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Sander Greenland - One of the best experts on this subject based on the ideXlab platform.
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the causal foundations of applied probability and statistics
arXiv: Other Statistics, 2020Co-Authors: Sander GreenlandAbstract:Statistical Science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators even for purely descriptive goals. Statistical decision theory requires more causality: Rational decisions are actions taken to minimize costs while maximizing benefits, and thus require explication of causes of loss and gain. Competent Statistical practice thus integrates logic, context, and probability into scientific inference and decision using narratives filled with causality. This reality was seen and accounted for intuitively by the founders of modern statistics, but was not well recognized in the ensuing Statistical theory (which focused instead on the causally inert properties of probability measures). Nonetheless, both Statistical foundations and basic statistics can and should be taught using formal causal models. The causal view of Statistical Science fits within a broader information-processing framework which illuminates and unifies frequentist, Bayesian, and related probability-based foundations of statistics. Causality theory can thus be seen as a key component connecting computation to contextual information, not extra-Statistical but instead essential for sound Statistical training and applications.
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semantic and cognitive tools to aid Statistical Science replace confidence and significance by compatibility and surprise
BMC Medical Research Methodology, 2020Co-Authors: Zad Rafi, Sander GreenlandAbstract:Researchers often misinterpret and misrepresent Statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and P-values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than Statistical, we review some simple methods to aid researchers in interpreting Statistical outputs. These methods emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. We use the Shannon transform of the P-value p, also known as the binary surprisal or S-value s = −log2(p), to provide a measure of the information supplied by the testing procedure, and to help calibrate intuitions against simple physical experiments like coin tossing. We also use tables or graphs of test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. Finally, we reinterpret P-values and interval estimates in unconditional terms, which describe compatibility of data with the entire set of analysis assumptions. We illustrate these methods with a reanalysis of data from an existing record-based cohort study. In line with other recent recommendations, we advise that teaching materials and research reports discuss P-values as measures of compatibility rather than significance, compute P-values for alternative hypotheses whenever they are computed for null hypotheses, and interpret interval estimates as showing values of high compatibility with data, rather than regions of confidence. Our recommendations emphasize cognitive devices for displaying the compatibility of the observed data with various hypotheses of interest, rather than focusing on single hypothesis tests or interval estimates. We believe these simple reforms are well worth the minor effort they require.
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semantic and cognitive tools to aid Statistical Science replace confidence and significance by compatibility and surprise
arXiv: Methodology, 2019Co-Authors: Zad Rafi, Sander GreenlandAbstract:Researchers often misinterpret and misrepresent Statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and $P$-values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than Statistical, we review simple aids to Statistical interpretations. These aids emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. We use the Shannon transform of the $P$-value $p$, also known as the binary surprisal or $S$-value $s=-\log_{2}(p)$, to measure the information supplied by the testing procedure, and to help calibrate intuitions against simple physical experiments like coin tossing. We also use tables or graphs of test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. Finally, we reinterpret $P$-values and interval estimates in unconditional terms, which describe compatibility of data with the entire set of analysis assumptions. We illustrate these methods with a reanalysis of data from an existing record-based cohort study. In line with other recent recommendations, we advise that teaching materials and research reports discuss $P$-values as measures of compatibility rather than significance, compute $P$-values for alternative hypotheses whenever they are computed for null hypotheses, and interpret interval estimates as showing values of high compatibility with data, rather than regions of confidence. Our recommendations emphasize cognitive devices for displaying the compatibility of the observed data with various hypotheses of interest, rather than focusing on single hypothesis tests or interval estimates. We believe these simple reforms are well worth the minor effort they require.
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the performance of random coefficient regression in accounting for residual confounding
Biometrics, 2006Co-Authors: Paul Gustafson, Sander GreenlandAbstract:Greenland (2000, Biometrics 56, 915-921) describes the use of random coefficient regression to adjust for residual confounding in a particular setting. We examine this setting further, giving theoretical and empirical results concerning the frequentist and Bayesian performance of random coefficient regression. Particularly, we compare estimators based on this adjustment for residual confounding to estimators based on the assumption of no residual confounding. This devolves to comparing an estimator from a nonidentified but more realistic model to an estimator from a less realistic but identified model. The approach described by Gustafson (2005, Statistical Science 20, 111-140) is used to quantify the performance of a Bayesian estimator arising from a nonidentified model. From both theoretical calculations and simulations we find support for the idea that superior performance can be obtained by replacing unrealistic identifying constraints with priors that allow modest departures from those constraints. In terms of point-estimator bias this superiority arises when the extent of residual confounding is substantial, but the advantage is much broader in terms of interval estimation. The benefit from modeling residual confounding is maintained when the prior distributions employed only roughly correspond to reality, for the standard identifying constraints are equivalent to priors that typically correspond much worse.
J A Nelder - One of the best experts on this subject based on the ideXlab platform.
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from statistics to Statistical Science
Journal of the Royal Statistical Society: Series D (The Statistician), 1999Co-Authors: J A NelderAbstract:It is asserted that statistics must be relevant to making inferences in Science and technology. The subject should be renamed Statistical Science and be focused on the experimental cycle, design–execute–analyse–predict. Its part in each component of the cycle is discussed. The P-value culture is claimed to be the main prop of non-scientific statistics, leading to the cult of the single study and the proliferation of multiple-comparison tests. The malign influence of P-values on protocols for the analysis of groups of experiments is discussed, and also the consequences of the formation of inferentially uninteresting linear models. Suggestions for action by statisticians include the sorting out of modes of inference, the removal of non-scientific procedures, the offering of help to editors, the promotion of good software and teaching methods built round the experimental cycle.
Zad Rafi - One of the best experts on this subject based on the ideXlab platform.
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semantic and cognitive tools to aid Statistical Science replace confidence and significance by compatibility and surprise
BMC Medical Research Methodology, 2020Co-Authors: Zad Rafi, Sander GreenlandAbstract:Researchers often misinterpret and misrepresent Statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and P-values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than Statistical, we review some simple methods to aid researchers in interpreting Statistical outputs. These methods emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. We use the Shannon transform of the P-value p, also known as the binary surprisal or S-value s = −log2(p), to provide a measure of the information supplied by the testing procedure, and to help calibrate intuitions against simple physical experiments like coin tossing. We also use tables or graphs of test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. Finally, we reinterpret P-values and interval estimates in unconditional terms, which describe compatibility of data with the entire set of analysis assumptions. We illustrate these methods with a reanalysis of data from an existing record-based cohort study. In line with other recent recommendations, we advise that teaching materials and research reports discuss P-values as measures of compatibility rather than significance, compute P-values for alternative hypotheses whenever they are computed for null hypotheses, and interpret interval estimates as showing values of high compatibility with data, rather than regions of confidence. Our recommendations emphasize cognitive devices for displaying the compatibility of the observed data with various hypotheses of interest, rather than focusing on single hypothesis tests or interval estimates. We believe these simple reforms are well worth the minor effort they require.
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semantic and cognitive tools to aid Statistical Science replace confidence and significance by compatibility and surprise
arXiv: Methodology, 2019Co-Authors: Zad Rafi, Sander GreenlandAbstract:Researchers often misinterpret and misrepresent Statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and $P$-values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than Statistical, we review simple aids to Statistical interpretations. These aids emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. We use the Shannon transform of the $P$-value $p$, also known as the binary surprisal or $S$-value $s=-\log_{2}(p)$, to measure the information supplied by the testing procedure, and to help calibrate intuitions against simple physical experiments like coin tossing. We also use tables or graphs of test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. Finally, we reinterpret $P$-values and interval estimates in unconditional terms, which describe compatibility of data with the entire set of analysis assumptions. We illustrate these methods with a reanalysis of data from an existing record-based cohort study. In line with other recent recommendations, we advise that teaching materials and research reports discuss $P$-values as measures of compatibility rather than significance, compute $P$-values for alternative hypotheses whenever they are computed for null hypotheses, and interpret interval estimates as showing values of high compatibility with data, rather than regions of confidence. Our recommendations emphasize cognitive devices for displaying the compatibility of the observed data with various hypotheses of interest, rather than focusing on single hypothesis tests or interval estimates. We believe these simple reforms are well worth the minor effort they require.
Greenland Sander - One of the best experts on this subject based on the ideXlab platform.
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The causal foundations of applied probability and statistics
2021Co-Authors: Greenland SanderAbstract:Statistical Science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more causality: Rational decisions are actions taken to minimize costs while maximizing benefits, and thus require explication of causes of loss and gain. Competent Statistical practice thus integrates logic, context, and probability into scientific inference and decision using narratives filled with causality. This reality was seen and accounted for intuitively by the founders of modern statistics, but was not well recognized in the ensuing Statistical theory (which focused instead on the causally inert properties of probability measures). Nonetheless, both Statistical foundations and basic statistics can and should be taught using formal causal models. The causal view of Statistical Science fits within a broader information-processing framework which illuminates and unifies frequentist, Bayesian, and related probability-based foundations of statistics. Causality theory can thus be seen as a key component connecting computation to contextual information, not extra-Statistical but instead essential for sound Statistical training and applications.Comment: 22 pages; in press for Dechter, R., Halpern, J., and Geffner, H., eds. Probabilistic and Causal Inference: The Works of Judea Pearl. ACM book
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Semantic and Cognitive Tools to Aid Statistical Science: Replace Confidence and Significance by Compatibility and Surprise
'Springer Science and Business Media LLC', 2020Co-Authors: Rafi Zad, Greenland SanderAbstract:Researchers often misinterpret and misrepresent Statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and $P$-values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than Statistical, we review simple aids to Statistical interpretations. These aids emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. We use the Shannon transform of the $P$-value $p$, also known as the binary surprisal or $S$-value $s=-\log_{2}(p)$, to measure the information supplied by the testing procedure, and to help calibrate intuitions against simple physical experiments like coin tossing. We also use tables or graphs of test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. Finally, we reinterpret $P$-values and interval estimates in unconditional terms, which describe compatibility of data with the entire set of analysis assumptions. We illustrate these methods with a reanalysis of data from an existing record-based cohort study. In line with other recent recommendations, we advise that teaching materials and research reports discuss $P$-values as measures of compatibility rather than significance, compute $P$-values for alternative hypotheses whenever they are computed for null hypotheses, and interpret interval estimates as showing values of high compatibility with data, rather than regions of confidence. Our recommendations emphasize cognitive devices for displaying the compatibility of the observed data with various hypotheses of interest, rather than focusing on single hypothesis tests or interval estimates. We believe these simple reforms are well worth the minor effort they require.Comment: 22 pages; 5 figures; 2 tables; 94 references; Published at BMC Medical Research Methodolog
Howell Daniel - One of the best experts on this subject based on the ideXlab platform.
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Final report for the REDUS project - Reduced Uncertainty in Stock Assessment
Havforskningsinstituttet, 2021Co-Authors: Olsen, Erik Joel Steinar, Aanes Sondre, Aldrin, Magne Tommy, Breivik, Olav Nikolai, Fuglebakk Edvin, Goto Daisuke, Handegard, Nils Olav, Hansen Cecilie, Holmin, Arne Johannes, Howell DanielAbstract:The REDUS project (2016-2020) has been a strategic project at the Institute of Marine Research (IMR) aimed at quantifying and reducing the uncertainty in data-rich and age-structured stock assessments (e.g., cod, herring, haddock, capelin). Work was organized in four topical work-packages: Fisheries-dependent (catch) surveys and assessment modeling (WP1), Fishery-independent (scientific) surveys (WP2), Evaluating and testing of long-term management strategies (WP3), and Communication of uncertainty, dissemination of project results and capacity building (WP4). The Norwegian Computing Center (NR) was contracted in as a strategic partner in Statistical modeling and analysis, contributing mainly to WP1 and WP2, but found the research of fundamental interest therefore also allocating internal (NR) funding to develop the Statistical Science base of several of the methods.publishedVersio
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Final report for the REDUS project - Reduced Uncertainty in Stock Assessment
Havforskningsinstituttet, 2021Co-Authors: Olsen, Erik Joel Steinar, Aanes Sondre, Aldrin, Magne Tommy, Breivik, Olav Nikolai, Fuglebakk Edvin, Goto Daisuke, Handegard, Nils Olav, Hansen Cecilie, Holmin, Arne Johannes, Howell DanielAbstract:The REDUS project (2016-2020) has been a strategic project at the Institute of Marine Research (IMR) aimed at quantifying and reducing the uncertainty in data-rich and age-structured stock assessments (e.g., cod, herring, haddock, capelin). Work was organized in four topical work-packages: Fisheries-dependent (catch) surveys and assessment modeling (WP1), Fishery-independent (scientific) surveys (WP2), Evaluating and testing of long-term management strategies (WP3), and Communication of uncertainty, dissemination of project results and capacity building (WP4). The Norwegian Computing Center (NR) was contracted in as a strategic partner in Statistical modeling and analysis, contributing mainly to WP1 and WP2, but found the research of fundamental interest therefore also allocating internal (NR) funding to develop the Statistical Science base of several of the methods
