Related papers: Shrinkage through multiple identifiability
Causal inference has received great attention across different fields from economics, statistics, education, medicine, to machine learning. Within this area, inferring causal effects at individual level in observational studies has become…
We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct…
In this paper, we consider simultaneous estimation of Poisson parameters in situations where we can use side information in aggregated data. We use standardized squared error and entropy loss functions. Bayesian shrinkage estimators are…
A method for implicit variable selection in mixture of experts frameworks is proposed. We introduce a prior structure where information is taken from a set of independent covariates. Robust class membership predictors are identified using a…
In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and in particular consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
Regularization in fitting regression models has been a highly active topic of research in the past few decades, but most of the existing methods are designed for particular situations, e.g. for the case of a sparse coefficient vector. We…
Quantile regression is a powerful data analysis tool that accommodates heterogeneous covariate-response relationships. We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver…
Modelling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model, and thus to obtain better predictions about the behavior of the corresponding…
Inferring causal effects of treatments is a central goal in many disciplines. The potential outcomes framework is a main statistical approach to causal inference, in which a causal effect is defined as a comparison of the potential outcomes…
A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and…
Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only…
A common strategy for sparse linear regression is to introduce regularization, which eliminates irrelevant features by letting the corresponding weights be zeros. However, regularization often shrinks the estimator for relevant features,…
We provide identification results for a broad class of learning models in which continuous outcomes depend on three types of unobservables: known heterogeneity, initially unknown heterogeneity that may be revealed over time, and transitory…
Disentangled representations seek to recover latent factors of variation underlying observed data, yet their identifiability is still not fully understood. We introduce a unified framework in which disentanglement is achieved through…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…