More Like this

1. Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection

   https://doi.org/10.3390/w11081579  

   Elshall, Ahmed S.; Ye, Ming (August 2019, Water)

   Elshall, Ahmed; Ye, Ming (Ed.)

   Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection and model averaging purposes. For strict Bayesian computation, the theoretically unbiased Monte Carlo based numerical estimators are preferred over semi-analytical solutions. This study examines five BME numerical estimators and asks how accurate estimation of the BME is important for penalizing model complexity. The limiting cases for numerical BME estimators are the prior sampling arithmetic mean estimator (AM) and the posterior sampling harmonic mean (HM) estimator, which are straightforward to implement, yet they result in underestimation and overestimation, respectively. We also consider the path sampling methods of thermodynamic integration (TI) and steppingstone sampling (SS) that sample multiple intermediate distributions that link the prior and the posterior. Although TI and SS are theoretically unbiased estimators, they could have a bias in practice arising from numerical implementation. For example, sampling errors of some intermediate distributions can introduce bias. We propose a variant of SS, namely the multiple one-steppingstone sampling (MOSS) that is less sensitive to sampling errors. We evaluate these five estimators using a groundwater transport model selection problem. SS and MOSS give the least biased BME estimation at an efficient computational cost. If the estimated BME has a bias that covariates with the true BME, this would not be a problem because we are interested in BME ratios and not their absolute values. On the contrary, the results show that BME estimation bias can be a function of model complexity. Thus, biased BME estimation results in inaccurate penalization of more complex models, which changes the model ranking. This was less observed with SS and MOSS as with the three other methods. 

   more » « less
2. Multiple bias calibration for valid statistical inference under nonignorable nonresponse

   https://doi.org/10.1093/biomtc/ujaf044  

   Cho, Seonghun; Kim, Jae_Kwang; Qiu, Yumou (April 2025, Biometrics)

   ABSTRACT Valid statistical inference is notoriously challenging when the sample is subject to nonresponse bias. We approach this difficult problem by employing multiple candidate models for the propensity score (PS) function combined with empirical likelihood. By incorporating multiple working PS models into the internal bias calibration constraint in the empirical likelihood, the selection bias can be safely eliminated as long as the working PS models contain the true model and their expectations are equal to the true missing rate. The bias calibration constraint for the multiple PS models is called the multiple bias calibration. The study delves into the asymptotic properties of the proposed method and provides a comparative analysis through limited simulation studies against existing methods. To illustrate practical implementation, we present a real data analysis on body fat percentage using the National Health and Nutrition Examination Survey dataset. 

   more » « less
3. A Bias Bound Approach to Non-parametric Inference

   https://doi.org/10.1093/restud/rdz065  

   Schennach, Susanne M (January 2020, The Review of Economic Studies)

   Abstract The traditional approach to obtain valid confidence intervals for non-parametric quantities is to select a smoothing parameter such that the bias of the estimator is negligible relative to its standard deviation. While this approach is apparently simple, it has two drawbacks: first, the question of optimal bandwidth selection is no longer well-defined, as it is not clear what ratio of bias to standard deviation should be considered negligible. Second, since the bandwidth choice necessarily deviates from the optimal (mean squares-minimizing) bandwidth, such a confidence interval is very inefficient. To address these issues, we construct valid confidence intervals that account for the presence of a non-negligible bias and thus make it possible to perform inference with optimal mean squared error minimizing bandwidths. The key difficulty in achieving this involves finding a strict, yet feasible, bound on the bias of a non-parametric estimator. It is well-known that it is not possible to consistently estimate the pointwise bias of an optimal non-parametric estimator (for otherwise, one could subtract it and obtain a faster convergence rate violating Stone’s bounds on the optimal convergence rates). Nevertheless, we find that, under minimal primitive assumptions, it is possible to consistently estimate an upper bound on the magnitude of the bias, which is sufficient to deliver a valid confidence interval whose length decreases at the optimal rate and which does not contradict Stone’s results. 

   more » « less
4. Causal Inference with Noisy and Missing Covariates via Matrix Factorization

   Kallus, Nathan; Mao, Xiaojie; Madeleine, Udell (January 2018, Advances in neural information processing systems)

   Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce bias induced by measurement noise using a large number of noisy measurements of the underlying confounders. We propose the use of matrix factorization to infer the confounders from noisy covariates. This flexible and principled framework adapts to missing values, accommodates a wide variety of data types, and can enhance a wide variety of causal inference methods. We bound the error for the induced average treatment effect estimator and show it is consistent in a linear regression setting, using Exponential Family Matrix Completion preprocessing. We demonstrate the effectiveness of the proposed procedure in numerical experiments with both synthetic data and real clinical data. 

   more » « less
5. An Empirical Likelihood Approach to Reduce Selection Bias in Voluntary Samples

   https://doi.org/10.1177/00080683231186488  

   Kim, Jae Kwang; Morikawa, Kosuke (May 2023, Calcutta Statistical Association Bulletin)

   How to construct the pseudo-weights in voluntary samples is an important practical problem in survey sampling. The problem is quite challenging when the sampling mechanism for the voluntary sample is allowed to be non-ignorable. Under the assumption that the sample participation model is correctly specified, we can compute a consistent estimator of the model parameter and construct the propensity score estimator of the population mean. We propose using the empirical likelihood method to construct the final weights for voluntary samples by incorporating the bias calibration constraints and the benchmarking constraints. Linearization variance estimation of the proposed method is developed. A toy example is also presented to illustrate the idea and the computational details. A limited simulation study is also performed to evaluate the performance of the proposed methods. 

   more » « less