The random variate m is, in combinatorics, a basis for comparing permutations, as well as the solution to a centuries-old riddle involving the mishandling of hats. In statistics, m is the test statistic for a disused null hypothesis statistical test (NHST) of association, the matching method. In this paper, I show that the matching method has an absolute and relatively low limit on its statistical power. I do so first by reinterpreting Rae's theorem, which describes the joint distributions of m with several rank correlation statistics under a true null. I then derive this property solely from m's unconditional sampling distribution, on which basis I develop the concept of a deficient statistic: a statistic that is insufficient and inconsistent and inefficient with respect to its parameter. Finally, I demonstrate an application for m that makes use of its deficiency to qualify the sampling error in a jointly estimated sample correlation.
{"title":"On statistical deficiency: Why the test statistic of the matching method is hopelessly underpowered and uniquely informative","authors":"M. C. Nelson","doi":"10.31234/osf.io/y6rmb","DOIUrl":"https://doi.org/10.31234/osf.io/y6rmb","url":null,"abstract":"The random variate m is, in combinatorics, a basis for comparing permutations, as well as the solution to a centuries-old riddle involving the mishandling of hats. In statistics, m is the test statistic for a disused null hypothesis statistical test (NHST) of association, the matching method. In this paper, I show that the matching method has an absolute and relatively low limit on its statistical power. I do so first by reinterpreting Rae's theorem, which describes the joint distributions of m with several rank correlation statistics under a true null. I then derive this property solely from m's unconditional sampling distribution, on which basis I develop the concept of a deficient statistic: a statistic that is insufficient and inconsistent and inefficient with respect to its parameter. Finally, I demonstrate an application for m that makes use of its deficiency to qualify the sampling error in a jointly estimated sample correlation.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133812346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a recent manuscript, Gelman & Yao (2020) claim that "the usual rules of conditional probability fail in the quantum realm" and that "probability theory isn't true (quantum physics)" and purport to support these statements with the example of a quantum double-slit experiment. The present note recalls some relevant literature in quantum theory and shows that (i) Gelman & Yao's statements are false; in fact, the quantum example confirms the rules of probability theory; (ii) the particular inequality found in the quantum example can be shown to appear also in very non-quantum examples, such as drawing from an urn; thus there is nothing peculiar to quantum theory in this matter. A couple of wrong or imprecise statements about quantum theory in the cited manuscript are also corrected.
{"title":"The rule of conditional probability is valid in quantum theory [Comment on Gelman & Yao's \"Holes in Bayesian statistics\"]","authors":"PierGianLuca Porta-Mana","doi":"10.31219/osf.io/bsnh7","DOIUrl":"https://doi.org/10.31219/osf.io/bsnh7","url":null,"abstract":"In a recent manuscript, Gelman & Yao (2020) claim that \"the usual rules of conditional probability fail in the quantum realm\" and that \"probability theory isn't true (quantum physics)\" and purport to support these statements with the example of a quantum double-slit experiment. The present note recalls some relevant literature in quantum theory and shows that (i) Gelman & Yao's statements are false; in fact, the quantum example confirms the rules of probability theory; (ii) the particular inequality found in the quantum example can be shown to appear also in very non-quantum examples, such as drawing from an urn; thus there is nothing peculiar to quantum theory in this matter. A couple of wrong or imprecise statements about quantum theory in the cited manuscript are also corrected.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130010135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.1007/978-3-030-67036-8_7
Youngjo Lee, Y. Pawitan
{"title":"Popper’s Falsification and Corroboration from the Statistical Perspectives","authors":"Youngjo Lee, Y. Pawitan","doi":"10.1007/978-3-030-67036-8_7","DOIUrl":"https://doi.org/10.1007/978-3-030-67036-8_7","url":null,"abstract":"","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126493635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-09DOI: 10.1101/2020.04.11.20062257
Román Marchant, Noelle I. Samia, O. Rosen, M. Tanner, Sally Cripps
A recent model developed at the Institute for Health Metrics and Evaluation (IHME) provides forecasts for ventilator use and hospital beds required for the care of COVID19 patients on a state-by-state basis throughout the United States over the period March 2020 through August 2020 (See the related website https://covid19.healthdata.org/projections for interactive data visualizations). In addition, the manuscript and associated website provide projections of deaths per day and total deaths throughout this period for the entire US, as well as for the District of Columbia. This research has received extensive attention in social media, as well as in the mass media. Moreover, this work has influenced policy makers at the highest levels of the United States government, having been mentioned at White House Press conferences, including March 31, 2020. In this paper, we evaluate the predictive validity of model forecasts for COVID19 outcomes as data become sequentially available, using the IHME prediction of daily deaths. We have found that the predictions for daily number of deaths provided by the IHME model have been highly inaccurate. The model has been found to perform poorly even when attempting to predict the number of next day deaths. In particular, the true number of next day deaths has been outside the IHME prediction intervals as much as 70% of the time.
{"title":"Learning as We Go: An Examination of the Statistical Accuracy of COVID19 Daily Death Count Predictions","authors":"Román Marchant, Noelle I. Samia, O. Rosen, M. Tanner, Sally Cripps","doi":"10.1101/2020.04.11.20062257","DOIUrl":"https://doi.org/10.1101/2020.04.11.20062257","url":null,"abstract":"A recent model developed at the Institute for Health Metrics and Evaluation (IHME) provides forecasts for ventilator use and hospital beds required for the care of COVID19 patients on a state-by-state basis throughout the United States over the period March 2020 through August 2020 (See the related website https://covid19.healthdata.org/projections for interactive data visualizations). In addition, the manuscript and associated website provide projections of deaths per day and total deaths throughout this period for the entire US, as well as for the District of Columbia. This research has received extensive attention in social media, as well as in the mass media. Moreover, this work has influenced policy makers at the highest levels of the United States government, having been mentioned at White House Press conferences, including March 31, 2020. In this paper, we evaluate the predictive validity of model forecasts for COVID19 outcomes as data become sequentially available, using the IHME prediction of daily deaths. We have found that the predictions for daily number of deaths provided by the IHME model have been highly inaccurate. The model has been found to perform poorly even when attempting to predict the number of next day deaths. In particular, the true number of next day deaths has been outside the IHME prediction intervals as much as 70% of the time.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130013205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work investigates whether and how COVID-19 containment policies had an immediate impact on crime trends in Los Angeles. The analysis is conducted using Bayesian structural time-series and focuses on nine crime categories and on the overall crime count, daily monitored from January 1st 2017 to March 28th 2020. We concentrate on two post-intervention time windows—from March 4th to March 16th and from March 4textsuperscript{th} to March 28th 2020—to dynamically assess the short-term effects of mild and strict policies. In Los Angeles, overall crime has significantly decreased, as well as robbery, shoplifting, theft, and battery. No significant effect has been detected for vehicle theft, burglary, assault with a deadly weapon, intimate partner assault, and homicide. Results suggest that, in the first weeks after the interventions are put in place, social distancing impacts more directly on instrumental and less serious crimes. Policy implications are also discussed.
{"title":"Exploring the Effects of COVID-19 Containment Policies on Crime: An Empirical Analysis of the Short-term Aftermath in Los Angeles","authors":"G. Campedelli, Alberto Aziani, Serena Favarin","doi":"10.31219/osf.io/gcpq8","DOIUrl":"https://doi.org/10.31219/osf.io/gcpq8","url":null,"abstract":"This work investigates whether and how COVID-19 containment policies had an immediate impact on crime trends in Los Angeles. The analysis is conducted using Bayesian structural time-series and focuses on nine crime categories and on the overall crime count, daily monitored from January 1st 2017 to March 28th 2020. We concentrate on two post-intervention time windows—from March 4th to March 16th and from March 4textsuperscript{th} to March 28th 2020—to dynamically assess the short-term effects of mild and strict policies. In Los Angeles, overall crime has significantly decreased, as well as robbery, shoplifting, theft, and battery. No significant effect has been detected for vehicle theft, burglary, assault with a deadly weapon, intimate partner assault, and homicide. Results suggest that, in the first weeks after the interventions are put in place, social distancing impacts more directly on instrumental and less serious crimes. Policy implications are also discussed.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125099792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-06DOI: 10.1007/978-3-030-62900-7_11
N. Singpurwalla, Boya Lai
{"title":"How and Why Did Probability Theory Come About?","authors":"N. Singpurwalla, Boya Lai","doi":"10.1007/978-3-030-62900-7_11","DOIUrl":"https://doi.org/10.1007/978-3-030-62900-7_11","url":null,"abstract":"","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131104624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Drawing inference from data is an important skill for students to understand their everyday life, so that the sampling distribution as a central topic in statistical inference is necessary to be learned by the students. However, little is known about how to teach the topic for high school students, especially in Indonesian context. Therefore, the present study provides a teaching experiment to support the students' informal inferential reasoning in understanding the sampling distribution, as well as the students' perceptions toward the teaching experiment. The subjects in the present study were three 11th-grader of one private school in Yogyakarta majoring in mathematics and natural science. The method of data collection was direct observation of sampling distribution learning process, interviews, and documentation. The present study found that that informal inferential reasoning with problem-based learning using contextual problems and real data could support the students to understand the sampling distribution, and they also gave positive responses about their learning experience.
{"title":"A Case Study of Promoting Informal Inferential Reasoning in Learning Sampling Distribution for High School Students","authors":"Geovani Debby Setyani, Y. D. Kristanto","doi":"10.35706/sjme.v4i1.3132","DOIUrl":"https://doi.org/10.35706/sjme.v4i1.3132","url":null,"abstract":"Drawing inference from data is an important skill for students to understand their everyday life, so that the sampling distribution as a central topic in statistical inference is necessary to be learned by the students. However, little is known about how to teach the topic for high school students, especially in Indonesian context. Therefore, the present study provides a teaching experiment to support the students' informal inferential reasoning in understanding the sampling distribution, as well as the students' perceptions toward the teaching experiment. The subjects in the present study were three 11th-grader of one private school in Yogyakarta majoring in mathematics and natural science. The method of data collection was direct observation of sampling distribution learning process, interviews, and documentation. The present study found that that informal inferential reasoning with problem-based learning using contextual problems and real data could support the students to understand the sampling distribution, and they also gave positive responses about their learning experience.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122917584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-14DOI: 10.1615/int.j.uncertaintyquantification.2020033516
M. Daza-Torres, J. C. Montesinos-L'opez, Marcos A. Capistr'an, J. Christen, H. Haario
We elaborate on results obtained in cite{christen2018} for controlling the numerical posterior error for Bayesian UQ problems, now considering forward maps arising from the solution of a semilinear evolution partial differential equation. Results in cite{christen2018} demand an error estimate for the numerical solution of the FM. Our contribution is a numerical method for computing after-the-fact (i.e. a posteriori) error estimates for semilinear evolution PDEs, and show the potential applicability of cite{christen2018} in this important wide range family of PDEs. Numerical examples are given to illustrate the efficiency of the proposed method, obtaining numerical posterior distributions for unknown parameters that are nearly identical to the corresponding theoretical posterior, by keeping their Bayes factor close to 1.
{"title":"ERROR CONTROL IN THE NUMERICAL POSTERIOR DISTRIBUTION IN THE BAYESIAN UQ ANALYSIS OF A SEMILINEAR EVOLUTION PDE","authors":"M. Daza-Torres, J. C. Montesinos-L'opez, Marcos A. Capistr'an, J. Christen, H. Haario","doi":"10.1615/int.j.uncertaintyquantification.2020033516","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2020033516","url":null,"abstract":"We elaborate on results obtained in cite{christen2018} for controlling the numerical posterior error for Bayesian UQ problems, now considering forward maps arising from the solution of a semilinear evolution partial differential equation. Results in cite{christen2018} demand an error estimate for the numerical solution of the FM. Our contribution is a numerical method for computing after-the-fact (i.e. a posteriori) error estimates for semilinear evolution PDEs, and show the potential applicability of cite{christen2018} in this important wide range family of PDEs. Numerical examples are given to illustrate the efficiency of the proposed method, obtaining numerical posterior distributions for unknown parameters that are nearly identical to the corresponding theoretical posterior, by keeping their Bayes factor close to 1.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124703362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We briefly expose some key aspects of the theory and use of dispersion models, for which Bent Jorgensen played a crucial role as a driving force and an inspiration source. Starting with the general notion of dispersion models, built using minimalistic mathematical assumptions, we specialize in two classes of families of distributions with different statistical flavors: exponential dispersion and proper dispersion models. The construction of dispersion models involves the solution of integral equations that are, in general, untractable. These difficulties disappear when a more mathematical structure is assumed: it reduces to the calculation of a moment generating function or of a Riemann-Stieltjes integral for the exponential dispersion and the proper dispersion models, respectively. A new technique for constructing dispersion models based on characteristic functions is introduced turning the integral equations above into a tractable convolution equation and yielding examples of dispersion models that are neither proper dispersion nor exponential dispersion models. A corollary is that the cardinality of regular and non-regular dispersion models are both large. Some selected applications are discussed including exponential families non-linear models (for which generalized linear models are particular cases) and several models for clustered and dependent data based on a latent Levy process.
{"title":"An introduction to Bent Jørgensen’s ideas","authors":"G. Cordeiro, R. Labouriau, D. Botter","doi":"10.1214/19-bjps458","DOIUrl":"https://doi.org/10.1214/19-bjps458","url":null,"abstract":"We briefly expose some key aspects of the theory and use of dispersion models, for which Bent Jorgensen played a crucial role as a driving force and an inspiration source. Starting with the general notion of dispersion models, built using minimalistic mathematical assumptions, we specialize in two classes of families of distributions with different statistical flavors: exponential dispersion and proper dispersion models. The construction of dispersion models involves the solution of integral equations that are, in general, untractable. These difficulties disappear when a more mathematical structure is assumed: it reduces to the calculation of a moment generating function or of a Riemann-Stieltjes integral for the exponential dispersion and the proper dispersion models, respectively. A new technique for constructing dispersion models based on characteristic functions is introduced turning the integral equations above into a tractable convolution equation and yielding examples of dispersion models that are neither proper dispersion nor exponential dispersion models. A corollary is that the cardinality of regular and non-regular dispersion models are both large. \u0000Some selected applications are discussed including exponential families non-linear models (for which generalized linear models are particular cases) and several models for clustered and dependent data based on a latent Levy process.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114394536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A growing awareness of the lack of reproducibility has undermined society’s trust and esteem in social sciences. In some cases, well-known results have been fabricated or the underlying data have turned out to have weak technical foundations.
{"title":"Open data, open review and open dialogue in making social sciences plausible","authors":"Q. Vuong","doi":"10.31219/osf.io/du8tj","DOIUrl":"https://doi.org/10.31219/osf.io/du8tj","url":null,"abstract":"A growing awareness of the lack of reproducibility has undermined society’s trust and esteem in social sciences. In some cases, well-known results have been fabricated or the underlying data have turned out to have weak technical foundations.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127721646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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