Marginal and conditional posterior predictive p-values in Bayesian SEM

The posterior predictive p-value (ppp-value) is currently the primary measure of fit for Bayesian SEM. It is a measure of discrepancy between observed data and a posited model, comparing an observed likelihood ratio test (LRT) statistic to the posterior distribution of LRT statistics under a fitted model. However, the LRT statistic requires a likelihood, and multiple likelihoods are available for a given SEM: we can use a marginal likelihood that integrates out the latent variable(s), or we can use a conditional likelihood that conditions on the latent variable(s). A ppp-value based on conditional likelihoods is unexplored in the SEM literature, so the goal of this project is to study its performance alongside the marginal ppp-value. We present comparisons of the marginal and conditional ppp-values using real and simulated data, leading to recommendations on uses of the metrics in practice.

Structured Output Learning with Conditional Generative Flows

Traditional structured prediction models try to learn the conditional likelihood, i.e., p(y|x), to capture the relationship between the structured output y and the input features x. For many models, computing the likelihood is intractable. These models are therefore hard to train, requiring the use of surrogate objectives or variational inference to approximate likelihood. In this paper, we propose conditional Glow (c-Glow), a conditional generative flow for structured output learning. C-Glow benefits from the ability of flow-based models to compute p(y|x exactly and efficiently. Learning with c-Glow does not require a surrogate objective or performing inference during training. Once trained, we can directly and efficiently generate conditional samples. We develop a sample-based prediction method, which can use this advantage to do efficient and effective inference. In our experiments, we test c-Glow on five different tasks. C-Glow outperforms the state-of-the-art baselines in some tasks and predicts comparable outputs in the other tasks. The results show that c-Glow is versatile and is applicable to many different structured prediction problems.

Weak-Instrument Robust Tests in Two-Sample Summary-Data Mendelian Randomization

Mendelian randomization (MR) is a popular method in genetic epidemiology to estimate the effect of an exposure on an outcome using genetic variants as instrumental variables (IV), with two-sample summary-data MR being the most popular due to privacy. Unfortunately, many MR methods for two-sample summary data are not robust to weak instruments, a common phenomena with genetic instruments; many of these methods are biased and no existing MR method has Type I error control under weak instruments. In this work, we propose test statistics that are robust to weak instruments by extending Anderson-Rubin, Kleibergen, and conditional likelihood ratio tests in econometrics to the two-sample summary data setting. We conclude with a simulation and an empirical study and show that the proposed tests control size and have better power than current methods.

A Bayesian Hydrometeor Classification Algorithm for C-Band Polarimetric Radar

A hydrometeor classification algorithm is developed by applying Bayes’ theorem to C-band polarimetric weather radar measurements. The Bayesian hydrometeor classification algorithm (BHCA) includes eight hydrometeor types: hail, rain, graupel, dry snow, wet snow, crystal, biological scatterers (BS) and ground clutter (GC). The conditional likelihood probability distribution functions (PDFs) for each hydrometeor type are constructed with training data from radar observations. The prior PDFs include not only temperature information but also background information about occurrence frequency of hydrometeor types at each altitude, which is incorporated by a hydrometeor classification algorithm for the first time. The BHCA is evaluated by comparing with the Marzano-Bayesian hydrometeor classification algorithm (MBHC) and NCAR fuzzy logic classifier (NFLC). Results show that wet snow is largely missed in MBHC, while crystals are not adequately identified by NFLC. This may be due to the inappropriate conditional likelihood PDFs or membership functions. The prior PDFs in the MBHC may cause unexpected hail due to unreasonable variation above 0 °C. In addition, the prior PDFs of graupel and dry snow in the MBHC appear below −52 °C, which is not realistic. The BHCA proposed in this study overcomes these shortcomings in the prior PDFs and produces an overall reasonable classification product over the Yangtze-Huaihe River Basin (YHRB), Eastern China.