Related papers: Targeting functional parameters with semiparametri…
In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…
Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…
In this review we cover the basics of efficient nonparametric parameter estimation (also called functional estimation), with a focus on parameters that arise in causal inference problems. We review both efficiency bounds (i.e., what is the…
The validity of two-step or plug-in inference methods is questioned in the Bayesian framework. We study semi-parametric models where the plug-in of a non-parametrically modelled nuisance component is used. We show that when the nuisance and…
Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…
We propose a Bayesian nonparametric (BNP) approach to causal inference using observational data consisting of outcome, treatment, and a set of confounders. The conditional distribution of the outcome given treatment and confounders is…
We consider constructing model selection criteria for evaluating nonlinear mixed effects models via basis expansions. Mean functions and random functions in the mixed effects model are expressed by basis expansions, then they are estimated…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…
We consider debiased inference on finite-dimensional functionals of infinite-dimensional least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not…
This paper introduces a probabilistic framework to estimate parameters of an acquisition function given observed human behavior that can be modeled as a collection of sample paths from a Bayesian optimization procedure. The methodology…
Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…
Many statistical problems in causal inference involve a probability distribution other than the one from which data are actually observed; as an additional complication, the object of interest is often a marginal quantity of this other…
Approximate Bayesian inference typically revolves around computing the posterior parameter distribution. In practice, however, the main object of interest is often a model's predictions rather than its parameters. In this work, we propose…
Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, which Arnold and Ng (2011) extend to 5 and 8 parameter models. The 3 parameter model…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
In causal estimation problems, the parameter of interest is often only partially identified, implying that the parameter cannot be recovered exactly, even with infinite data. Here, we study Bayesian inference for partially identified…
Using nonparametric methods has been increasingly explored in Bayesian hierarchical modeling as a way to increase model flexibility. Although the field shows a lot of promise, inference in many models, including Hierachical Dirichlet…
Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…