Consistent
Bayes
1.
What is a QoI Map?
A Motivating Example
Vector-Valued
Scalar-Valued
The Objective
2.
Minute Measure Theory
a.
The Forward Problem
Mapping a Point
Mapping a Set
Mapping a Distribution
b.
The Inverse Problem
Inverting a Point
Inverting a Set
Inverting a Distribution
3.
Translating Uncertainties
A Single Datum
Repeated Trials
Assimilation
4.
Framework
Disintegration Theorem
Identify the Contour
Define Indexing Set
Map onto Manifold
Posterior
Prior
Observed
5.
Examples
The Set Up
Identity Map
Experiment 1
Experiment 2
Prior Predictive
Posterior Predictive
Harmonic Oscillator
Prior Predictive
Posterior Predictive
Optimal Experimental Design
Conclusion
Future Work
Clear History
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Consistent Bayes
A novel measure-theoretic framework
$$\pi^{\dagger}_\Lambda(\lambda) := \pi_\Lambda(\lambda)\frac{\pi_{\mathcal{D}}(Q(\lambda))}{\pi^{Q}_{\mathcal{D}}(Q(\lambda))} $$