Statistical Rethinking: A Bayesian Course with Examples in R and Stan

Mallik, Abhirup

doi:10.1080/00401706.2021.1945329

Cited by 450 publications

(685 citation statements)

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“…The prior distribution is updated with the likelihood of the data to form a posterior distribution, which reflects expectations about likely parameter values after having seen the data. For a more extensive introduction to Bayesian estimation, see 21 A regularizing prior distribution shrinks small coefficients towards zero by assigning high probability mass to near-zero values. There are many different regularizing prior distributions, some of which are analogous to specific frequentist methods.…”

Section: Bayesian Estimationmentioning

confidence: 99%

“…Two commonly used Bayesian probability intervals are the credible interval and the highest posterior density interval. 21 The credible interval (CI) is the Bayesian counterpart of a confidence interval, and it is obtained by taking the 2.5% and 97.5% quantiles of the posterior distribution. The highest posterior density interval (HDPI) is the narrowest possible interval that contains 95% of the probability mass.…”

Section: Bayesian Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…One can use probability intervals to determine which population effects are likely non‐zero; for example, by selecting moderators whose 95% interval excludes zero. Two commonly used Bayesian probability intervals are the credible interval and the highest posterior density interval 21 . The credible interval (CI) is the Bayesian counterpart of a confidence interval, and it is obtained by taking the 2.5% and 97.5% quantiles of the posterior distribution.…”

Section: Introductionmentioning

confidence: 99%

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Selecting relevant moderators with Bayesian regularized meta‐regression

Lissa

Erp

Clapper

2023

Research Synthesis Methods

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When meta-analyzing heterogeneous bodies of literature, meta-regression can be used to account for potentially relevant between-studies differences. A key challenge is that the number of candidate moderators is often high relative to the number of studies. This introduces risks of overfitting, spurious results, and model non-convergence. To overcome these challenges, we introduce Bayesian Regularized Meta-Analysis (BRMA), which selects relevant moderators from a larger set of candidates by shrinking small regression coefficients towards zero with regularizing (LASSO or horseshoe) priors. This method is suitable when there are many potential moderators, but it is not known beforehand which of them are relevant. A simulation study compared BRMA against state-of-the-art random effects meta-regression using restricted maximum likelihood (RMA). Results indicated that BRMA outperformed RMA on three metrics: BRMA had superior predictive performance, which means that the results generalized better; BRMA was better at rejecting irrelevant moderators, and worse at detecting true effects of relevant moderators, while the overall proportion of Type I and Type II errors was equivalent to RMA. BRMA regression coefficients were slightly biased towards zero (by design), but its residual heterogeneity estimates were less biased than those of RMA. BRMA performed well with as few as 20 studies, suggesting its suitability as a small sample solution. We present free open source software implementations in the R-package pema (for penalized meta-analysis) and in the stand-alone statistical program JASP. An applied example demonstrates the use of the R-package.

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Section: Bayesian Estimationmentioning

confidence: 99%

Section: Bayesian Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Selecting relevant moderators with Bayesian regularized meta‐regression

Lissa

Erp

Clapper

2023

Research Synthesis Methods

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“…where the degrees-of-freedom parameter, ν, is fixed to 2 as there are insufficient extreme data to estimate it (McElreath, 2020). Mean growth, µ mipq , is positive-valued and a function of both intrinsic and extrinsic factors.…”

Section: Statistical Modelmentioning

confidence: 99%

Biotic interactions among temperate rainforest trees are non-additive and environmentally dependent

Lai

Bellingham²,

McCarthy

et al. 2023

Preprint

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1. Species performance in the realised niche is jointly shaped by both abiotic and biotic processes. Moreover, interactions between and within abiotic and biotic processes generate non-additivities, resulting in density dependence that varies in strength or even direction across environments. If ignored, these non-additivities can lead to inaccurate predictions of species responses to changes in environment and community composition. 2. There are increasing empirical efforts to test the constancy of pairwise biotic interactions along environmental and compositional gradients, but rarely along both. We address this gap using nationwide forest inventory data that span broad ambient temperature and moisture gradients throughout New Zealand. 3. We analysed tree diameter growth of six focal tree species as a function of neighbour densities and climate, while accounting for potential abiotic and biotic non-additivities arising from neighbour × climate and neighbour × neighbour statistical interactions, respectively. We kept the large number of parameters manageable using Bayesian shrinkage priors and interpretable using average predictive comparisons. 4. We found that the most complex model—featuring biotic interactions that changed with climate and higher-order interactions with intermediary species—had the highest predictive accuracy of tree diameter growth. Compared to climate, biotic interactions typically had stronger effects on tree diameter growth, especially when they were subjected to non-additivities from local climate and the density of a third species. Most non-additivities tended to weakly exacerbate pairwise competition, whereas the few strong non-additivities tended to alleviate pairwise competition or even produce pairwise facilitation. 5. Synthesis: Our study highlights the importance of the interplay between abiotic and biotic processes when predicting how biotic interactions may structure communities under global change. When quantifying the relative importance of biotic and abiotic processes on species performance, we show that the conclusion varies depending on whether we are looking at direct or indirect effects. With accumulating evidence of non-additive biotic interactions, the next crucial step is to uncover their underlying mechanisms.

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Risk of Depression in the Adolescent and Adult Offspring of Mothers With Perinatal Depression

et al. 2020

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IMPORTANCE Maternal depression during pregnancy is associated with emotional and behavioral difficulties of offspring during childhood that can increase the risk of depression in adolescence and adulthood. OBJECTIVE To investigate the association between perinatal maternal depression and an increased long-term risk of depression in their adolescent and adult offspring. DATA SOURCES A systematic search of the electronic databases of PubMed and PsycINFO was conducted from May 2019 to June 2019. STUDY SELECTION A total of 6309 articles were identified, of which 88 articles were extracted for full-text review by 2 reviewers. Only articles reporting data from prospective longitudinal studies that assessed maternal depression during antenatal and/or postnatal periods and resulting offspring 12 years or older with measures of established psychometric properties were included. Exclusion criteria consisted of all other study designs, mothers with other medical and psychiatric comorbidities, and offspring younger than 12 years. DATA EXTRACTION AND SYNTHESIS Data were extracted by 2 independent reviewers, and discrepancies were mediated by an expert third reviewer. Meta-analysis was performed using Bayesian statistical inference and reported using Meta-analysis of Observational Studies in Epidemiology (MOOSE) guideline. The association of depression timing with the sex of offspring was explored using metaregression. MAIN OUTCOMES AND MEASURES Offspring depression was evaluated using standardized depression scales or clinical interviews. RESULTS Six studies with a total of 15 584 mother-child dyads were included in the meta-analysis, which found the offspring of mothers who experienced perinatal depression to have increased odds of depression (odds ratio [OR], 1.70; 95% credible interval [CrI], 1.60-2.65; posterior probability [PP] [OR >1], 98.6%). Although metaregression found no evidence for an overall association between perinatal depression timing and offspring depression (antenatal vs postnatal, PP [OR >1] = 53.8%), subgroup analyses showed slightly higher pooled odds for the antenatal studies (OR, 1.78; 95% CrI, 0.93-3.33; PP [OR >1] = 96.2%) than for the postnatal studies (OR, 1.66; 95% CrI, 0.65-3.84; PP [OR >1] = 88.0%). Female adolescent offspring recorded higher rates of depression in metaregression analyses, such that a 1% increase in the percentage of female (relative to male) offspring was (continued)

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Statistical Rethinking: A Bayesian Course with Examples in R and Stan

Cited by 450 publications

References 0 publications

Selecting relevant moderators with Bayesian regularized meta‐regression

Selecting relevant moderators with Bayesian regularized meta‐regression

Biotic interactions among temperate rainforest trees are non-additive and environmentally dependent

Risk of Depression in the Adolescent and Adult Offspring of Mothers With Perinatal Depression

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