Related papers: Priors for New Physics

While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittle's Likelihood, involving the second order…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

The two-level normal hierarchical model has played an important role in statistical theory and applications. In this paper, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the…

One of the core facets of Bayesianism is in the updating of prior beliefs in light of new evidence$\text{ -- }$so how can we maintain a Bayesian approach if we have no prior beliefs in the first place? This is one of the central challenges…

Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…

Semiparametric mixture models are parametric models with latent variables. They are defined kernel, $p_\theta(x | z)$, where z is the unknown latent variable, and $\theta$ is the parameter of interest. We assume that the latent variables…

Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…

The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated…

Fitting models to data using Bayesian inference is quite common, but when each point in parameter space gives a curve, fitting the curve to a data set requires new nuisance parameters, which specify the metric embedding the one-dimensional…

Machine Learning is becoming more prevalent in science and engineering, but many approaches do not provide meaningful uncertainty estimates and predictions may also violate known physical knowledge. We propose a Bayesian framework to embed…

Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…

We present a Bayesian approach to machine learning with probabilistic programs. In our approach, training on available data is implemented as inference on a hierarchical model. The posterior distribution of model parameters is then used to…

A typical Bayesian inference on the values of some parameters of interest $\bf q$ from some data $D$ involves running a Markov Chain (MC) to sample from the posterior $p({\bf q},{\bf n} | D) \propto \mathcal{L}(D | {\bf q},{\bf n}) p({\bf…

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…

Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…

Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…

This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…

This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a…

In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…

It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…