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Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation.

ABSTRACT: Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a high-dimensional or otherwise computationally challenging nuisance parameter. The focus is on regression models and the key idea is to separate the likelihood into two components through a rotation. One component involves only the nuisance parameters, which can then be integrated out using a novel type of Gaussian approximation. We provide theory on approximation accuracy that holds for a broad class of forms of the nuisance component and priors. Applying our method to simulated and real data sets shows that it can outperform state-of-the-art posterior approximation approaches.

SUBMITTER: VAN DEN Boom W

PROVIDER: S-EPMC9216391 | biostudies-literature | 2021 Jun

REPOSITORIES: biostudies-literature

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Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation.

VAN DEN Boom W W Reeves G G Dunson D B DB

Biometrika 20200826 2

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a high-dimensional or otherwise computationally challenging nuisance parameter. The focus is on regression models and the key idea is to separate the likelihood into two components through a rotation. One component involves only the nuisance parameters, which can then ...[more]

PMID: 35747172

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Project description:BackgroundThe expected value of sample information (EVSI) measures the expected benefits that could be obtained by collecting additional data. Estimating EVSI using the traditional nested Monte Carlo method is computationally expensive, but the recently developed Gaussian approximation (GA) approach can efficiently estimate EVSI across different sample sizes. However, the conventional GA may result in biased EVSI estimates if the decision models are highly nonlinear. This bias may lead to suboptimal study designs when GA is used to optimize the value of different studies. Therefore, we extend the conventional GA approach to improve its performance for nonlinear decision models.MethodsOur method provides accurate EVSI estimates by approximating the conditional expectation of the benefit based on 2 steps. First, a Taylor series approximation is applied to estimate the conditional expectation of the benefit as a function of the conditional moments of the parameters of interest using a spline, which is fitted to the samples of the parameters and the corresponding benefits. Next, the conditional moments of parameters are approximated by the conventional GA and Fisher information. The proposed approach is applied to several data collection exercises involving non-Gaussian parameters and nonlinear decision models. Its performance is compared with the nested Monte Carlo method, the conventional GA approach, and the nonparametric regression-based method for EVSI calculation.ResultsThe proposed approach provides accurate EVSI estimates across different sample sizes when the parameters of interest are non-Gaussian and the decision models are nonlinear. The computational cost of the proposed method is similar to that of other novel methods.ConclusionsThe proposed approach can estimate EVSI across sample sizes accurately and efficiently, which may support researchers in determining an economically optimal study design using EVSI.HighlightsThe Gaussian approximation method efficiently estimates the expected value of sample information (EVSI) for clinical trials with varying sample sizes, but it may introduce bias when health economic models have a nonlinear structure.We introduce the spline-based Taylor series approximation method and combine it with the original Gaussian approximation to correct the nonlinearity-induced bias in EVSI estimation.Our approach can provide more precise EVSI estimates for complex decision models without sacrificing computational efficiency, which can enhance the resource allocation strategies from the cost-effective perspective.

Dataset Information

Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation.

Publications

Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation.

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