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Molecular structures are usually calculated from experimental data with some method of energy minimisation or non-linear optimisation. Key aims of a structure calculation are to estimate the coordinate uncertainty, and to provide ...
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Molecular structures are usually calculated from experimental data with some method of energy minimisation or non-linear optimisation. Key aims of a structure calculation are to estimate the coordinate uncertainty, and to provide a meaningful measure of the quality of the fit to the data. We discuss approaches to optimally combine prior information and experimental data and the connection to probability theory. We analyse the appropriate statistics for NOEs and NOE-derived distances, and the related question of restraint potentials. Finally, we will discuss approaches to determine the appropriate weight on the experimental evidence and to obtain in this way an estimate of the data quality from the structure calculation. Whereas objective estimates of coordinates and their uncertainties can only be obtained by a full Bayesian treatment of the problem, standard structure calculation methods continue to play an important role. To obtain the full benefit of these methods, they should be founded on a rigorous Bayesian analysis.
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While there are many computer programs that derive the likelihood ratio for genetic and other types of evidence, the Bayesian method of combination of prior probability coupled with the likelihood ratio, used by courts to ascertai...
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While there are many computer programs that derive the likelihood ratio for genetic and other types of evidence, the Bayesian method of combination of prior probability coupled with the likelihood ratio, used by courts to ascertain posterior probability, has less support from software and other practical aids. Without proper instructions to a court, Bayes' rule is either applied subconsciously by the judge, or prior probability is, by default, assigned a flat 50% probability by a forensic expert. In the worst case, it can be interpreted wrongly. A graphical representation using a nomogram is a proven way of representing Bayes' theorem but remains underused in the field of forensics and the law. For this paper, I used the freeware package PyNomo to prepare two simple forensic nomograms allowing the graphical calculation of posterior probability by increasing or decreasing the prior probability due to evidence.
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Case histories are necessary besides other types of evidence to convince doctors of a specific type action of homeopathic medicines. Prognosis of treatment does not merely depend on efficacy. Some considerations based on consensus...
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Case histories are necessary besides other types of evidence to convince doctors of a specific type action of homeopathic medicines. Prognosis of treatment does not merely depend on efficacy. Some considerations based on consensus meetings about best cases and prospective research into the relationship between symptoms and result. Many data in homeopathic literature are unreliable because of wrong interpretation, insufficient numbers and confirmation bias. Causal relationship between medicine and 'cure' could be documented better. Extraordinary cases are not helpful to increase reproducibility. Conclusion: For acceptance and improvement of homeopathy cases should be reproducible. 'Normal' cases reflecting daily practice contribute more to this goal than extraordinary cases. Accuracy can be increased by larger samples of comparable cases. Causal relationship between medicine and improvement should be further explored.
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摘要 :
Case histories are necessary besides other types of evidence to convince doctors of a specific type action of homeopathic medicines. Prognosis of treatment does not merely depend on efficacy.Some considerations based on consensus ...
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Case histories are necessary besides other types of evidence to convince doctors of a specific type action of homeopathic medicines. Prognosis of treatment does not merely depend on efficacy.Some considerations based on consensus meetings about best cases and prospective research into the relationship between symptoms and result.Many data in homeopathic literature are unreliable because of wrong interpretation, insufficient numbers and confirmation bias. Causal relationship between medicine and 'cure' could be documented better. Extraordinary cases are not helpful to increase reproducibility. Conclusion: For acceptance and improvement of homeopathy cases should be reproducible. 'Normal' cases reflecting daily practice contribute more to this goal than extraordinary cases. Accuracy can be increased by larger samples of comparable cases. Causal relationship between medicine and improvement should be further explored.
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Failures of government policies often provoke opposite reactions from citizens; some call for a reversal of the policy, whereas others favor its continuation in stronger form. We offer an explanation of such polarization, based on...
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Failures of government policies often provoke opposite reactions from citizens; some call for a reversal of the policy, whereas others favor its continuation in stronger form. We offer an explanation of such polarization, based on a natural bimodality of preferences in political and economic contexts and consistent with Bayesian rationality.
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Application of Bayes' theorem for the evaluation of diagnostic results of electric facilities is described. A concept of risk assessment method based on the diagnosis results is proposed and the effects of various parameters on th...
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Application of Bayes' theorem for the evaluation of diagnostic results of electric facilities is described. A concept of risk assessment method based on the diagnosis results is proposed and the effects of various parameters on the risk are clarified. Based on these results, a rational renewal scheme using diagnostic results is proposed. In addition, the prior probability based on the data of actual facilities is investigated and it is found that the data available so far is insufficient and more data are required for the detailed analysis.
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The COVID19 crisis has provided a portal to revisit and understand qualities of screening tests and the importance of Bayes' theorem in understanding how to interpret results and implications of next actions. (C) 2020 The Author(s...
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The COVID19 crisis has provided a portal to revisit and understand qualities of screening tests and the importance of Bayes' theorem in understanding how to interpret results and implications of next actions. (C) 2020 The Author(s). Published by Elsevier Inc.
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In a recent article, Gorski and Novella state that prior probabilities can be so low that putting them to the test makes no sense [1]. A few decades ago the randomised controlled trial (RCT) was demanded because of the low prior p...
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In a recent article, Gorski and Novella state that prior probabilities can be so low that putting them to the test makes no sense [1]. A few decades ago the randomised controlled trial (RCT) was demanded because of the low prior probability of clinical methods such as homeopathy. Interestingly, the mention of prior chance and its updating using Bayes' theorem arose after a considerable number of RCTs of homeopathy were subjected to meta-analysis; this concluded that the results were not compatible with the placebo hypothesis for homeopathy [2]. Extremely low priors, based on theory, are now proposed as sufficient reason to disregard scientific evidence.
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摘要 :
In a recent article, Gorski and Novella state that prior probabilities can be so low that putting them to the test makes no sense [1]. A few decades ago the randomised controlled trial (RCT) was demanded because of the low prior p...
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In a recent article, Gorski and Novella state that prior probabilities can be so low that putting them to the test makes no sense [1]. A few decades ago the randomised controlled trial (RCT) was demanded because of the low prior probability of clinical methods such as homeopathy. Interestingly, the mention of prior chance and its updating using Bayes' theorem arose after a considerable number of RCTs of homeopathy were subjected to meta-analysis; this concluded that the results were not compatible with the placebo hypothesis for homeopathy [2]. Extremely low priors, based on theory, are now proposed as sufficient reason to disregard scientific evidence.
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Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian ana...
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Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Solving the inverse problem in digital image restoration and Bayesian modeling of neural networks are discussed in detail. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making.
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