Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue).
- MeSH
- Bayes Theorem * MeSH
- Humans MeSH
- Psychology * MeSH
- Research Design MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder's BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.
- MeSH
- Bayes Theorem * MeSH
- Humans MeSH
- Psychology * MeSH
- Software * MeSH
- Research Design MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
Generalist parasites have the capacity to infect multiple hosts. The temporal pattern of host specificity by generalist parasites is rarely studied, but is critical to understanding what variables underpin infection and thereby the impact of parasites on host species and the way they impose selection on hosts. Here, the temporal dynamics of infection of four species of freshwater mussel by European bitterling fish (Rhodeus amarus) was investigated over three spawning seasons. Bitterling lay their eggs in the gills of freshwater mussels, which suffer reduced growth, oxygen stress, gill damage and elevated mortality as a result of parasitism. The temporal pattern of infection of mussels by European bitterling in multiple populations was examined. Using a Bernoulli Generalized Additive Mixed Model with Bayesian inference it was demonstrated that one mussel species, Unio pictorum, was exploited over the entire bitterling spawning season. As the season progressed, bitterling showed a preference for other mussel species, which were inferior hosts. Temporal changes in host use reflected elevated density-dependent mortality in preferred hosts that were already infected. Plasticity in host specificity by bitterling conformed with the predictions of the host selection hypothesis. The relationship between bitterling and their host mussels differs qualitatively from that of avian brood parasites.
- MeSH
- Bayes Theorem MeSH
- Cyprinidae MeSH
- Host Specificity * MeSH
- Host-Parasite Interactions * MeSH
- Parasites MeSH
- Animals MeSH
- Check Tag
- Animals MeSH
- Publication type
- Journal Article MeSH
3rd ed. xv, 351 s. : il.
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
- Bayes Theorem MeSH
- Psychology, Experimental * methods MeSH
- Data Interpretation, Statistical MeSH
- Humans MeSH
- Models, Statistical * MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Review MeSH
Statistics in practice
1st ed. xi, 266 s.
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.
- MeSH
- Bayes Theorem MeSH
- Humans MeSH
- Colonic Neoplasms * drug therapy MeSH
- Disease-Free Survival MeSH
- Retrospective Studies MeSH
- Research Design * MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
Bayesian inference is used to determine the Air Kerma Rate based on in-situ gamma spectrum measurement performed with an NaI(Tl) scintillation detector. The procedure accounts for uncertainties in the measurement and in the mass energy transfer coefficients needed for the calculation. The WinBUGS program (Spiegelhalter et al., 1999) was used. The results show that the relative uncertainties in the Air Kerma estimate are of about 1%, and that the choice of unfolding procedure may lead to an estimate systematic error of 3%.
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
- Bayes Theorem MeSH
- Biodiversity MeSH
- Models, Biological * MeSH
- Time MeSH
- Cichlids classification MeSH
- Phylogeny * MeSH
- Genetic Speciation MeSH
- Fossils MeSH
- Animals MeSH
- Check Tag
- Animals MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
- Geographicals
- Atlantic Ocean MeSH
Wiley series in probability and statistics
[1st ed.] xviii, 451 s., vzorce
