Christian P. Robert, Kerrie L. Mengersen, Carla Chen
The new perspectives on ABC and Bayesian model criticisms presented in Ratmann et al.(2009) are challenging standard approaches to Bayesian model choice. We discuss here some issues arising from the authors' approach, including prior influence, model assessment and criticism, and the meaning of error in ABC.
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We study the signal detection problem in high dimensional noise data (possibly) containing rare and weak signals. Log-likelihood ratio (LLR) tests depend on unknown parameters, but they are needed to judge the quality of detection tests since they determine the detection regions. The popular Tukey's higher criticism (HC) test was shown to achieve the same completely detectable region as the LLR test does for different (mainly) parametric models. We present a novel technique to prove this result for very general signal models, including even nonparametric $p$-value models. Moreover, we address …
We propose a framework for the statistical evaluation of variational auto-encoders (VAEs) and test two instances of this framework in the context of modelling images of handwritten digits and a corpus of English text. Our take on evaluation is based on the idea of statistical model criticism, popular in Bayesian data analysis, whereby a statistical model is evaluated in terms of its ability to reproduce statistics of an unknown data generating process from which we can obtain samples. A VAE learns not one, but two joint distributions over a shared sample space, each exploiting a choice of fact…
In their letter to PNAS and a comprehensive set of notes on arXiv [arXiv:0909.5673v2], Christian Robert, Kerrie Mengersen and Carla Chen (RMC) represent our approach to model criticism in situations when the likelihood cannot be computed as a way to "contrast several models with each other". In addition, RMC argue that model assessment with Approximate Bayesian Computation under model uncertainty (ABCmu) is unduly challenging and question its Bayesian foundations. We disagree, and clarify that ABCmu is a probabilistically sound and powerful too for criticizing a model against aspects of the ob…
The Poisson distribution is often used as a standard model for count data. Quite often, however, such data sets are not well fit by a Poisson model because they have more zeros than are compatible with this model. For these situations, a zero-inflated Poisson (ZIP) distribution is often proposed. This article addresses testing a Poisson versus a ZIP model, using Bayesian methodology based on suitable objective priors. Specific choices of objective priors are justified and their properties investigated. The methodology is extended to include covariates in regression models. Several applications…
Computational convenience has led to widespread use of Bayesian inference with vague or flat priors to analyze state-space models in ecology. Vague priors are claimed to be objective and to let the data speak. Neither of these claims is valid. Statisticians have criticized the use of vague priors from philosophical to computational to pragmatic reasons. Ecologists, however, dismiss such criticisms as empty philosophical wonderings with no practical implications. We illustrate that use of vague priors in population viability analysis and occupancy models can have significant impact on the analy…
In model-based-clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al (2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with $K$ components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than $K$ with high probability. The number of cluster is then inferred a posteriori from the data. The present paper makes the following contributions in the context of sparse finite mixture modelling. Fi…
A frequent and well-founded criticism of the maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimates of a continuous parameter γtaking values in a differentiable manifold Γis that they are not invariant to arbitrary ``reparameterizations'' of Γ. This paper clarifies the issues surrounding this problem, by pointing out the difference between coordinate invariance, which is a sine qua non for a mathematically well-defined problem, and diffeomorphism invariance, which is a substantial issue, and then provides a solution. We first show that the presence of a metric structure on …
Causation versus Prediction: Comparing Causal Discovery and Inference with Artificial Neural Networks in Travel Mode Choice Modeling
本研究在芝加哥三个社区比较了因果模型与人工神经网络预测模型在出行方式选择建模中的表现，发现因果建模虽少被探索但具变革潜力，两种方法各有其用。
In Templeton (2010), the Approximate Bayesian Computation (ABC) algorithm (see, e.g., Pritchard et al., 1999, Beaumont et al., 2002, Marjoram et al., 2003, Ratmann et al., 2009) is criticised on mathematical and logical grounds: "the [Bayesian] inference is mathematically incorrect and formally illogical". Since those criticisms turn out to be bearing on Bayesian foundations rather than on the computational methodology they are primarily directed at, we endeavour to point out in this note the statistical errors and inconsistencies in Templeton (2010), refering to Beaumont et al. (2010) for a r…
Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a dependence structure from many, the use of standard model choice methods is hampered by the unavailability of the normalising constant in the Gibbs likelihood. In particular, from a Bayesian perspective, the computation of the posterior probabilities of the models under competition requires special likelihood-free simulation techniques like the Approximate Baye…
When Sample-Splitting Choices Matter in TMLE and AIPW: Cross-Fitting, Targeting, and Repetition
该研究探讨TMLE与AIPW中样本拆分选择的影响，通过模拟与真实数据分析发现交叉拟合干扰项、评估截断及AIPW-TMLE敏感性可提升估计性能。
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