On the computational complexity of MCMC-based estimators in large samples
大样本下基于 MCMC 的估计量的计算复杂度AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要讨论通用贝叶斯与准贝叶斯计算复杂度，未明确对应结构估计、因子模型或其他所列应用方向。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
大样本下基于 MCMC 的估计量的计算复杂度
- 研究问题
- 当后验或准后验在大样本下趋近正态且参数维数增长时，Metropolis 随机游走估计能否获得可控的计算复杂度？
- 方法与思路
- 作者利用后验正态近似所需条件，限制目标函数偏离连续性与对数凹性的程度，据此建立随机游走算法的复杂度界。
- 材料陈述的贡献
- 摘要称运行时间在概率意义下受参数维数的多项式界控制，并讨论高斯随机游走、指数族和递增维数的 Z 估计。
- 阅读关注点
- 应核对正态近似与维数增长条件、初始分布和预热成本，以及运行时间对应的误差标准及目标函数允许的不规则程度。
- 阅读边界
- 依据稿件版本未注明的 OpenAlex 索引摘要；复杂度保证有条件。原文中的“d2”排版不清，具体阶数需查阅原 PDF。
原文摘要
In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace–Bernstein–Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a normal density. Using the conditions required for the central limit theorem to hold, we establish polynomial bounds on the computational complexity of general Metropolis random walks methods in large samples. Our analysis covers cases where the underlying log-likelihood or extremum criterion function is possibly nonconcave, discontinuous, and with increasing parameter dimension. However, the central limit theorem restricts the deviations from continuity and log-concavity of the log-likelihood or extremum criterion function in a very specific manner. Under minimal assumptions required for the central limit theorem to hold under the increasing parameter dimension, we show that the Metropolis algorithm is theoretically efficient even for the canonical Gaussian walk which is studied in detail. Specifically, we show that the running time of the algorithm in large samples is bounded in probability by a polynomial in the parameter dimension d and, in particular, is of stochastic order d2 in the leading cases after the burn-in period. We then give applications to exponential families, curved exponential families and Z-estimation of increasing dimension.