Related papers: Adjusted Bayesian inference for selected parameter…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…
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…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
Simultaneously performing variable selection and inference in high-dimensional models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of specific…
Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
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…
We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…