Quantile mechanics II: changes of variables in Monte Carlo methods and GPU-optimised normal quantiles

With financial modelling requiring a better understanding of model risk, it is helpful to be able to vary assumptions about underlying probability distributions in an efficient manner, preferably without the noise induced by resampling distributions managed by Monte Carlo methods. This paper presents differential equations and solution methods for the functions of the form Q(x) = F −1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of the traditional Cornish–Fisher expansion. In this manner the model risk of distributional risk may be assessed free of the Monte Carlo noise associated with resampling. The method may also be regarded as providing both analytical and numerical bases for doing more precise Cornish–Fisher transformations. Examples are given of equations for converting normal samples to Student t, and converting exponential to normal. In the case of the normal distribution, the change of variables employed allows the sampling to take place to good accuracy based on a single rational approximation over a very wide range of sample space. The avoidance of branching statements is of use in optimal graphics processing unit (GPU) computations as it avoids the effect of branch divergence. We give a branch-free normal quantile that offers performance improvements in a GPU environment while retaining the best precision characteristics of well-known methods. We also offer models with low probability branch divergence. Comparisons of new and existing forms are made on Nvidia GeForce GTX Titan and Tesla C2050 GPUs. We argue that in both single- and double-precisions, the change-of-variables approach offers the most GPU-optimal Gaussian quantile yet, working faster than the Cuda 5.5 built-in function

Precautionary Regulation in Europe and the United States: A Quantitative Comparison

Much attention has been addressed to the question of whether Europe or the United States adopts a more precautionary stance to the regulation of potential environmental, health, and safety risks. Some commentators suggest that Europe is more risk-averse and precautionary, whereas the US is seen as more risk-taking and optimistic about the prospects for new technology. Others suggest that the US is more precautionary because its regulatory process is more legalistic and adversarial, while Europe is more lax and corporatist in its regulations. The flip-flop hypothesis claims that the US was more precautionary than Europe in the 1970s and early 1980s, and that Europe has become more precautionary since then. We examine the levels and trends in regulation of environmental, health, and safety risks since 1970. Unlike previous research, which has studied only a small set of prominent cases selected non-randomly, we develop a comprehensive list of almost 3,000 risks and code the relative stringency of regulation in Europe and the US for each of 100 risks randomly selected from that list for each year from 1970 through 2004. Our results suggest that: (a) averaging over risks, there is no significant difference in relative precaution over the period, (b) weakly consistent with the flip-flop hypothesis, there is some evidence of a modest shift toward greater relative precaution of European regulation since about 1990, although (c) there is a diversity of trends across risks, of which the most common is no change in relative precaution (including cases where Europe and the US are equally precautionary and where Europe or the US has been consistently more precautionary). The overall finding is of a mixed and diverse pattern of relative transatlantic precaution over the period

The risk of stroke and stroke type in patients with atrial fibrillation and chronic kidney disease

Background: Atrial fibrillation (AF) and chronic kidney disease (CKD) are known to increase the risk of stroke. Objectives: We set out to examine the risk of stroke by kidney function and albuminuria in patients with and without AF. Design: Retrospective cohort study. Settings: Ontario, Canada. Participants: A total of 736 666 individuals (>40 years) from 2002 to 2015. Measurements: New-onset AF, albumin-to-creatinine ratio (ACR), and an estimated glomerular filtration rate (eGFR). Methods: A total of 39 120 matched patients were examined for the risk of ischemic, hemorrhagic, or any stroke event, accounting for the competing risk of all-cause mortality. Interaction terms for combinations of ACR/eGFR and the outcome of stroke with and without AF were examined. Results: In a total of 4086 (5.2%) strokes (86% ischemic), the presence of AF was associated with a 2-fold higher risk for any stroke event and its subtypes of ischemic and hemorrhagic stroke. Across eGFR levels, the risk of stroke was 2-fold higher with the presence of AF except for low levels of eGFR (eGFR < 30 mL/min/1.73 m2, hazard ratio [HR]: 1.38, 95% confidence interval [CI]: 0.99-1.92). Similarly across ACR levels, the risk of stroke was 2-fold higher except for high levels of albuminuria (ACR > 30 mg/g, HR: 1.61, 95% CI: 1.31-1.99). The adjusted risk of stroke with AF differed by combinations of ACR and eGFR categories (interaction P value = .04) compared with those without AF. Both stroke types were more common in patients with AF, and ischemic stroke rates differed significantly by eGFR and ACR categories. Limitations: Medication information was not included. Conclusions: Patients with CKD and AF are at a high risk of total, ischemic, and hemorrhagic strokes; the risk is highest with lower eGFR and higher ACR and differs based on eGFR and the degree of ACR

Efficient Photoionization-Loading of Trapped Cadmium Ions with Ultrafast Pulses

Atomic cadmium ions are loaded into radiofrequency ion traps by photoionization of atoms in a cadmium vapor with ultrafast laser pulses. The photoionization is driven through an intermediate atomic resonance with a frequency-quadrupled mode-locked Ti:Sapphire laser that produces pulses of either 100 fsec or 1 psec duration at a central wavelength of 229 nm. The large bandwidth of the pulses photoionizes all velocity classes of the Cd vapor, resulting in high loading efficiencies compared to previous ion trap loading techniques. Measured loading rates are compared with a simple theoretical model, and we conclude that this technique can potentially ionize every atom traversing the laser beam within the trapping volume. This may allow the operation of ion traps with lower levels of background pressures and less trap electrode surface contamination. The technique and laser system reported here should be applicable to loading most laser-cooled ion species.Comment: 11 pages, 12 figure

Mean Arterial Pressure Change Associated with Cerebral Blood Flow in Healthy Older Adults

We investigate over a 12-year period the association between regional cerebral blood flow (CBF) and cardiovascular risk factors in a prospective cohort of healthy older adults (81.96 +/- 3.82 year-old) from the Cognitive REServe and Clinical ENDOphenotype (CRESCENDO) study. Cardiovascular risk factors were measured over 12 years, and gray matter CBF was measured at the end of the study from high-resolution magnetic resonance imaging using arterial spin labeling. The association between cardiovascular risk factors, their long-term change, and CBF was assessed using multivariate linear regression models. Women were observed to have higher CBF than men (p < 0.05). Increased mean arterial pressure (MAP) over the 12-year period was correlated with a low cerebral blood flow (p < 0.05, R(2) = 0.21), whereas no association was detected between CBF and MAP at the time of imaging. High levels of glycemia tended to be associated with low cerebral blood flow values (p < 0.05). Age, alcohol consumption, smoking status, body mass index, history of cardiovascular disease, and hypertension were not associated with CBF. Our main result suggests that change in MAP is the most significant predictor of future CBF in older adults

The use of happiness research for public policy

Research on happiness tends to follow a "benevolent dictator" approach where politicians pursue people's happiness. This paper takes an antithetic approach based on the insights of public choice theory. First, we inquire how the results of happiness research may be used to improve the choice of institutions. Second, we show that the policy approach matters for the choice of research questions and the kind of knowledge happiness research aims to provide. Third, we emphasize that there is no shortcut to an optimal policy maximizing some happiness indicator or social welfare function since governments have an incentive to manipulate this indicator

The cross-national pattern of happiness. Test of predictions implied in three theories of happiness

ABSTRACT. Predictions about level and dispersion of happiness in nations are derived from three theories of happiness: comparison-theory, folklore-theory and livability-theory. The predictions are tested on two cross national data-sets: a comparative survey among university students in 38 nations in 1985 and a collection of comparable general population surveys in 28 nations around 1980. Most predictions of comparison-theory and folklore-theory are defied by the data. The predictions of livability-theory are all confirmed

Rare Variants Imputation in Admixed Populations: Comparison Across Reference Panels and Bioinformatics Tools

BackgroundImputation has become a standard approach in genome-wide association studies (GWAS) to infer in silico untyped markers. Although feasibility for common variants imputation is well established, we aimed to assess rare and ultra-rare variants’ imputation in an admixed Caribbean Hispanic population (CH).MethodsWe evaluated imputation accuracy in CH (N = 1,000), focusing on rare (0.1% ≤ minor allele frequency (MAF) ≤ 1%) and ultra-rare (MAF &lt; 0.1%) variants. We used two reference panels, the Haplotype Reference Consortium (HRC; N = 27,165) and 1000 Genome Project (1000G phase 3; N = 2,504) and multiple phasing (SHAPEIT, Eagle2) and imputation algorithms (IMPUTE2, MACH-Admix). To assess imputation quality, we reported: (a) high-quality variant counts according to imputation tools’ internal indexes (e.g., IMPUTE2 “Info” ≥ 80%). (b) Wilcoxon Signed-Rank Test comparing imputation quality for genotyped variants that were masked and imputed; (c) Cohen’s kappa coefficient to test agreement between imputed and whole-exome sequencing (WES) variants; (d) imputation of G206A mutation in the PSEN1 (ultra-rare in the general population an more frequent in CH) followed by confirmation genotyping. We also tested ancestry proportion (European, African and Native American) against WES-imputation mismatches in a Poisson regression fashion.ResultsSHAPEIT2 retrieved higher percentage of imputed high-quality variants than Eagle2 (rare: 51.02% vs. 48.60%; ultra-rare 0.66% vs. 0.65%, Wilcoxon p-value &lt; 0.001). SHAPEIT-IMPUTE2 employing HRC outperformed 1000G (64.50% vs. 59.17%; 1.69% vs. 0.75% for high-quality rare and ultra-rare variants, respectively, Wilcoxon p-value &lt; 0.001). SHAPEIT-IMPUTE2 outperformed MaCH-Admix. Compared to 1000G, HRC-imputation retrieved a higher number of high-quality rare and ultra-rare variants, despite showing lower agreement between imputed and WES variants (e.g., rare: 98.86% for HRC vs. 99.02% for 1000G). High Kappa (K = 0.99) was observed for both reference panels. Twelve G206A mutation carriers were imputed and all validated by confirmation genotyping. African ancestry was associated with higher imputation errors for uncommon and rare variants (p-value &lt; 1e-05).ConclusionReference panels with larger numbers of haplotypes can improve imputation quality for rare and ultra-rare variants in admixed populations such as CH. Ethnic composition is an important predictor of imputation accuracy, with higher African ancestry associated with poorer imputation accuracy

Cruel to be kind but not cruel for cash : harm aversion in the dictator game

People regularly take prosocial actions, making individual sacrifices for the greater good. Similarly, people generally avoid causing harm to others. These twin desires to do good and avoid harm often align, but sometimes they can diverge, creating situations of moral conflict. Here, we examined this moral conflict using a modified dictator game. Participants chose how much money to allocate away from a recipient who was designated as an orphan, creating a sense of harm. This money was then reallocated to either the participant or a charity. People were strongly prosocial: they allocated more money away from the orphan for charity than for themselves. Furthermore, people left more money with the orphan when the harm was framed as a means (taking) than as a side effect (splitting). As is predicted by dual-process theories of moral decision making, response times were longer with the take action and were positively correlated with the amount taken from the orphan. We concluded that just as people take positive actions for the greater good, they are similarly more willing to cause harm when it benefits others rather than themselves