Related papers: Mixed Beta Regression: A Bayesian Perspective
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…
The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be…
We outline a Bayesian model-averaged meta-analysis for standardized mean differences in order to quantify evidence for both treatment effectiveness $\delta$ and across-study heterogeneity $\tau$. We construct four competing models by…
Model-based Bayesian reinforcement learning has generated significant interest in the AI community as it provides an elegant solution to the optimal exploration-exploitation tradeoff in classical reinforcement learning. Unfortunately, the…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…
The beta distribution is the best-known distribution for modelling doubly-bounded data, \eg percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random…
We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…
We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may…
We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…
We introduce a mixture-model of beta distributions to identify significant correlations among $P$ predictors when $P$ is large. The method relies on theorems in convex geometry, which we use to show how to control the error rate of edge…
In this work, we offer a thorough analytical investigation into the role of shared hyperparameters in a hierarchical Bayesian model, examining their impact on information borrowing and posterior inference. Our approach is rooted in a…
A wide range of machine learning algorithms iteratively add data to the training sample. Examples include semi-supervised learning, active learning, multi-armed bandits, and Bayesian optimization. We embed this kind of data addition into…
Regression models for circular variables are less developed, since the concept of building a linear predictor from linear combinations of covariates and various random effects, breaks the circular nature of the variable. In this paper, we…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
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…