Related papers: The diachronic Bayesian
Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
In a Bayesian analysis, the likelihood that specific candidate parameters govern the evolution of a quantum system are conditioned on the outcome of measurements which, in turn, cause measurement backaction on the state of the system [M.…
This paper proposes a unified theoretical model to identify and test a comprehensive set of probabilistic updating biases within a single framework. The model achieves separate identification by focusing on the updating of belief…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…
Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential…
In a quantum-Bayesian take on quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, we argue…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…
Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and…
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…
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…
This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes' rule given some…
Calibration is a classical notion from the forecasting literature which aims to address the question: how should predicted probabilities be interpreted? In a world where we only get to observe (discrete) outcomes, how should we evaluate a…
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…