论文标题
顺序贝叶斯推断以进行因子分析
Sequential Bayesian Inference for Factor Analysis
论文作者
论文摘要
我们为通过各种数据类型（例如连续，二元和序数数据）观察到的因子分析模型开发了有效的贝叶斯顺序推理框架。在连续的数据案例中，有可能在潜在因素上边缘化，拟议的方法论量身定制了Chopin（2002）的迭代批次重要性采样（IBIS）来处理此类模型，我们结合了汉密尔顿Markov Chain Chain Monte Carlo。对于二进制和序数数据，我们开发了一种有效的IBIS方案来处理参数和潜在因素，并结合拉普拉斯或变异贝叶斯近似值。该方法可用于通过贝叶斯因素进行顺序假设检验的背景，该假设检验与传统的无原假设检验相比具有优势。此外，即使在非顺序的情况下，开发的顺序框架也可以通过一口气提供后验分布，模型证据和评分规则（在孕前框架下），并通过提供更强大的替代计算方案来马可夫链Carlo，从而在有问题的目标分布中有用。
We develop an efficient Bayesian sequential inference framework for factor analysis models observed via various data types, such as continuous, binary and ordinal data. In the continuous data case, where it is possible to marginalise over the latent factors, the proposed methodology tailors the Iterated Batch Importance Sampling (IBIS) of Chopin (2002) to handle such models and we incorporate Hamiltonian Markov Chain Monte Carlo. For binary and ordinal data, we develop an efficient IBIS scheme to handle the parameter and latent factors, combining with Laplace or Variational Bayes approximations. The methodology can be used in the context of sequential hypothesis testing via Bayes factors, which are known to have advantages over traditional null hypothesis testing. Moreover, the developed sequential framework offers multiple benefits even in non-sequential cases, by providing posterior distribution, model evidence and scoring rules (under the prequential framework) in one go, and by offering a more robust alternative computational scheme to Markov Chain Monte Carlo that can be useful in problematic target distributions.
