On the adequacy of variational lower bound functions for likelihood‐based inference in Markovian models with missing values
On the adequacy of variational lower bound functions for likelihood‐based inference in Markovian models with missing values
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关于具有缺失值的马尔可夫模型中基于似然性的推理的变分下界函数的充分性
DOI：
10.1111/1467-9868.00350
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
D. Titterington
中科院分区：
文献类型：
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作者：
P. Hall;Keith Humphreys;D. Titterington
总结。已有变分方法被提出用于获得丢失数据问题中对数似然的确定性下界，但很少有形式上的证明或对作为推理工具的下界曲面的价值的调查。在一般的马氏背景下，我们给出了变分逼近的估计量与极大似然估计量渐近等价的充分条件，并以一阶有缺失值的自回归模型为例，实证地证明了在非渐近情形下，下界曲面的形状可以非常类似于真对数似然。
Summary. Variational methods have been proposed for obtaining deterministic lower bounds for log‐likelihoods within missing data problems, but with little formal justification or investigation of the worth of the lower bound surfaces as tools for inference. We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for the simple example of a first‐order autoregressive model with missing values, that the lower bound surface can be very similar in shape to the true log‐likelihood in non‐asymptotic situations.