[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125529-en":3,"doc-seo-125529-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125529,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Detecting and diagnosing prior and likelihood sensitivity with power-scaling","Determining how sensitive Bayesian posteriors are to perturbations of the prior and likelihood is central to reliable Bayesian inference. The work introduces a practical, computationally efficient sensitivity analysis method using power-scaling perturbations applied to either the prior or likelihood. A diagnostic is derived to reveal prior-data conflict or likelihood noninformativity. The approach integrates into existing Bayesian workflows with minimal model-builder effort and is implemented in the R package priorsense, demonstrated on real-data case studies.","View metadata, citation and similar [papers at ](papers at core.ac.uk)[core.ac.uk](papers at core.ac.uk) brought to you by CORE  \n[provided by](provided by arXiv.org)[ arXiv.org](provided by arXiv.org) e-Print Archive  \narXiv :2 107 . 14054v1 [ stat .ME] 29 Jul 2021  \nDetecting and diagnosing prior and likelihood sensitivity with power-scaling  \nNoa Kallioinen 1 , Topi Paananen 1 , Paul-Christian Bürkner2 , and Aki  \nVehtari 1  \n1 Department of Computer Science, Aalto University, Espoo, Finland  \n2 Cluster of Excellence SimTech, University of Stuttgart, Stuttgart,  \nGermany  \nJuly 30, 2021  \nDetermining the sensitivity of the posterior to perturbations of the prior and likelihood isan important part of the Bayesian workflow. We introduce a practical and computationally efficient sensitivity analysis approach that is applicable to a wide range of models, based on power-scaling perturbations. We suggest a diagnostic based on this that can indicate the presence of prior-data conflict or likelihood noninformativity. The approach can be easily included in Bayesian workflows with minimal work by the model builder. We present the implementation of the approach in our new R package priorsense and demonstrate the workflow on case studies of real data.  \n1 Introduction  \nBayesian inference is characterised by the derivation of a posterior from a prior and a likelihood. As the posterior is dependent on the specification of these two components, investigating the sensitivity of the posterior to perturbations of the prior and likelihood (sensitivity analysis) is a critical step in the Bayesian workflow (Depaoli et al., 2020; Gelman et al., 2020; Lopes & Tobias, 2011) . Along with indicating the robustness of an inference in general, sensitivity is related to issues of prior-data conflict (Al Labadi & Evans, 2017; Evans & Moshonov, 2006; Reimherr et al., 2020) and likelihood noninformativity (Gelmanet al., 2017; Poirier, 1998; Roos et al., 2015) .  \nHistorically, sensitivity analysis has been an important topic in Bayesian methods research (e.g. Berger, 1990; Berger et al., 1994; Canavos, 1975; Hill & Spall, 1994; Skene et al., 1986) . However, the amount of research on the topic has diminished (Berger et al., 2000; Watson & Holmes, 2016) and results from sensitivity analyses are seldom reported in empirical studies employing Bayesian methods (van de Schoot et al., 2017) . We suggest that one of the main reasons for this is the lack of a sensitivity analysis approach that is easily incorporated into existing modelling workflows.  \nModern modelling workflows (e.g. those described in Gelman et al., 2020; Grinsztajn et al., 2021; Schad et al., 2020) generally involve specifying a model in a probabilistic programming language (such as Stan; Stan Development Team, 2021) and using Markov chain Monte Carlo algorithms to approximate the posterior via posterior draws. Refitting a model multiple times this way with different perturbations to the prior or likelihood can require substantial amounts of both user and computing time (Jacobi et al., 2018; Pérez et al., 2006) . The use of computationally more efficient methods can reduce the computation time, but existing methods have limitations as they are specific to particular models (Hunanyan & Roos, 2020) or inference mechanisms (Roos et al. , 2015), require manual specification of perturbations (McCartan, 2021), require substantial or technically complex changes to the model code that hinder widespread use (Giordano et al., 2018; Jacobi et al., 2018), or may still require a substantial amount of computation time (Bornn et al., 2010; Ho, 2020) .  \n-5 0 5 10 15 -5 0 5 10 15 -5 0 5 10 15  \nθ  \nFigure 1 : Example of power-scaling the prior. In this case the prior is normal(0, 2.5) and the likelihood is equivalent to normal(10, 1) . Scaling the prior by raising it to different α values (in this case 0.5 and 2.0)  \nchanges the posterior (shaded for emphasis), indicating prior sensitivity.  \nIn this work, we present an appro","cbCaiq221mLselqv","https://ap.wps.com/l/cbCaiq221mLselqv","pdf",811885,1,21,"English","en",105,"# Introduction\n## Bayesian sensitivity analysis and motivation\n## Limitations of existing approaches\n## Power-scaling sensitivity analysis approach\n## Importance sampling and automated diagnostics\n## Proposed workflow and figures/tables","[{\"question\":\"What is the main goal of the proposed method?\",\"answer\":\"To provide a computationally efficient sensitivity analysis that diagnoses how posteriors change when the prior or likelihood is power-scaled.\"},{\"question\":\"How does power-scaling work in this approach?\",\"answer\":\"The method raises either the prior or the likelihood to an exponent α\\u003e0, producing perturbed posteriors whose changes can be quantified and visualized.\"},{\"question\":\"What does the diagnostic indicate?\",\"answer\":\"It can indicate the presence of prior-data conflict or likelihood noninformativity, based on the observed pattern of prior and likelihood sensitivity.\"}]","Detecting and diagnosing prior and likelihood sensitivity with power-scaling | 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is the main goal of the proposed method?","Question",{"text":75,"@type":76},"To provide a computationally efficient sensitivity analysis that diagnoses how posteriors change when the prior or likelihood is power-scaled.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does power-scaling work in this approach?",{"text":80,"@type":76},"The method raises either the prior or the likelihood to an exponent α>0, producing perturbed posteriors whose changes can be quantified and visualized.",{"name":82,"@type":73,"acceptedAnswer":83},"What does the diagnostic indicate?",{"text":84,"@type":76},"It can indicate the presence of prior-data conflict or likelihood noninformativity, based on the observed pattern of prior and likelihood 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