Scandinavian Journal of Statistics最新文献

{"title":"Comments on Divergence vs. Decision P‐values","authors":"Paul W. Vos","doi":"10.1111/sjos.12647","DOIUrl":"https://doi.org/10.1111/sjos.12647","url":null,"abstract":"The distinction between the two uses of p-values described by Professor Greenland is related to two distinct interpretations of frequentist probability—that is, probability used to describe a random event. I will illustrate with a simple example. In the North Carolina Pick-4 lottery, 10 ping pong balls labeled with distinct digits from I9 = {0, 1,..., 9} are mixed in a clear container and opening a door allows a single ball to be selected. Prior to opening the door, blown air mixes the balls making equally likely selection of each ball plausible. This is repeated with three identical containers to obtain the remaining three digits. If a winning ticket is defined as one where the sum of the four digits exceeds 28, the state can charge $5 for a ticket with a $100 prize and expect a profit. There are 330 of 104 possible outcomes where the sum exceeds 28 so the expected value is 0.033 × $100 = $3.30. This calculation requires no repeated sampling but it is natural for the state to interpret this value in the long run. For an individual ticket holder, all that is required is that each ball is given an equal chance to be selected for the drawing associated with his ticket. The ticket holder does not need to imagine a long sequence of draws just as a cancer patient does not need to consider a long sequence of 5-year periods to understand a 30% 5-year survival. Using terminology from Vos and Holbert (2022), the scope for the ticket holder is specific while that of the state is generic. The uniform distribution on 4-tuples I4 9 = I9 × I9 × I9 × I9 provides a model for repeated draws of the Pick-4 lottery, that is, of the data generation process. For most inference applications, the distribution of an unknown population can be modeled rather than the process that generated the data. We modify this example to consider inference. We are told the sum of a single lottery draw and we are to infer whether the draw came from the NC lottery or lottery A that also has four containers but each contains 8 balls with labels from I7 = {0, 1,..., 7}. The sum of the digits is 29 but no other information is given. A reduction-to-contradiction argument establishes that the result came from the NC lottery. Premise: lottery A produced our data; every possible sum from lottery A belongs to the set {0, 1,..., 28}; 29 is not in this set; conclusion: the contradiction means it is impossible that the premise is true.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"920 - 922"},"PeriodicalIF":1.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44877146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Statistical evidence and surprise unified under possibility theory","authors":"D. Bickel","doi":"10.1111/sjos.12648","DOIUrl":"https://doi.org/10.1111/sjos.12648","url":null,"abstract":"Sander Greenland argues that reported results of hypothesis tests should include the surprisal, the base‐2 logarithm of the reciprocal of a p‐value. The surprisal measures how many bits of evidence in the data warrant rejecting the null hypothesis. A generalization of surprisal also can measure how much the evidence justifies rejecting a composite hypothesis such as the complement of a confidence interval. That extended surprisal, called surprise, quantifies how many bits of astonishment an agent believing a hypothesis would experience upon observing the data. While surprisal is a function of a point in hypothesis space, surprise is a function of a subset of hypothesis space. Satisfying the conditions of conditional min‐plus probability, surprise inherits a wealth of tools from possibility theory. The equivalent compatibility function has been recently applied to the replication crisis, to adjusting p‐values for prior information, and to comparing scientific theories.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"923 - 928"},"PeriodicalIF":1.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43372143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Epistemic confidence in the observed confidence interval","authors":"Y. Pawitan, Hangbin Lee, Youngjo Lee","doi":"10.1111/sjos.12654","DOIUrl":"https://doi.org/10.1111/sjos.12654","url":null,"abstract":"We define confidence to be epistemic if it applies to an observed confidence interval. Epistemic confidence is unavailable—or even denied—in orthodox frequentist inference, as the confidence level is understood to apply to the procedure. Yet there are obvious practical and psychological needs to think about the uncertainty in the observed interval. We extend the Dutch Book argument used in the classical Bayesian justification of subjective probability to a stronger market‐based version, which prevents external agents from exploiting unused information in any relevant subset. We previously showed that confidence is an extended likelihood, and the likelihood principle states that the likelihood contains all the information in the data, hence leaving no relevant subset. Intuitively, this implies that confidence associated with the full likelihood is protected from the Dutch Book, and hence is epistemic. Our goal is to validate this intuitive notion through theoretical backing and practical illustrations.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47752304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discussion on the SJS invited paper by Sander Greenland Divergence vs. Decision P$$ P $$‐values: A Distinction worth making in theory and keeping in Practice","authors":"Dario Gasbarra","doi":"10.1111/sjos.12649","DOIUrl":"https://doi.org/10.1111/sjos.12649","url":null,"abstract":"It is shown in the cited paper written by Michael Lavine and in several others works that the p -value of the test-statistics is not a consistent measure of evidence in the context of testing alternative hypothesis. As Sander Greenland points out, these should not be confused with the p -values of realized goodness of-fit-test statistics. Goodness-of-fit tests are useful sanity checks in order to decide, (and there would be also a decision to be taken there !) whether our model and/or assumptions are compatible with the available data, or we need to take a step back and look for what could be wrong. Greenland argues that although using the p -value in a goodness of fit test violates the likelihood principle, these p -values do not suffer the inconsistencies of p -values arising from testing alternative hypothesis, and can be used as a measure of evidence against the model, (following Popper, scientific theories and models can be only falsified and never verified), on an absolute scale in the [ 0 , 1 ] range, where a zero left-sided p -value corresponds to perfect fit, and every p -value strictly greater than zero should be considered as negative evidence of some level. I find this peculiar, unless we would be dealing only with fully deterministic models. Fitting the data is not","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"929 - 930"},"PeriodicalIF":1.0,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43628758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comments on Divergence vs. Decision P‐values: A Distinction Worth Making in Theory and Keeping in Practice – or, How Divergence P‐values Measure Evidence Even When Decision P‐values Do Not by Greenland in Scandinavian Journal of Statistics, 2023","authors":"M. Lavine","doi":"10.1111/sjos.12646","DOIUrl":"https://doi.org/10.1111/sjos.12646","url":null,"abstract":"Greenland (2023) distinguishes between P‐values used for data description and P‐values used for declaring significance. That's a useful distinction and Greenland has advanced our field by making it. That distinction comes with the idea that describing data with statistical models is often a useful task for statisticians. Again, we agree. Along the way, Greenland also says (i) there is such a thing as a “measure …of evidence [from data] against a statistical hypothesis or model” without regard to alternatives; (ii) “a discrepancy P‐value is an ordinal description …”; (iii) descriptive “P‐values can be derived to provide coherent measures of refutational evidence”; and a few other things that deserve comment and discussion.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"915 - 919"},"PeriodicalIF":1.0,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42858391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Time‐varying\u0000 β\u0000 ‐model for dynamic directed networks","authors":"Yuqing Du, Lianqiang Qu, T. Yan, Yuan Zhang","doi":"10.1111/sjos.12650","DOIUrl":"https://doi.org/10.1111/sjos.12650","url":null,"abstract":"We extend the well-known $beta$-model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel-smoothed likelihood approach for estimating $2n$ time-varying parameters in a network with $n$ nodes, from $N$ snapshots. We establish consistency and asymptotic normality properties of our kernel-smoothed estimators as either $n$ or $N$ diverges. Our results contrast their counterparts in single-network analyses, where $ntoinfty$ is invariantly required in asymptotic studies. We conduct comprehensive simulation studies that confirm our theory's prediction and illustrate the performance of our method from various angles. We apply our method to an email data set and obtain meaningful results.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46331041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Connecting simple and precise P‐values to complex and ambiguous realities (includes rejoinder to comments on “Divergence vs. decision P‐values”)","authors":"S. Greenland","doi":"10.1111/sjos.12645","DOIUrl":"https://doi.org/10.1111/sjos.12645","url":null,"abstract":"Mathematics is a limited component of solutions to real‐world problems, as it expresses only what is expected to be true if all our assumptions are correct, including implicit assumptions that are omnipresent and often incorrect. Statistical methods are rife with implicit assumptions whose violation can be life‐threatening when results from them are used to set policy. Among them are that there is human equipoise or unbiasedness in data generation, management, analysis, and reporting. These assumptions correspond to levels of cooperation, competence, neutrality, and integrity that are absent more often than we would like to believe. Given this harsh reality, we should ask what meaning, if any, we can assign to the P‐values, “statistical significance” declarations, “confidence” intervals, and posterior probabilities that are used to decide what and how to present (or spin) discussions of analyzed data. By themselves, P‐values and CI do not test any hypothesis, nor do they measure the significance of results or the confidence we should have in them. The sense otherwise is an ongoing cultural error perpetuated by large segments of the statistical and research community via misleading terminology. So‐called inferential statistics can only become contextually interpretable when derived explicitly from causal stories about the real data generator (such as randomization), and can only become reliable when those stories are based on valid and public documentation of the physical mechanisms that generated the data. Absent these assurances, traditional interpretations of statistical results become pernicious fictions that need to be replaced by far more circumspect descriptions of data and model relations.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"899 - 914"},"PeriodicalIF":1.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48002057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Targeted estimation of state occupation probabilities for the non‐Markov illness‐death model","authors":"Anders Munch, Marie Skov Breum, T. Martinussen, T. Gerds","doi":"10.1111/sjos.12644","DOIUrl":"https://doi.org/10.1111/sjos.12644","url":null,"abstract":"We use semi‐parametric efficiency theory to derive a class of estimators for the state occupation probabilities of the continuous‐time irreversible illness‐death model. We consider both the setting with and without additional baseline information available, where we impose no specific functional form on the intensity functions of the model. We show that any estimator in the class is asymptotically linear under suitable assumptions about the estimators of the intensity functions. In particular, the assumptions are weak enough to allow the use of data‐adaptive methods, which is important for making the identifying assumption of coarsening at random plausible in realistic settings. We suggest a flexible method for estimating the transition intensity functions of the illness‐death model based on penalized Poisson regression. We apply this method to estimate the nuisance parameters of an illness‐death model in a simulation study and a real‐world application.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"1532 - 1551"},"PeriodicalIF":1.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47243862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Historical Overview of Textbook Presentations of Statistical Science","authors":"A. Agresti","doi":"10.1111/sjos.12641","DOIUrl":"https://doi.org/10.1111/sjos.12641","url":null,"abstract":"We discuss the evolution in the presentation of statistical science in English‐language textbooks, focusing on the period 1900–1970 as the field became increasingly influenced by research contributions of R. A. Fisher and Jerzy Neyman. George Udny Yule authored an early popular book that had 14 editions. Methods books authored by Fisher and George Snedecor guided scientists in implementing modern statistical methods. In the World War 2 era, textbooks authored by Maurice Kendall, Samuel Wilks, and Harald Cramér presented a dramatically different “mathematical statistics” portrayal that centered on theoretical foundations. The textbook emergence of the Bayesian approach occurred later, influenced by books by Harold Jeffreys and Leonard J. Savage. The quarter century after World War 2 saw an explosion of books in mathematical statistics and in particular topic areas. In addition to his highly cited research contributions, Sir David Cox was a prolific author of books on a great variety of topics. Most were published after the 1900–1970 period considered in this article, but we also summarize them as part of this special issue to honor his memory. We conclude by discussing the future of textbooks on the foundations of statistical science in the emerging, ever‐broader, era of data science.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45893190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Daisee: Adaptive importance sampling by balancing exploration and exploitation","authors":"Xiaoyu Lu, Tom Rainforth, Y. Teh","doi":"10.1111/sjos.12637","DOIUrl":"https://doi.org/10.1111/sjos.12637","url":null,"abstract":"We study adaptive importance sampling (AIS) as an online learning problem and argue for the importance of the trade‐off between exploration and exploitation in this adaptation. Borrowing ideas from the online learning literature, we propose Daisee, a partition‐based AIS algorithm. We further introduce a notion of regret for AIS and show that Daisee has 𝒪(T(logT)34) cumulative pseudo‐regret, where T$$ T $$ is the number of iterations. We then extend Daisee to adaptively learn a hierarchical partitioning of the sample space for more efficient sampling and confirm the performance of both algorithms empirically.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"1298 - 1324"},"PeriodicalIF":1.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47118543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}