马尔可夫链过程的最大熵设计

IF 1.6 4区数学 Q2 SOCIAL SCIENCES, MATHEMATICAL METHODS

Journal of Survey Statistics and Methodology Pub Date : 2023-06-14 DOI:10.1093/jssam/smad010

Yves Tillé, Bardia Panahbehagh

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引用次数: 0

摘要

摘要本文研究了一种利用马尔可夫链实现最大熵设计的方法。这种设计，也被称为条件泊松抽样设计，很难实现。我们首先提出了一种计算条件泊松抽样相关权值的新方法。然后，我们研究了一种非常简单的单位随机交换方法，它允许从一个样本切换到另一个样本。该交换系统定义了一个不可约的非周期马尔可夫链，其ME设计为平稳分布。该设计可以在不列举所有可能的样本的情况下实现。通过多次重复交换过程，可以选择符合设计的样品。该方法实现简单，并对其收敛速度进行了理论和仿真研究，结果令人满意。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Maximum Entropy Design by a Markov Chain Process

Abstract In this article, we study an implementation of maximum entropy (ME) design utilizing a Markov chain. This design, which is also called the conditional Poisson sampling design, is difficult to implement. We first present a new method for calculating the weights associated with conditional Poisson sampling. Then, we study a very simple method of random exchanges of units, which allows switching from one sample to another. This exchange system defines an irreducible and aperiodic Markov chain whose ME design is the stationary distribution. The design can be implemented without enumerating all possible samples. By repeating the exchange process a large number of times, it is possible to select a sample that respects the design. The process is simple to implement, and its convergence rate has been investigated theoretically and by simulation, which led to promising results.

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来源期刊

Journal of Survey Statistics and Methodology Multiple-

CiteScore

4.30

自引率

9.50%

发文量

期刊介绍： The Journal of Survey Statistics and Methodology, sponsored by AAPOR and the American Statistical Association, began publishing in 2013. Its objective is to publish cutting edge scholarly articles on statistical and methodological issues for sample surveys, censuses, administrative record systems, and other related data. It aims to be the flagship journal for research on survey statistics and methodology. Topics of interest include survey sample design, statistical inference, nonresponse, measurement error, the effects of modes of data collection, paradata and responsive survey design, combining data from multiple sources, record linkage, disclosure limitation, and other issues in survey statistics and methodology. The journal publishes both theoretical and applied papers, provided the theory is motivated by an important applied problem and the applied papers report on research that contributes generalizable knowledge to the field. Review papers are also welcomed. Papers on a broad range of surveys are encouraged, including (but not limited to) surveys concerning business, economics, marketing research, social science, environment, epidemiology, biostatistics and official statistics. The journal has three sections. The Survey Statistics section presents papers on innovative sampling procedures, imputation, weighting, measures of uncertainty, small area inference, new methods of analysis, and other statistical issues related to surveys. The Survey Methodology section presents papers that focus on methodological research, including methodological experiments, methods of data collection and use of paradata. The Applications section contains papers involving innovative applications of methods and providing practical contributions and guidance, and/or significant new findings.