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# System prepended metadata

title: Paper Readings

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# Paper Readings

[Diagnostics for Gaussian Process Emulators](https://www2.stat.duke.edu/courses/Spring14/sta961.01/ref/BastOHag2009.pdf)

[Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://arxiv.org/pdf/2002.08791.pdf)

[Stochastic Normalizing Flows](https://arxiv.org/pdf/2002.06707.pdf)

[Understanding the Ensemble Kalman Filter](https://www.math.umd.edu/~slud/RITF17/enkf-tutorial.pdf)
Covers the EnKF basics, the idea of deterministics vs stochastic updates for the forward time prediction, as well as relevant variants such as smoothing.

[A Brief Tutorial on the Ensemble Kalman Filter](https://arxiv.org/pdf/0901.3725.pdf)
Introduces Extended KF (EnKF), which is an approximation of KF that works well in high dimensions. Essentially, the error covariance $Q$ is replaced by sample covariance $C$. The idea of prediction and update/correction is largely similar.

[An Elementary Introduction to Kalman Filtering](https://arxiv.org/pdf/1710.04055.pdf)
A bottom-up intuitive tutorial on KF. This was very helpful to those with only a basic probability theory background and builds the idea of how KF is optimal under some Gaussian assumption on the model and noise. 


[Introduction to Kalman Filters and its Applications](https://www.intechopen.com/books/introduction-and-implementations-of-the-kalman-filter/introduction-to-kalman-filter-and-its-applications)
An operational introduction to Kalman Filters and some examples. Sufficient for basic implementation but not much more.

[Roll-Back HMC](https://arxiv.org/pdf/1709.02855.pdf)
A small paper on an HMC variant that applies to truncated distributions via sigmoid (or an indicator-like function). Essentially, if the sampler goes near the boundary, it 'rolls up' and falls back down into the regions of support of interest.  

[Stabilities of Shape Identification Inverse Problems in a Bayesian Framework](https://arxiv.org/pdf/2002.07337.pdf)
The paper considers the inverse problem of domain identification, e.g. for heat PDE. Given some assumption on the forward operator, the paper proofs the Lipschitz stability of the posterior and the domain ratio (conditional probability that a certain point is inside the domain). The measure-theoretic proofs rely heavily on notions of metric spaces and notions of continuity.
Problems: Lack of familiarity with measure-theoretic proofs and weak intuitions on different types of continuity.


