Sensitivity and identification quantification by a relative latent model complexity perturbation in Bayesian meta‐analysis

Roos, Małgorzata; Sona, Hunanyan,; Bakka, Haakon; Rue, Haåvard

doi:10.1002/bimj.202000193

Cited by 5 publications

(10 citation statements)

References 62 publications

(139 reference statements)

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“…Following Roos et al (2021), we consider the Bhattacharyya coefficient (BC) (Bhattacharyya, 1943) between two probability density functions, which is given by…”

Section: Affinity Measure Bhattacharyya Coefficientmentioning

confidence: 99%

“…Moreover, BC is 1 if and only if the two densities are equal and is 0 when the domains of the two densities have no overlap. BC has convenient numerical properties and is invariant under any one-to-one transformation (for example, logarithmic) (Jeffreys, 1961;Roos and Held, 2011;Roos et al, 2015Roos et al, , 2021. Furthermore, BC is directly connected to the Hellinger distance (H), by H 2 = 1 − BC.…”

Section: Affinity Measure Bhattacharyya Coefficientmentioning

confidence: 99%

“…where π N j is the density of a N (m j , s 2 j ) distribution with j = {1, w}. Following Roos et al (2021), we approximate the marginal posterior distribution π(ψ | y) for ψ ∈ {μ, τ, θ 1 , . .…”

Section: Affinity Measure Bhattacharyya Coefficientmentioning

confidence: 99%

“…Following Roos et al (2021), we define the TED(ψ) measure as the negative second derivative of the Bhattacharyya coefficient (BC) between the base and weighted posterior distributions for each parameter of the model. Here,…”

Section: Quantification Of the Total Empirical Determinacymentioning

confidence: 99%

“…We expect that likelihood weighting will affect both the location and the spread of the marginal posterior distributions. Because the method proposed by Roos et al (2021) quantifies the total impact of the scaling on the posteriors without focusing on location and spread, a refined method is needed. Ideally, such a refined method should quantify what proportion of the total impact of the data on the posterior affects the location and what proportion affects the spread.…”

Section: Introductionmentioning

confidence: 99%

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Quantification of Empirical Determinacy: The Impact of Likelihood Weighting on Posterior Location and Spread in Bayesian Meta-Analysis Estimated with JAGS and INLA

et al. 2023

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The popular Bayesian meta-analysis expressed by the normal-normal hierarchical model synthesizes knowledge from several studies and is highly relevant in practice. The normal-normal hierarchical model is the simplest Bayesian hierarchical model, but illustrates problems typical in more complex Bayesian hierarchical models. Until now, it has been unclear to what extent the data determines the marginal posterior distributions of the parameters in the normal-normal hierarchical model. To address this issue we computed the second derivative of the Bhattacharyya coefficient with respect to the weighted likelihood. This quantity, which we define as the total empirical determinacy (TED), can be written as the sum of two terms: the empirical determinacy of location (EDL), and the empirical determinacy of spread (EDS). We implemented this method in the R package ed4bhm and considered two case studies and one simulation study. We quantified TED, EDL and EDS under different modeling conditions such as model parametrization, the primary outcome, and the prior. This clarifies to what extent the location and spread of the marginal posterior distributions of the parameters are determined by the data. Although these investigations focused on Bayesian normal-normal hierarchical model, the method proposed is applicable more generally to complex Bayesian hierarchical models.

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“…Following Roos et al (2021), we consider the Bhattacharyya coefficient (BC) (Bhattacharyya, 1943) between two probability density functions, which is given by…”

Section: Affinity Measure Bhattacharyya Coefficientmentioning

confidence: 99%

Section: Affinity Measure Bhattacharyya Coefficientmentioning

confidence: 99%

Section: Affinity Measure Bhattacharyya Coefficientmentioning

confidence: 99%

Section: Quantification Of the Total Empirical Determinacymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantification of Empirical Determinacy: The Impact of Likelihood Weighting on Posterior Location and Spread in Bayesian Meta-Analysis Estimated with JAGS and INLA

et al. 2023

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Sensitivity and identification quantification by a relative latent model complexity perturbation in Bayesian meta‐analysis

et al. 2021

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Detecting and diagnosing prior and likelihood sensitivity with power-scaling

Kallioinen,

Paananen,

Bürkner

et al. 2023

Stat Comput

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Determining the sensitivity of the posterior to perturbations of the prior and likelihood is an important part of the Bayesian workflow. We introduce a practical and computationally efficient sensitivity analysis approach using importance sampling to estimate properties of posteriors resulting from power-scaling the prior or likelihood. On this basis, we suggest a diagnostic that can indicate the presence of prior-data conflict or likelihood noninformativity and discuss limitations to this power-scaling approach. The approach can be easily included in Bayesian workflows with minimal effort by the model builder and we present an implementation in our new R package . We further demonstrate the workflow on case studies of real data using models varying in complexity from simple linear models to Gaussian process models.

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Sensitivity and identification quantification by a relative latent model complexity perturbation in Bayesian meta‐analysis

Cited by 5 publications

References 62 publications

Quantification of Empirical Determinacy: The Impact of Likelihood Weighting on Posterior Location and Spread in Bayesian Meta-Analysis Estimated with JAGS and INLA

Quantification of Empirical Determinacy: The Impact of Likelihood Weighting on Posterior Location and Spread in Bayesian Meta-Analysis Estimated with JAGS and INLA

Sensitivity and identification quantification by a relative latent model complexity perturbation in Bayesian meta‐analysis

Detecting and diagnosing prior and likelihood sensitivity with power-scaling

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