Descripción del proyecto
Nueva teoría estadística flexible basada en valores e ampliados
Muchos métodos estadísticos requieren una recopilación de datos y una inferencia predeterminadas, lo que en la práctica limita la flexibilidad. Esa falta de flexibilidad limita el control de errores en los metaanálisis y contribuye a la crisis de reproducción de estudios en las ciencias. En el proyecto FLEX, financiado por el Consejo Europeo de Investigación, se concebirá una nueva teoría estadística para situaciones en las que la recopilación de datos y la toma de decisiones son desconocidas y se determinan «post hoc». Esta teoría ofrecerá un control de errores en muestras pequeñas y se basará en valores e ampliados, que proporcionan una alternativa más clara a los valores p para capturar la evidencia. El equipo del proyecto desarrollará principios de diseño para los valores e en problemas comunes, como los modelos lineales generalizados, e introducirá e posterior, que amplía los intervalos de confianza cuando los priores se han elegido mal. Esta nueva teoría integrará los métodos Wald-Neyman-Pearson y bayesianos existentes.
Objetivo
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.
Palabras clave
Programa(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Régimen de financiación
HORIZON-ERC - HORIZON ERC GrantsInstitución de acogida
3526 KV Utrecht
Países Bajos