Related papers: Bayesian Renormalization
Gene and protein networks are very important to model complex large-scale systems in molecular biology. Inferring or reverseengineering such networks can be defined as the process of identifying gene/protein interactions from experimental…
Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been…
Bayesian networks are graphical models to represent the probabilistic relationships between variables in the Bayesian framework. The knowledge of all variables can be updated using new information about some of the variables. We show that…
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…
Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…
This work addresses the reconstruction of a scatterer's shape from phaseless far field-intensity data arising from multiple incident waves interacting with the scatterer. We formulate the reconstruction as a statistical inverse scattering…
We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the…
Bayesian model selection provides a natural alternative to classical hypothesis testing based on p-values. While many papers mention that Bayesian model selection is frequently sensitive to prior specification on the parameters, there are…
As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
In physics we attempt to infer the rules governing a system given only the results of imprecise measurements. This is an ill-posed problem because certain features of the system's state cannot be resolved by the measurements. However, by…
In this paper we introduce five different algorithms based on method of moments, maximum likelihood and full Bayesian estimation for learning the parameters of the Inverse Gamma distribution. We also provide an expression for the KL…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…