(Don’t) Make My Vote Count

Proponents of proportional electoral rules often argue that majority rule depresses turnout and may lower welfare due to the 'tyranny of the majority' problem. The present paper studies the impact of electoral rules on turnout and social welfare. We analyze a model of instrumental voting where citizens have private information over their individual cost of voting and over the alternative they prefer. The electoral rule used to select the winning alternative is a combination of majority rule and proportional rule. Results show that the above arguments against majority rule do not hold in this set up. Social welfare and turnout increase with the weight that the electoral rule gives to majority rule when the electorate is expected to be split, and they are independent of the electoral rule employed when the expected size of the minority group tends to zero. However, more proportional rules can increase turnout within the minority group. This effect is stronger the smaller the minority group. We then conclude that majority rule fosters overall turnout and increases social welfare, whereas proportional rule fosters the participation of minorities.

Comparison of time-lapse GPR data collected under natural and forced infiltration conditions to estimate vadose zone hydraulic parameters

Time-lapse crosshole ground-penetrating radar (GPR) data, collected while infiltration occurs, can provide valuable information regarding the hydraulic properties of the unsaturated zone. In particular, the stochastic inversion of such data provides estimates of parameter uncertainties, which are necessary for hydrological prediction and decision making. Here, we investigate the effect of different infiltration conditions on the stochastic inversion of time-lapse, zero-offset-profile, GPR data. Inversions are performed using a Bayesian Markov-chain-Monte-Carlo methodology. Our results clearly indicate that considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions

Enhancing the vertical resolution of surface georadar data

There are far-reaching conceptual similarities between bi-static surface georadar and post-stack, "zero-offset" seismic reflection data, which is expressed in largely identical processing flows. One important difference is, however, that standard deconvolution algorithms routinely used to enhance the vertical resolution of seismic data are notoriously problematic or even detrimental to the overall signal quality when applied to surface georadar data. We have explored various options for alleviating this problem and have tested them on a geologically well-constrained surface georadar dataset. Standard stochastic and direct deterministic deconvolution approaches proved to be largely unsatisfactory. While least-squares-type deterministic deconvolution showed some promise, the inherent uncertainties involved in estimating the source wavelet introduced some artificial "ringiness". In contrast, we found spectral balancing approaches to be effective, practical and robust means for enhancing the vertical resolution of surface georadar data, particularly, but not exclusively, in the uppermost part of the georadar section, which is notoriously plagued by the interference of the direct air- and groundwaves. For the data considered in this study, it can be argued that band-limited spectral blueing may provide somewhat better results than standard band-limited spectral whitening, particularly in the uppermost part of the section affected by the interference of the air- and groundwaves. Interestingly, this finding is consistent with the fact that the amplitude spectrum resulting from least-squares-type deterministic deconvolution is characterized by a systematic enhancement of higher frequencies at the expense of lower frequencies and hence is blue rather than white. It is also consistent with increasing evidence that spectral "blueness" is a seemingly universal, albeit enigmatic, property of the distribution of reflection coefficients in the Earth. Our results therefore indicate that spectral balancing techniques in general and spectral blueing in particular represent simple, yet effective means of enhancing the vertical resolution of surface georadar data and, in many cases, could turn out to be a preferable alternative to standard deconvolution approaches.

A gamma camera count rate saturation correction method for whole-body planar imaging.

Whole-body (WB) planar imaging has long been one of the staple methods of dosimetry, and its quantification has been formalized by the MIRD Committee in pamphlet no 16. One of the issues not specifically addressed in the formalism occurs when the count rates reaching the detector are sufficiently high to result in camera count saturation. Camera dead-time effects have been extensively studied, but all of the developed correction methods assume static acquisitions. However, during WB planar (sweep) imaging, a variable amount of imaged activity exists in the detector's field of view as a function of time and therefore the camera saturation is time dependent. A new time-dependent algorithm was developed to correct for dead-time effects during WB planar acquisitions that accounts for relative motion between detector heads and imaged object. Static camera dead-time parameters were acquired by imaging decaying activity in a phantom and obtaining a saturation curve. Using these parameters, an iterative algorithm akin to Newton's method was developed, which takes into account the variable count rate seen by the detector as a function of time. The algorithm was tested on simulated data as well as on a whole-body scan of high activity Samarium-153 in an ellipsoid phantom. A complete set of parameters from unsaturated phantom data necessary for count rate to activity conversion was also obtained, including build-up and attenuation coefficients, in order to convert corrected count rate values to activity. The algorithm proved successful in accounting for motion- and time-dependent saturation effects in both the simulated and measured data and converged to any desired degree of precision. The clearance half-life calculated from the ellipsoid phantom data was calculated to be 45.1 h after dead-time correction and 51.4 h with no correction; the physical decay half-life of Samarium-153 is 46.3 h. Accurate WB planar dosimetry of high activities relies on successfully compensating for camera saturation which takes into account the variable activity in the field of view, i.e. time-dependent dead-time effects. The algorithm presented here accomplishes this task.

Modelling structural zeros in compositional data

This analysis was stimulated by the real data analysis problem of householdexpenditure data. The full dataset contains expenditure data for a sample of 1224 households. The expenditure is broken down at 2 hierarchical levels: 9 major levels (e.g. housing, food, utilities etc.) and 92 minor levels. There are also 5 factors and 5 covariates at the household level. Not surprisingly, there are a small number of zeros at the major level, but many zeros at the minor level. The question is how best to model the zeros. Clearly, models that tryto add a small amount to the zero terms are not appropriate in general as at least some of the zeros are clearly structural, e.g. alcohol/tobacco for households that are teetotal. The key question then is how to build suitable conditional models. For example, is the sub-composition of spendingexcluding alcohol/tobacco similar for teetotal and non-teetotal households?In other words, we are looking for sub-compositional independence. Also, what determines whether a household is teetotal? Can we assume that it is independent of the composition? In general, whether teetotal will clearly depend on the household level variables, so we need to be able to model this dependence. The other tricky question is that with zeros on more than onecomponent, we need to be able to model dependence and independence of zeros on the different components. Lastly, while some zeros are structural, others may not be, for example, for expenditure on durables, it may be chance as to whether a particular household spends money on durableswithin the sample period. This would clearly be distinguishable if we had longitudinal data, but may still be distinguishable by looking at the distribution, on the assumption that random zeros will usually be for situations where any non-zero expenditure is not small.While this analysis is based on around economic data, the ideas carry over tomany other situations, including geological data, where minerals may be missing for structural reasons (similar to alcohol), or missing because they occur only in random regions which may be missed in a sample (similar to the durables)

An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemicalcomposition of archaeological material such as ceramic and glass artefacts. Data of thistype can be explored using a variety of techniques, from standard multivariate methodssuch as principal components analysis and cluster analysis, to methods based upon theuse of log-ratios. The general aim is to identify groups of chemically similar artefactsthat could potentially be used to answer questions of provenance.This paper will demonstrate work in progress on the development of a documentedlibrary of methods, implemented using the statistical package R, for the analysis ofcompositional data. R is an open source package that makes available very powerfulstatistical facilities at no cost. We aim to show how, with the aid of statistical softwaresuch as R, traditional exploratory multivariate analysis can easily be used alongside, orin combination with, specialist techniques of compositional data analysis.The library has been developed from a core of basic R functionality, together withpurpose-written routines arising from our own research (for example that reported atCoDaWork'03). In addition, we have included other appropriate publicly availabletechniques and libraries that have been implemented in R by other authors. Availablefunctions range from standard multivariate techniques through to various approaches tolog-ratio analysis and zero replacement. We also discuss and demonstrate a smallselection of relatively new techniques that have hitherto been little-used inarchaeometric applications involving compositional data. The application of the libraryto the analysis of data arising in archaeometry will be demonstrated; results fromdifferent analyses will be compared; and the utility of the various methods discussed

Inference about the number of contributors to a DNA mixture: Comparative analyses of a Bayesian network approach and the maximum allele count method.

In the forensic examination of DNA mixtures, the question of how to set the total number of contributors (N) presents a topic of ongoing interest. Part of the discussion gravitates around issues of bias, in particular when assessments of the number of contributors are not made prior to considering the genotypic configuration of potential donors. Further complication may stem from the observation that, in some cases, there may be numbers of contributors that are incompatible with the set of alleles seen in the profile of a mixed crime stain, given the genotype of a potential contributor. In such situations, procedures that take a single and fixed number contributors as their output can lead to inferential impasses. Assessing the number of contributors within a probabilistic framework can help avoiding such complication. Using elements of decision theory, this paper analyses two strategies for inference on the number of contributors. One procedure is deterministic and focuses on the minimum number of contributors required to 'explain' an observed set of alleles. The other procedure is probabilistic using Bayes' theorem and provides a probability distribution for a set of numbers of contributors, based on the set of observed alleles as well as their respective rates of occurrence. The discussion concentrates on mixed stains of varying quality (i.e., different numbers of loci for which genotyping information is available). A so-called qualitative interpretation is pursued since quantitative information such as peak area and height data are not taken into account. The competing procedures are compared using a standard scoring rule that penalizes the degree of divergence between a given agreed value for N, that is the number of contributors, and the actual value taken by N. Using only modest assumptions and a discussion with reference to a casework example, this paper reports on analyses using simulation techniques and graphical models (i.e., Bayesian networks) to point out that setting the number of contributors to a mixed crime stain in probabilistic terms is, for the conditions assumed in this study, preferable to a decision policy that uses categoric assumptions about N.

Gender differences in cardiovascular risk factors in HIV infected patients on antiretroviral therapy: Data from the Spanish Coronator study.

Purpose: HIV-infected patients present an increased cardiovascular risk (CVR) of multifactorial origin, usually lower in women than in men. Information by gender about prevalence of modifiable risk factors is scarce. Methods: Coronator is a cross-sectional survey of a representative sample of HIV-infected patients on ART within 10 hospitals across Spain in 2011. Variables include sociodemographics, CVR factors and 10-year CV disease risk estimation (Regicor: Framingham score adapted to the Spanish population). Results: We included 860 patients (76.3% male) with no history of CVD. Median age 45.6 years; 84.1% were Spaniards; 29.9% women were IDUs. Median time since HIV diagnosis for men and women was 10 and 13 years (p=0.001), 28% had an AIDS diagnosis. Median CD4 cell count was 596 cells/mm3, 88% had undetectable viral load. Median time on ART was 91 and 108 months (p=0.017). There was a family history of early CVD in 113 men (17.9%) and 41 women (20.6%). Classical CVR factors are described in the table. Median (IQR) Regicor Score was 3% (2-5) for men and 2% (1-3) for women (p=0.000), and the proportion of subjects with mid-high risk (>5%) was 26.1% for men and 9.4% for women (p=0.000). Conclusions: In this population of HIV-infected patients, women have lower cardiovascular risk than men, partly due to higher levels of HDL cholesterol. Of note is the high frequency of smoking, abdominal obesity and sedentary lifestyle in our population. (Table Presented).

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

CODAMAT: a modern analogue techinque for compositional data

The quantitative estimation of Sea Surface Temperatures from fossils assemblages is afundamental issue in palaeoclimatic and paleooceanographic investigations. TheModern Analogue Technique, a widely adopted method based on direct comparison offossil assemblages with modern coretop samples, was revised with the aim ofconforming it to compositional data analysis. The new CODAMAT method wasdeveloped by adopting the Aitchison metric as distance measure. Modern coretopdatasets are characterised by a large amount of zeros. The zero replacement was carriedout by adopting a Bayesian approach to the zero replacement, based on a posteriorestimation of the parameter of the multinomial distribution. The number of modernanalogues from which reconstructing the SST was determined by means of a multipleapproach by considering the Proxies correlation matrix, Standardized Residual Sum ofSquares and Mean Squared Distance. This new CODAMAT method was applied to theplanktonic foraminiferal assemblages of a core recovered in the Tyrrhenian Sea.Kew words: Modern analogues, Aitchison distance, Proxies correlation matrix,Standardized Residual Sum of Squares

Examining the information content of time-lapse crosshole GPR data collected under different infiltration conditions to estimate unsaturated soil hydraulic properties

Time-lapse geophysical data acquired during transient hydrological experiments are being increasingly employed to estimate subsurface hydraulic properties at the field scale. In particular, crosshole ground-penetrating radar (GPR) data, collected while water infiltrates into the subsurface either by natural or artificial means, have been demonstrated in a number of studies to contain valuable information concerning the hydraulic properties of the unsaturated zone. Previous work in this domain has considered a variety of infiltration conditions and different amounts of time-lapse GPR data in the estimation procedure. However, the particular benefits and drawbacks of these different strategies as well as the impact of a variety of key and common assumptions remain unclear. Using a Bayesian Markov-chain-Monte-Carlo stochastic inversion methodology, we examine in this paper the information content of time-lapse zero-offset-profile (ZOP) GPR traveltime data, collected under three different infiltration conditions, for the estimation of van Genuchten-Mualem (VGM) parameters in a layered subsurface medium. Specifically, we systematically analyze synthetic and field GPR data acquired under natural loading and two rates of forced infiltration, and we consider the value of incorporating different amounts of time-lapse measurements into the estimation procedure. Our results confirm that, for all infiltration scenarios considered, the ZOP GPR traveltime data contain important information about subsurface hydraulic properties as a function of depth, with forced infiltration offering the greatest potential for VGM parameter refinement because of the higher stressing of the hydrological system. Considering greater amounts of time-lapse data in the inversion procedure is also found to help refine VGM parameter estimates. Quite importantly, however, inconsistencies observed in the field results point to the strong possibility that posterior uncertainties are being influenced by model structural errors, which in turn underlines the fundamental importance of a systematic analysis of such errors in future related studies.

When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’tincludes below detection limits and/or zero values, and since most of the geological dataresponds to lognormal distributions, these “zero data” represent a mathematicalchallenge for the interpretation.We need to start by recognizing that there are zero values in geology. For example theamount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-existswith nepheline. Another common essential zero is a North azimuth, however we canalways change that zero for the value of 360°. These are known as “Essential zeros”, butwhat can we do with “Rounded zeros” that are the result of below the detection limit ofthe equipment?Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimeswe need to differentiate between a sodic and a potassic alteration. Pre-classification intogroups requires a good knowledge of the distribution of the data and the geochemicalcharacteristics of the groups which is not always available. Considering the zero valuesequal to the limit of detection of the used equipment will generate spuriousdistributions, especially in ternary diagrams. Same situation will occur if we replace thezero values by a small amount using non-parametric or parametric techniques(imputation).The method that we are proposing takes into consideration the well known relationshipsbetween some elements. For example, in copper porphyry deposits, there is always agood direct correlation between the copper values and the molybdenum ones, but whilecopper will always be above the limit of detection, many of the molybdenum values willbe “rounded zeros”. So, we will take the lower quartile of the real molybdenum valuesand establish a regression equation with copper, and then we will estimate the“rounded” zero values of molybdenum by their corresponding copper values.The method could be applied to any type of data, provided we establish first theircorrelation dependency.One of the main advantages of this method is that we do not obtain a fixed value for the“rounded zeros”, but one that depends on the value of the other variable.Key words: compositional data analysis, treatment of zeros, essential zeros, roundedzeros, correlation dependency

Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

Biases of the ordinary least squares and instrumental variables estimators of the intergenerational earnings elasticity : revisited in the light of panel data

The OLS estimator of the intergenerational earnings correlation is biased towards zero, while the instrumental variables estimator is biased upwards. The first of these results arises because of measurement error, while the latter rests on the presumption that the education of the parent family is an invalid instrument. We propose a panel data framework for quantifying the asymptotic biases of these estimators, as well as a mis-specification test for the IV estimator. [Author]

Data Download, Iowa Department of Corrections, August 2008

A startlingly new development has occurred over the past year: The number of offenders residing in Iowa’s correctional institutions has actually dropped. An ever increasing prison population – in 1990 the prison count stood at 3,842 offenders – reached an all-time high of 8,940 offenders on October 3,2007, an increase of 233% over 17 years. A significant cause for the increase has been longer stays in prison, due in part to the long-term effect of restrictions on parole eligibility. Over the past nine months, however, the prison population has been declining – to 8,573 on July 15, 2008 (not including 129 jail prisoners temporarily housed at ASP and IMCC due to the flooding). This represents a decrease of 367 offenders – or 4.1% - from the October 3, 2007 high.