Related papers: Normalized Power Prior Bayesian Analysis
Scaling has been a major driver of recent advancements in deep learning. Numerous empirical studies have found that scaling laws often follow the power-law and proposed several variants of power-law functions to predict the scaling behavior…
Bayesian inference provides a natural framework for updating knowledge as new information becomes available, often in a sequential manner by incorporating datasets in stages or reusing previous posteriors as priors. In practice, this is…
Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients…
Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been…
The power-expected-posterior (PEP) prior provides an objective, automatic, consistent and parsimonious model selection procedure. At the same time it resolves the conceptual and computational problems due to the use of imaginary data.…
Updating $\textit{a priori}$ information given some observed data is the core tenet of Bayesian inference. Bayesian transfer learning extends this idea by incorporating information from a related dataset to improve the inference on the…
We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
Models of updating a set of priors either do not allow a decision maker to make inference about her priors (full bayesian updating or FB) or require an extreme degree of selection (maximum likelihood updating or ML). I characterize a…
We study frequentist properties of Bayesian and $L_0$ model selection, with a focus on (potentially non-linear) high-dimensional regression. We propose a construction to study how posterior probabilities and normalized $L_0$ criteria…
The prediction of the variance-covariance matrix of the multivariate normal distribution is important in the multivariate analysis. We investigated Bayesian predictive distributions for Wishart distributions under the Kullback-Leibler…
Bayesian inference provides a powerful tool for leveraging observational data to inform model predictions and uncertainties. However, when such data is limited, Bayesian inference may not adequately constrain uncertainty without the use of…
A typical power calculation is performed by replacing unknown population-level quantities in the power function with what is observed in external studies. Many authors and practitioners view this as an assumed value of power and offer the…
In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model…
Although the likelihood function is normalizeable with respect to the data there is no guarantee that the same holds with respect to the model parameters. This may lead to singularities in the expectation value integral of these parameters,…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
Hypothesis testing of structure in correlation and covariance matrices is of broad interest in many application areas. In high dimensions and/or small to moderate sample sizes, high error rates in testing is a substantial concern. This…
Modern data analysis frequently involves variables with highly non-Gaussian marginal distributions. However, commonly used analysis methods are most effective with roughly Gaussian data. This paper introduces an automatic transformation…
We revisit the classical credibility results of Jewell and B\"uhlmann to obtain credibility premiums for a GLM using a modern Bayesian approach. Here the prior distributions can be chosen without restrictions to be conjugate to the response…
Prior information about the input state can be utilized to enhance the efficiency of quantum teleportation which we quantify using the first two moments of fidelity. The input knowledge is introduced by relaxing the uniformity assumption in…