Bayesian modelling
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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.
- MeSH
- lidé MeSH
- matematika MeSH
- pravděpodobnost MeSH
- teoretické modely MeSH
- výuka - hodnocení 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
3rd ed. xv, 351 s. : il.
Statistics in practice
1st ed. xi, 266 s.
Although seasonal variation has a known influence on the transmission of several respiratory viral infections, its role in SARS-CoV-2 transmission remains unclear. While there is a sizable and growing literature on environmental drivers of COVID-19 transmission, recent reviews have highlighted conflicting and inconclusive findings. This indeterminacy partly owes to the fact that seasonal variation relates to viral transmission by a complicated web of causal pathways, including many interacting biological and behavioural factors. Since analyses of specific factors cannot determine the aggregate strength of seasonal forcing, we sidestep the challenge of disentangling various possible causal paths in favor of a holistic approach. We model seasonality as a sinusoidal variation in transmission and infer a single Bayesian estimate of the overall seasonal effect. By extending two state-of-the-art models of non-pharmaceutical intervention (NPI) effects and their datasets covering 143 regions in temperate Europe, we are able to adjust our estimates for the role of both NPIs and mobility patterns in reducing transmission. We find strong seasonal patterns, consistent with a reduction in the time-varying reproduction number R(t) (the expected number of new infections generated by an infectious individual at time t) of 42.1% (95% CI: 24.7%-53.4%) from the peak of winter to the peak of summer. These results imply that the seasonality of SARS-CoV-2 transmission is comparable in magnitude to the most effective individual NPIs but less than the combined effect of multiple interventions.
- MeSH
- Bayesova věta MeSH
- COVID-19 * epidemiologie MeSH
- lidé MeSH
- podnebí MeSH
- roční období MeSH
- SARS-CoV-2 * MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
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.
Human and animal diet reconstruction studies that rely on tissue chemical signatures aim at providing estimates on the relative intake of potential food groups. However, several sources of uncertainty need to be considered when handling data. Bayesian mixing models provide a natural platform to handle diverse sources of uncertainty while allowing the user to contribute with prior expert information. The Bayesian mixing model FRUITS (Food Reconstruction Using Isotopic Transferred Signals) was developed for use in diet reconstruction studies. FRUITS incorporates the capability to account for dietary routing, that is, the contribution of different food fractions (e.g. macronutrients) towards a dietary proxy signal measured in the consumer. FRUITS also provides relatively straightforward means for the introduction of prior information on the relative dietary contributions of food groups or food fractions. This type of prior may originate, for instance, from physiological or metabolic studies. FRUITS performance was tested using simulated data and data from a published controlled animal feeding experiment. The feeding experiment data was selected to exemplify the application of the novel capabilities incorporated into FRUITS but also to illustrate some of the aspects that need to be considered when handling data within diet reconstruction studies. FRUITS accurately predicted dietary intakes, and more precise estimates were obtained for dietary scenarios in which expert prior information was included. FRUITS represents a useful tool to achieve accurate and precise food intake estimates in diet reconstruction studies within different scientific fields (e.g. ecology, forensics, archaeology, and dietary physiology).
- MeSH
- analýza potravin metody statistika a číselné údaje MeSH
- Bayesova věta MeSH
- dieta * MeSH
- izotopy dusíku MeSH
- krmivo pro zvířata analýza MeSH
- lidé MeSH
- nejistota MeSH
- statistické modely * MeSH
- stravovací zvyklosti fyziologie psychologie MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Divergence-time estimation based on molecular phylogenies and the fossil record has provided insights into fundamental questions of evolutionary biology. In Bayesian node dating, phylogenies are commonly time calibrated through the specification of calibration densities on nodes representing clades with known fossil occurrences. Unfortunately, the optimal shape of these calibration densities is usually unknown and they are therefore often chosen arbitrarily, which directly impacts the reliability of the resulting age estimates. As possible solutions to this problem, two nonexclusive alternative approaches have recently been developed, the “fossilized birth–death” (FBD) model and “total-evidence dating.” While these approaches have been shown to perform well under certain conditions, they require including all (or a random subset) of the fossils of each clade in the analysis, rather than just relying on the oldest fossils of clades. In addition, both approaches assume that fossil records of different clades in the phylogeny are all the product of the same underlying fossil sampling rate, even though this rate has been shown to differ strongly between higher level taxa. We here develop a flexible new approach to Bayesian age estimation that combines advantages of node dating and the FBD model. In our new approach, calibration densities are defined on the basis of first fossil occurrences and sampling rate estimates that can be specified separately for all clades. We verify our approach with a large number of simulated data sets, and compare its performance to that of the FBD model. We find that our approach produces reliable age estimates that are robust to model violation, on par with the FBD model. By applying our approach to a large data set including sequence data from over 1000 species of teleost fishes as well as 147 carefully selected fossil constraints, we recover a timeline of teleost diversification that is incompatible with previously assumed vicariant divergences of freshwater fishes. Our results instead provide strong evidence for transoceanic dispersal of cichlids and other groups of teleost fishes.
- MeSH
- Bayesova věta MeSH
- biodiverzita MeSH
- biologické modely * MeSH
- čas MeSH
- cichlidy klasifikace MeSH
- fylogeneze * MeSH
- vznik druhů (genetika) MeSH
- zkameněliny MeSH
- zvířata MeSH
- Check Tag
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Geografické názvy
- Atlantský oceán MeSH
The Iowa Gambling Task (IGT) is one of the most popular experimental paradigms for comparing complex decision-making across groups. Most commonly, IGT behavior is analyzed using frequentist tests to compare performance across groups, and to compare inferred parameters of cognitive models developed for the IGT. Here, we present a Bayesian alternative based on Bayesian repeated-measures ANOVA for comparing performance, and a suite of three complementary model-based methods for assessing the cognitive processes underlying IGT performance. The three model-based methods involve Bayesian hierarchical parameter estimation, Bayes factor model comparison, and Bayesian latent-mixture modeling. We illustrate these Bayesian methods by applying them to test the extent to which differences in intuitive versus deliberate decision style are associated with differences in IGT performance. The results show that intuitive and deliberate decision-makers behave similarly on the IGT, and the modeling analyses consistently suggest that both groups of decision-makers rely on similar cognitive processes. Our results challenge the notion that individual differences in intuitive and deliberate decision styles have a broad impact on decision-making. They also highlight the advantages of Bayesian methods, especially their ability to quantify evidence in favor of the null hypothesis, and that they allow model-based analyses to incorporate hierarchical and latent-mixture structures.
- MeSH
- Bayesova věta * MeSH
- exekutivní funkce fyziologie MeSH
- interpretace statistických dat * MeSH
- lidé MeSH
- neuropsychologické testy * MeSH
- posilování (psychologie) * MeSH
- psychologické modely * MeSH
- rozhodování fyziologie MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- přehledy MeSH
- Research Support, U.S. Gov't, Non-P.H.S. MeSH
