The nonlinear Bernstein-Schr\"odinger equation in Economics

In this paper we relate the Equilibrium Assignment Problem (EAP), which is underlying in several economics models, to a system of nonlinear equations that we call the "nonlinear Bernstein-Schr\"odinger system", which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.Comment: 8 pages, submitted to Lecture Notes in Computer Scienc

lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their corresponding unit spheres). We also assume mixture weights for the different components. We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces. We study the recovery of the most significant subspace by minimizing the lp-averaged distances of data points from d-dimensional subspaces, where p>0. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 0<p<=1, then for any fraction of outliers the most significant subspace can be recovered by lp minimization with overwhelming probability (which depends on the generating distribution and its parameters). We show that when adding small noise around the underlying subspaces the most significant subspace can be nearly recovered by lp minimization for any 0<p<=1 with an error proportional to the noise level. On the other hand, if p>1 and there is more than one underlying subspace, then with overwhelming probability the most significant subspace cannot be recovered or nearly recovered. This last result does not require spherically symmetric outliers.Comment: This is a revised version of the part of 1002.1994 that deals with single subspace recovery. V3: Improved estimates (in particular for Lemma 3.1 and for estimates relying on it), asymptotic dependence of probabilities and constants on D and d and further clarifications; for simplicity it assumes uniform distributions on spheres. V4: minor revision for the published versio

Markov Chain-based Cost-Optimal Control Charts for Healthcare Data

Control charts have traditionally been used in industrial statistics, but are constantly seeing new areas of application, especially in the age of Industry 4.0. This paper introduces a new method, which is suitable for applications in the healthcare sector, especially for monitoring a health-characteristic of a patient. We adapt a Markov chain-based approach and develop a method in which not only the shift size (i.e. the degradation of the patient's health) can be random, but the effect of the repair (i.e. treatment) and time between samplings (i.e. visits) too. This means that we do not use many often-present assumptions which are usually not applicable for medical treatments. The average cost of the protocol, which is determined by the time between samplings and the control limit, can be estimated using the stationary distribution of the Markov chain. Furthermore, we incorporate the standard deviation of the cost into the optimisation procedure, which is often very important from a process control viewpoint. The sensitivity of the optimal parameters and the resulting average cost and cost standard deviation on different parameter values is investigated. We demonstrate the usefulness of the approach for real-life data of patients treated in Hungary: namely the monitoring of cholesterol level of patients with cardiovascular event risk. The results showed that the optimal parameters from our approach can be somewhat different from the original medical parameters

A global optimisation approach to range-restricted survey calibration

Survey calibration methods modify minimally unit-level sample weights to fit domain-level benchmark constraints (BC). This allows exploitation of auxiliary information, e.g. census totals, to improve the representativeness of sample data (addressing coverage limitations, non-response) and the quality of estimates of population parameters. Calibration methods may fail with samples presenting small/zero counts for some benchmark groups or when range restrictions (RR), such as positivity, are imposed to avoid unrealistic or extreme weights. User-defined modifications of BC/RR performed after encountering non-convergence allow little control on the solution, and penalization approaches modelling infeasibility may not guarantee convergence. Paradoxically, this has led to underuse in calibration of highly disaggregated information, when available. We present an always-convergent flexible two-step Global Optimisation (GO) survey calibration approach. The feasibility of the calibration problem is assessed, and automatically controlled minimum errors in BC or changes in RR are allowed to guarantee convergence in advance, while preserving the good properties of calibration estimators. Modelling alternatives under different scenarios, using various error/change and distance measures are formulated and discussed. The GO approach is validated by calibrating the weights of the 2012 Health Survey for England to a fine age-gender-region cross-tabulation (378 counts) from the 2011 Census in England and Wales

A global optimisation approach to range-restricted survey calibration

Survey calibration methods modify minimally unit-level sample weights to fit domain-level benchmark constraints (BC). This allows exploitation of auxiliary information, e.g. census totals, to improve the representativeness of sample data (addressing coverage limitations, non-response) and the quality of estimates of population parameters. Calibration methods may fail with samples presenting small/zero counts for some benchmark groups or when range restrictions (RR), such as positivity, are imposed to avoid unrealistic or extreme weights. User-defined modifications of BC/RR performed after encountering non-convergence allow little control on the solution, and penalization approaches modelling infeasibility may not guarantee convergence. Paradoxically, this has led to underuse in calibration of highly disaggregated information, when available. We present an always-convergent flexible two-step Global Optimisation (GO) survey calibration approach. The feasibility of the calibration problem is assessed, and automatically controlled minimum errors in BC or changes in RR are allowed to guarantee convergence in advance, while preserving the good properties of calibration estimators. Modelling alternatives under different scenarios, using various error/change and distance measures are formulated and discussed. The GO approach is validated by calibrating the weights of the 2012 Health Survey for England to a fine age-gender-region cross-tabulation (378 counts) from the 2011 Census in England and Wales

Beyond chance? The persistence of performance in online poker

A major issue in the widespread controversy about the legality of poker and the appropriate taxation of winnings is whether poker should be considered a game of skill or a game of chance. To inform this debate we present an analysis into the role of skill in the performance of online poker players, using a large database with hundreds of millions of player-hand observations from real money ring games at three different stakes levels. We find that players whose earlier profitability was in the top (bottom) deciles perform better (worse) and are substantially more likely to end up in the top (bottom) performance deciles of the following time period. Regression analyses of performance on historical performance and other skill-related proxies provide further evidence for persistence and predictability. Simulations point out that skill dominates chance when performance is measured over 1,500 or more hands of play

Immediate Outcome Indicators in Perioperative Care: A Controlled Intervention Study on Quality Improvement in Hospitals in Tanzania.

Outcome assessment is the standard for evaluating the quality of health services worldwide. In this study, outcome has been divided into immediate and final outcome. Aim was to compare an intervention hospital with a Continuous Quality Improvement approach to a control group using benchmark assessments of immediate outcome indicators in surgical care. Results were compared to final outcome indicators. Surgical care quality in six hospitals in Tanzania was assessed from 2006-2011, using the Hospital Performance Assessment Tool. Independent observers assessed structural, process and outcome quality using checklists based on evidence-based guidelines. The number of surgical key procedures over the benchmark of 80% was compared between the intervention hospital and the control group. Results were compared to Case Fatality Rates. In the intervention hospital, in 2006, two of nine key procedures reached the benchmark, one in 2009, and four in 2011. In the control group, one of nine key procedures reached the benchmark in 2006, one in 2009, and none in 2011. Case Fatality Rate for all in-patients in the intervention hospital was 5.5% (n = 12,530) in 2006, 3.5% (n = 21,114) in 2009 and 4.6% (n = 18,840) in 2011. In the control group it was 3.1% (n = 17,827) in 2006, 4.2% (n = 13,632) in 2009 and 3.8% (n = 17,059) in 2011. Results demonstrated that quality assurance improved performance levels in both groups. After the introduction of Continuous Quality Improvement, performance levels improved further in the intervention hospital while quality in the district hospital did not. Immediate outcome indicators appeared to be a better steering tool for quality improvement compared to final outcome indicators. Immediate outcome indicators revealed a need for improvement in pre- and postoperative care. Quality assurance programs based on immediate outcome indicators can be effective if embedded in Continuous Quality Improvement. Nevertheless, final outcome indicators cannot be neglected

Public Acceptability in the UK and USA of Nudging to Reduce Obesity: The Example of Reducing Sugar-Sweetened Beverages Consumption.

BACKGROUND: "Nudging"-modifying environments to change people's behavior, often without their conscious awareness-can improve health, but public acceptability of nudging is largely unknown. METHODS: We compared acceptability, in the United Kingdom (UK) and the United States of America (USA), of government interventions to reduce consumption of sugar-sweetened beverages. Three nudge interventions were assessed: i. reducing portion Size, ii. changing the Shape of the drink containers, iii. changing their shelf Location; alongside two traditional interventions: iv. Taxation and v. Education. We also tested the hypothesis that describing interventions as working through non-conscious processes decreases their acceptability. Predictors of acceptability, including perceived intervention effectiveness, were also assessed. Participants (n = 1093 UK and n = 1082 USA) received a description of each of the five interventions which varied, by randomisation, in how the interventions were said to affect behaviour: (a) via conscious processes; (b) via non-conscious processes; or (c) no process stated. Acceptability was derived from responses to three items. RESULTS: Levels of acceptability for four of the five interventions did not differ significantly between the UK and US samples; reducing portion size was less accepted by the US sample. Within each country, Education was rated as most acceptable and Taxation the least, with the three nudge-type interventions rated between these. There was no evidence to support the study hypothesis: i.e. stating that interventions worked via non-conscious processes did not decrease their acceptability in either the UK or US samples. Perceived effectiveness was the strongest predictor of acceptability for all interventions across the two samples. CONCLUSION: In conclusion, nudge interventions to reduce consumption of sugar-sweetened beverages seem similarly acceptable in the UK and USA, being more acceptable than taxation, but less acceptable than education. Contrary to prediction, we found no evidence that highlighting the non-conscious processes by which nudge interventions may work decreases their acceptability. However, highlighting the effectiveness of all interventions has the potential to increase their acceptability.The study was funded by the UK Department of Health Policy Research Programme (Policy Research Unit in Behaviour and Health) (Grant ID: PRUN-0409-10109)This is the final version of the article. It first appeared from the Public Library of Science via http://dx.doi.org/10.1371/journal.pone.015599