Bayesian analysis
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Zpracování znalostí zatížených nejistotou je jednou z nejdůležitějších aplikací metod umělé inteligence. Použití technologie bayesovských sítí umožňuje pro tyto ucely využít výsledky po několik století budované teorie pravděpodobnosti a pracovat s mnohorozměrnými pravdepodobnostními distribucemi V tomto případě muže být rozměr distribucí roven stovkám, případně i tisícům. To znamená, že tato technologie může být použita na reálné aplikace, na skutečné problémy, jejichž složitost přesahuje možnosti většiny dalších přístupů pro modelování nejistých znalostí. Vzhledem k tomu, že se jedná o poměrně mladou disciplínu, nelze říci, že všechny teoretické problémy a problémy spojené s návrhem aplikací již byly úspěšně vyřešeny. Nejvíce otevřených problémů je spojeno právě s konstrukcí bayesovských sítu Přesto sejižobjevují aplikace, které naznačují, že bayesovské sítě se stanoujednítn z mocných nástrojů umělé inteligence pro řešení složitých problémů. Proto lze předpokládat, že se s bayesovskými sítěmi budeme v blízké budoucnosti setkávat i v medicíně, která je jednou z oblastí, kde deterministická znalost je spíše výjimkou.
Uncertain knowledge processing is one of the most important applications of artificial intelligence. Bayesian network technology, taking advantage of for several centuries developed results of probability theory, enables processing of multidimensional probability distributions whose dimensionality equals hundreds or even thousands. Therefore, this technology can be applied to real-life problems whose complexity goes beyond cambility of most other approaches for uncertain knowledge processing. It cannot be said that this relatively new discipline has Iready solved all its theoretical and practical problems. Most of still open problems are connected with zonstraction of Bayesian network models for practical applications. Nevertheless, recently published applications suggest that Bayesian network will become one of he most powerful tool of artificial intelligence for uncertain knowledge processing. Therefore, we can assume that in near future we shall meet Bayesian network in medical applications as this field is one of those where deterministic knowledge is exception.
BACKGROUND: We provide an overview of Bayesian estimation, hypothesis testing, and model-averaging and illustrate how they benefit parametric survival analysis. We contrast the Bayesian framework to the currently dominant frequentist approach and highlight advantages, such as seamless incorporation of historical data, continuous monitoring of evidence, and incorporating uncertainty about the true data generating process. METHODS: We illustrate the application of the outlined Bayesian approaches on an example data set, retrospective re-analyzing a colon cancer trial. We assess the performance of Bayesian parametric survival analysis and maximum likelihood survival models with AIC/BIC model selection in fixed-n and sequential designs with a simulation study. RESULTS: In the retrospective re-analysis of the example data set, the Bayesian framework provided evidence for the absence of a positive treatment effect of adding Cetuximab to FOLFOX6 regimen on disease-free survival in patients with resected stage III colon cancer. Furthermore, the Bayesian sequential analysis would have terminated the trial 10.3 months earlier than the standard frequentist analysis. In a simulation study with sequential designs, the Bayesian framework on average reached a decision in almost half the time required by the frequentist counterparts, while maintaining the same power, and an appropriate false-positive rate. Under model misspecification, the Bayesian framework resulted in higher false-negative rate compared to the frequentist counterparts, which resulted in a higher proportion of undecided trials. In fixed-n designs, the Bayesian framework showed slightly higher power, slightly elevated error rates, and lower bias and RMSE when estimating treatment effects in small samples. We found no noticeable differences for survival predictions. We have made the analytic approach readily available to other researchers in the RoBSA R package. CONCLUSIONS: The outlined Bayesian framework provides several benefits when applied to parametric survival analyses. It uses data more efficiently, is capable of considerably shortening the length of clinical trials, and provides a richer set of inferences.
Texts in statistical science
2nd ed. xxv, 668 s.
Texts in statistical science
1st ed. xix, 526 s.
3rd ed. xv, 351 s. : il.
3rd ed. xv, 351 s. : il. ; 24 cm
- MeSH
- statistika jako téma metody MeSH
- Publikační typ
- monografie MeSH
- Konspekt
- Statistika
- NLK Obory
- statistika, zdravotnická statistika
Statistics in practice
1st ed. xi, 266 s.
- MeSH
- Bayesova věta MeSH
- diagnóza počítačová metody MeSH
- lidé MeSH
- nádory plic MeSH
- plicní nemoci MeSH
- Check Tag
- lidé MeSH
One of the most common statistical analyses in experimental psychology concerns the comparison of two means using the frequentist t test. However, frequentist t tests do not quantify evidence and require various assumption tests. Recently, popularized Bayesian t tests do quantify evidence, but these were developed for scenarios where the two populations are assumed to have the same variance. As an alternative to both methods, we outline a comprehensive t test framework based on Bayesian model averaging. This new t test framework simultaneously takes into account models that assume equal and unequal variances, and models that use t-likelihoods to improve robustness to outliers. The resulting inference is based on a weighted average across the entire model ensemble, with higher weights assigned to models that predicted the observed data well. This new t test framework provides an integrated approach to assumption checks and inference by applying a series of pertinent models to the data simultaneously rather than sequentially. The integrated Bayesian model-averaged t tests achieve robustness without having to commit to a single model following a series of assumption checks. To facilitate practical applications, we provide user-friendly implementations in JASP and via the RoBTT package in R . A tutorial video is available at https://www.youtube.com/watch?v=EcuzGTIcorQ.
- MeSH
- Bayesova věta MeSH
- experimentální psychologie * metody MeSH
- interpretace statistických dat MeSH
- lidé MeSH
- statistické modely * MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- přehledy MeSH
