Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Asymptotic Normality, Concentration, and Coverage of Generalized Posteriors
Authors: Jeffrey W. Miller
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this article, we provide sufficient conditions under which generalized posteriors exhibit concentration, asymptotic normality (Bernstein von Mises), an asymptotically correct Laplace approximation, and asymptotically correct frequentist coverage. We apply our results in detail to generalized posteriors for a wide array of generalized likelihoods, including pseudolikelihoods in general, the Gaussian Markov random field pseudolikelihood, the fully observed Boltzmann machine pseudolikelihood, the Ising model pseudolikelihood, the Cox proportional hazards partial likelihood, and a median-based likelihood for robust inference of location. Further, we show how our results can be used to easily establish the asymptotics of standard posteriors for exponential families and generalized linear models. We make no assumption of model correctness so that our results apply with or without misspecification. |
| Researcher Affiliation | Academia | Jeffrey W. Miller EMAIL Department of Biostatistics Harvard T.H. Chan School of Public Health Boston, MA 02115, USA |
| Pseudocode | No | The paper does not contain any sections or figures explicitly labeled as 'Pseudocode' or 'Algorithm'. The content consists of theoretical results, theorems, lemmas, and proofs. |
| Open Source Code | No | The paper does not mention the release of any source code, nor does it provide links to code repositories. The focus of the paper is theoretical. |
| Open Datasets | No | The paper focuses on theoretical models and their properties (e.g., exponential families, GLMs, Gaussian Markov random fields, Boltzmann machines, Ising model, Cox proportional hazards model). While it mentions 'data set Y n' within these theoretical contexts, it does not refer to any specific, publicly available datasets used for empirical evaluation. No links, DOIs, or citations to established public datasets are provided. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical experiments with datasets, thus there is no mention of dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is purely theoretical and does not describe any experiments that would require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe any computational implementations or experiments that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical, focusing on mathematical conditions and proofs. It does not describe any experimental setups, hyperparameters, or training configurations. |