Related papers: Bayesian approach for g-mode detection, or how to …
Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…
Once upon a time, predictions for the accuracy of inference on gravitational-wave signals relied on computationally inexpensive but often inaccurate techniques. Recently, the approach has shifted to actual inference on noisy signals with…
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.…
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
A Bayesian treatment of the problem of detecting an unmodelled gravitational wave burst with a global network of gravitational wave observatories reveals that several previously proposed statistics have implicit biases that render them…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…
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…
Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…
The number of modes in a probability density function is representative of the complexity of a model and can also be viewed as the number of subpopulations. Despite its relevance, there has been limited research in this area. A novel…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…
Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…
Over the past 10 years Bayesian methods have rapidly grown more popular as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper, we begin with a general description of…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…