Related papers: Two Modeling Strategies for Empirical Bayes Estima…
{\bf Abstract} Consider a Non-Parametric Empirical Bayes (NPEB) setup. We observe $Y_i, \sim f(y|\theta_i)$, $\theta_i \in \Theta$ independent, where $\theta_i \sim G$ are independent $i=1,...,n$. The mixing distribution $G$ is unknown $G…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and…
We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function in combining information from multiple sources to improve traditional survey estimates of finite population…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…
We provide a brief overview of both Bayes and classical model selection. We argue tentatively that model selection has at least two major goals, that of finding the correct model or predicting well, and that in general both these goals may…
A general challenge in statistics is prediction in the presence of multiple candidate models or learning algorithms. Model aggregation tries to combine all predictive distributions from individual models, which is more stable and flexible…
The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…
Parametric empirical Bayes (EB) estimators have been widely used in variety of fields including small area estimation, disease mapping. Since EB estimator is constructed by plugging in the estimator of parameters in prior distributions, it…
Generative Bayesian Computation (GBC) methods are developed for Casual Inference. Generative methods are simulation-based methods that use a large training dataset to represent posterior distributions as a map (a.k.a. optimal transport) to…
Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…
Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and…
Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
A two-stage normal hierarchical model called the Fay--Herriot model and the empirical Bayes estimator are widely used to provide indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes…
The methods for parameter estimation under assumption of agreement between observation and model are reviewed. The distribution parameters are obtained for one set of experimental data by using different estimation methods under assumption…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
We explore the performance of sample average approximation in comparison with several other methods for stochastic optimization when there is information available on the underlying true probability distribution. The methods we evaluate are…
Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are…
Motivated by the proliferation of observational datasets and the need to integrate non-randomized evidence with randomized controlled trials, causal inference researchers have recently proposed several new methodologies for combining biased…