Project description
New, flexible statistical theory based on extended e-values
Many statistical methods require predetermined data collection and inference, which limits flexibility in practice. This rigidity complicates error control in meta-analyses and contributes to the replication crisis in the sciences. The ERC-funded FLEX project will create a new statistical theory for situations where data collection and decision-making are unknown and determined post hoc. This theory will provide small-sample error control and rely on extended e-values, which offer a cleaner alternative to p-values for capturing evidence. The project will develop design principles for e-values in common problems, such as generalised linear models, and introduce the e-posterior, which broadens confidence intervals when priors are poorly chosen. This new theory will integrate existing Wald-Neyman-Pearson and Bayesian methods.
Objective
Most statistical methods require that all aspects of data collection and inference are determined in advance, independently of the data. These include when to stop collecting data, what decisions can be made (e.g. accept/reject hypothesis, classify new point) and how to measure their quality (e.g. loss function/significance level). This is wildly at odds with the flexibility required in practice! It makes it impossible to achieve error control in meta-analyses, and contributes to the replication crisis in the applied sciences.
I will develop a novel statistical theory in which all data-collection and decision-aspects may be unknown in advance, possibly imposed post-hoc, depending on data itself in unknowable ways. Yet this new theory will provide small-sample frequentist error control, risk bounds and confidence sets.
I base myself on far-reaching extensions of e-values/processes. These generalize likelihood ratios and replace p-values, capturing 'evidence' in a much cleaner fashion. As lead author of the first paper (2019) that gave e-values a name and demonstrated their enormous potential, I kicked off and then played an essential role in the extremely rapid development of anytime-valid inference, the one aspect of flexibility that is by now well-studied. Still, efficient e-value design principles for many standard problems (e.g. GLMs and other settings with covariates) are still lacking, and I will provide them. I will also develop theory for full decision-task flexibility, about which currently almost nothing is known. A major innovation is the e-posterior, which behaves differently from the Bayesian one: if priors are chosen badly, e-posterior based confidence intervals get wide rather than wrong.
Both the existing Wald-Neyman-Pearson and Bayesian statistical theories will arise as special, extreme cases of the new theory, based on perfect (hence unrealistic) knowledge of the data-collection/decision problem or the underlying distribution(s), respectively.
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2023-ADG
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3526 KV Utrecht
Netherlands
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