通过伪边际方法分析符号数据
Analysing symbolic data by pseudo-marginal methods
AI总结：
本文提出基于伪边际MCMC的贝叶斯框架，解决符号数据推断中积分不可行和参数估计偏置问题，通过路径采样和泊松估计等方法提升计算效率。
摘要：
符号数据分析（SDA）将大规模个体数据汇总为少量分布摘要，如随机矩形或直方图，以替代原始数据进行推断，从而获得计算优势但损失部分信息。在基于似然的SDA中，似然函数由包含大指数的积分定义，限制了其在典型模型中的实用性，因为该积分无法以闭式形式表达。此外，似然函数在某些情况下会导致参数估计偏置。本文在这些设定下开发了SDA方法的贝叶斯框架，利用伪边际MCMC方法解决积分不可行和参数估计偏置问题。我们开发了基于路径采样和泊松估计的精确但计算成本高的方法，以及基于泰勒展开的快速但近似的方法。通过模拟和实际数据示例，我们展示了所开发方法的性能，证明与全数据分析相比，计算时间大幅减少，仅损失少量信息。
英文摘要：
Symbolic data analysis (SDA) aggregates large individual-level datasets into a small number of distributional summaries, such as random rectangles or random histograms. The inference is carried out using these summaries in place of the original dataset, resulting in computational gains at the loss of some information. In likelihood-based SDA, the likelihood function is characterised by an integral with a large exponent, which limits the method's utility as for typical models the integral is unavailable in closed form. In addition, the likelihood function is known to produce biased parameter estimates in some circumstances. Our article develops a Bayesian framework for SDA methods in these settings that resolves the issues resulting from integral intractability and biased parameter estimation using pseudo-marginal Markov chain Monte Carlo methods. We develop an exact but computationally expensive method based on path sampling and the Poisson estimator, and a much faster, but approximate, method based on a Taylor expansion. Through simulation and real-data examples we demonstrate the performance of the developed methods, showing large reductions in computation time compared to the full-data analysis, with only a small loss of information.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
