveys.