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Null Hypothesis
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Jan Sprenger – One of the best experts on this subject based on the ideXlab platform.

Testing a Precise Null Hypothesis: The Case of Lindley’s Paradox
Philosophy of Science, 2013CoAuthors: Jan SprengerAbstract:Testing a point Null Hypothesis is a classical but controversial issue in statistical methodology. A prominent illustration is Lindley’s Paradox, which emerges in Hypothesis tests with large sample size and exposes a salient divergence between Bayesian and frequentist inference. A close analysis of the paradox reveals that both Bayesians and frequentists fail to satisfactorily resolve it. As an alternative, I suggest Bernardo’s Bayesian Reference Criterion: (i) it targets the predictive performance of the Null Hypothesis in future experiments; (ii) it provides a proper decisiontheoretic model for testing a point Null Hypothesis; (iii) it convincingly addresses Lindley’s Paradox.

testing a precise Null Hypothesis the case of lindley s paradox
Philosophy of Science, 2013CoAuthors: Jan SprengerAbstract:Testing a point Null Hypothesis is a classical but controversial issue in statistical methodology. A prominent illustration is Lindley’s Paradox, which emerges in Hypothesis tests with large sample size and exposes a salient divergence between Bayesian and frequentist inference. A close analysis of the paradox reveals that both Bayesians and frequentists fail to satisfactorily resolve it. As an alternative, I suggest Bernardo’s Bayesian Reference Criterion: (i) it targets the predictive performance of the Null Hypothesis in future experiments; (ii) it provides a proper decisiontheoretic model for testing a point Null Hypothesis; (iii) it convincingly addresses Lindley’s Paradox.
Richard D. Morey – One of the best experts on this subject based on the ideXlab platform.

Beyond Statistics: Accepting the Null Hypothesis in Mature Sciences:
Advances in Methods and Practices in Psychological Science, 2018CoAuthors: Richard D. Morey, Saskia Homer, Travis ProulxAbstract:Scientific theories explain phenomena using simplifying assumptions—for instance, that the speed of light does not depend on the direction in which the light is moving, or that the shape of a pea plant’s seeds depends on a small number of alleles randomly obtained from its parents. These simplifying assumptions often take the form of statistical Null hypotheses; hence, supporting these simplifying assumptions with statistical evidence is crucial to scientific progress, though it might involve “accepting” a Null Hypothesis. We review two historical examples in which statistical evidence was used to accept a simplifying assumption (that there is no luminiferous ether and that genetic traits are passed on in discrete forms) and one in which the Null Hypothesis was not accepted despite repeated failures (gravitational waves), drawing lessons from each. We emphasize the role of the scientific context in acceptance of the Null: Accepting a Null Hypothesis is never a purely statistical affair.

Beyond statistics: accepting the Null Hypothesis in mature sciences
, 2018CoAuthors: Richard D. Morey, Saskia Homer, Travis ProulxAbstract:Scientific theories explain phenomena using simplifying assumptions: for instance, that the speed of light does not depend on the direction in which the light is moving, or that the height of a pea plant depends on a small number of alleles randomly obtained from its parents. The ability to support these simplifying assumptions with statistical evidence is crucial to scientific progress, though it might involve “accepting” the Null Hypothesis. We review two historical examples where statistical evidence was used to accept a simplifying assumption (rejecting the luminiferous aether and genetic theory) and one where the Null Hypothesis was not accepted in spite of repeated failures (gravitational waves), drawing lessons from each. We emphasize the role of the scientific context in the acceptance of the Null: accepting the Null is never a purely statistical affair.

bayesian t tests for accepting and rejecting the Null Hypothesis
Psychonomic Bulletin & Review, 2009CoAuthors: Jeffrey N Rouder, Richard D. Morey, Paul L Speckman, Dongchu Sun, Geoffrey J IversonAbstract:Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to Null hypotheses. As is commonly known, it is not possible to state evidence for the Null Hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the Null Hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easytouse, Webbased program that performs the necessary calculations.
Ludmil B. Alexandrov – One of the best experts on this subject based on the ideXlab platform.

Generating realistic Null Hypothesis of cancer mutational landscapes using SigProfilerSimulator.
BMC Bioinformatics, 2020CoAuthors: Erik N. Bergstrom, Mark Barnes, Inigo Martincorena, Ludmil B. AlexandrovAbstract:BACKGROUND Performing a statistical test requires a Null Hypothesis. In cancer genomics, a key challenge is the fast generation of accurate somatic mutational landscapes that can be used as a realistic Null Hypothesis for making biological discoveries. RESULTS Here we present SigProfilerSimulator, a powerful tool that is capable of simulating the mutational landscapes of thousands of cancer genomes at different resolutions within seconds. Applying SigProfilerSimulator to 2144 wholegenome sequenced cancers reveals: (i) that most doublet base substitutions are not due to two adjacent single base substitutions but likely occur as single genomic events; (ii) that an extended sequencing context of ± 2 bp is required to more completely capture the patterns of substitution mutational signatures in human cancer; (iii) information on falsepositive discovery rate of commonly used bioinformatics tools for detecting driver genes. CONCLUSIONS SigProfilerSimulator’s breadth of features allows one to construct a tailored Null Hypothesis and use it for evaluating the accuracy of other bioinformatics tools or for downstream statistical analysis for biological discoveries. SigProfilerSimulator is freely available at https://github.com/AlexandrovLab/SigProfilerSimulator with an extensive documentation at https://osf.io/usxjz/wiki/home/ .

Generating realistic Null Hypothesis of cancer mutational landscapes using SigProfilerSimulator
bioRxiv, 2020CoAuthors: Erik N. Bergstrom, Mark Barnes, Inigo Martincorena, Ludmil B. AlexandrovAbstract:Performing a statistical test requires a Null Hypothesis. In cancer genomics, a key challenge is the fast generation of accurate somatic mutational landscapes that can be used as a realistic Null Hypothesis for making biological discoveries. Here we present SigProfilerSimulator, a powerful tool that is capable of simulating the mutational landscapes of thousands of cancer genomes at different resolutions within seconds. Applying SigProfilerSimulator to 2,144 wholegenome sequenced cancers reveals: (i) that most doublet base substitutions are not due to two adjacent single base substitutions but likely occur as single genomic events; (ii) that an extended sequencing context of +/2bp is required to more completely capture the patterns of substitution mutational signatures in human cancer; (iii) information on falsepositive discovery rate of commonly used bioinformatics tools for detecting driver genes. SigProfilerSimulator9s breadth of features allows one to construct a tailored Null Hypothesis and use it for evaluating the accuracy of other bioinformatics tools or for downstream statistical analysis for biological discoveries.