es/iode’s Post

I am happy to share the results from our last research paper “Testing for time-varying nonlinear dependence structures: #Regime-#switching and #local #Gaussian #correlation”. This paper examines nonlinear and time-varying dependence structures between a pair of stochastic variables, using a novel approach which combines regime-switching models and local Gaussian correlation (LGC). We propose an LGC-based bootstrap test for examining whether the dependence structure between two variables is equal across different regimes. We examine this test in a Monte Carlo study, where it shows good level and power properties. We argue that this approach is more intuitive than competing approaches, typically combining regime-switching models with copula theory. Furthermore, LGC is a semi-parametric approach, hence avoids any parametric specification of the dependence structure. We illustrate our approach using financial returns from the US–UK stock markets and the US stock and government bond markets, and provide detailed insight into their dependence structures. https://lnkd.in/djstFuu5

In InSAR analysis, topographic phase residuals are conceptually simple but often challenging to remove. When the look angles of two satellite passes differ significantly, topographic errors have a large impact on the interferometric phase. Conversely, if the satellite positions are nearly identical, these topographic effects are negligible. Typically, a straightforward linear regression is all that’s needed to detect and extract the topographic residual phase. The difficulty, however, lies in the need for unwrapped phase data, which introduces additional unwrapping errors into an already noisy signal. Fortunately, there’s a direct way to handle this using wrapped phase. By fitting the wrapped phase to the baseline with sine and cosine functions and then applying an arctan transformation, we can remove topographic residuals without first unwrapping the data. This approach allows for a cleaner unwrapped phase if desired later, after atmospheric and topographic effects have been minimized. Below is an illustration: one plot shows a perfectly linear relationship between topographic residual phase and baseline, while the other is more nonlinear. This difference is key. The mathematics involved here are simple trigonometry—well within the grasp of primary-school level math—yet they are central to understanding InSAR processing. What do you think causes this difference? Please share your thoughts below. Hint: This nonlinearity is expected and cannot be eliminated unless… what?

📃Scientific paper: Enhancing nonlinear solvers for the Navier-Stokes equations with continuous \(noisy\) data assimilation Abstract: We consider nonlinear solvers for the incompressible, steady \(or at a fixed time step for unsteady\) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is incorporated/assimilated into the solution through a nudging term addition to the the Picard iteration that penalized the difference between the coarse mesh interpolants of the true solution and solver solution, analogous to how continuous data assimilation \(CDA\) is implemented for time dependent PDEs. This was considered in the paper \[Li et al. \{\it CMAME\} 2023\], and we extend the methodology by improving the analysis to be in the $L^2$ norm instead of a weighted $H^1$ norm where the weight depended on the coarse mesh width, and to the case of noisy measurement data. For noisy measurement data, we prove that the CDA-Picard method is stable and convergent, up to the size of the noise. Numerical tests illustrate the results, and show that a very good strategy when using noisy data is to use CDA-Picard to generate an initial guess for the classical Newton iteration. Continued on ES/IODE ➡️ https://etcse.fr/y7b ------- If you find this interesting, feel free to follow, comment and share. We need your help to enhance our visibility, so that our platform continues to serve you.

Nonparametric rank-based inference methods (e.g., the Wilcoxon-Mann-Whitney test) comprise a few of the mostly used statistical procedures. But how to estimate the variance of the Mann-Whitney effect without bias? Jointly with my supervisor Edgar Brunner, who supervised my Diploma thesis in Mathematics, PhD advisor and habilitation mentor, we finally could develop an unbiased estimator of the variance: https://lnkd.in/es3eZ2C3

Batch Gradient Descent vs. Stochastic Gradient Descent Batch gradient Descent involves aggregating the errors for all data points in the training set and updating the model parameters only after completing evaluation across all examples, defining a training epoch. One disadvantage of Batch Gradient Descent is its high computational cost, especially when dealing with large datasets. Stochastic gradient descent (SGD) conducts a training epoch for each example in the dataset, updating parameters one example at a time. Due to its focus on individual examples and the need to hold only one at a time, SGD offers simplicity. However, its frequent updates, while potentially offering more detailed insights and speed, can lead to computational inefficiencies compared to batch gradient descent. * Credit to "ResearchGate" for the illustration image!

I am thrilled to share that our work: On Statistical Properties of A Veracity Scoring Method for Spatial Data has been accepted and published online at Technometrics. In this work we have introduced a veracity scoring (VS) methodology for statistical analysis of noisy spatial data. We have further analysed the asymptotic properties of this proposed spatial regression under mixed-increasing domain asymptotic framework. With an extension of Ghosh-Bahadur representation of sample quantiles for α-mixing irregularly spaced dependent data, we have justified theoretical robustness of VS-based spatial regression estimators. Finally, we have applied this method on a real dataset to showcase the advantages over the existing robust spatial kriging approaches both in terms of precision and computational complexity. The paper is now available online at Taylor & Francis: https://lnkd.in/g93zF9Pr I want to sincerely thank my PhD advisor and co-author Soumendra Lahiri for his constant guidance and support thought this work.

NEW PAPER: Provable robustness of Bayesian filters with simple modifications (nudging) against model misspecification in the transition kernel: https://lnkd.in/dhagZF6X Background: during my PhD, I burnt several months to show that simple gradient steps can robustify the filters against transition model misspecification, to no avail - with the exception of Appendix C here (which didn't fully prove the result): https://lnkd.in/dgiw8EgA When the student of my PhD advisor came for a visit at Imperial last year, I saw an opportunity for a little payback by assigning him the problem that had caused me so much headache. Now done properly, we show that there are simple algorithmic ways to provably robustify state-space models with misspecified transition models - there is even more to come soon!

Hi everyone! I recently wrote an informal blog post that may offer valuable insights for those involved in quantitative continuous time modeling. In this post, I cover the following topics: 1. An explanation of the monotonicity condition in designing numerical schemes for second-order elliptic and parabolic PDEs. 2. A heuristic approach to deriving CFL conditions. 3. An introduction to proving monotonicity conditions within various numerical schemes, supported by several intuitive examples. Additionally, the blog highlights a significant point: in common practices for solving elliptic/parabolic PDEs (such as economic models formulated as HJB equations) using finite difference and implicit methods, the property of unconditional monotonicity loses when approximating the value function with interpolation or approximation methods. This loss of monotonicity is irreparable with many widely used interpolation techniques. However, unconditional monotonicity can be restored if specific conditions are met by the chosen interpolation/approximation methods. I hope this preliminary discussion will be both insightful and inspiring for those navigating these complex areas. 😄 Here is the URL to the post: https://lnkd.in/eD8wAtQ7

A simple explanation. I also wonder this the reason of L/D ratio of long columns/horizontal vessels.

📃Scientific paper: Minimal spanning arborescence Abstract: We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient trees, the infinite volume limit exists almost surely. We also prove that for nonamenable, unimodular graphs, the limit is almost surely one-ended assuming a certain sufficient condition that guarantees the existence of the limit. This object cannot be studied using well-known algorithms, such as Kruskal's or Prim's algorithm, to sample the minimal spanning tree which has been instrumental in getting analogous results about them \(Lyons, Peres, and Schramm\). Instead, we use a recursive algorithm due to Chu, Liu, Edmonds, and Bock, which leads to a novel stochastic process which we call the \emph\{loop contracting random walk\}. This is similar to the well-known and widely studied loop erased random walk, except instead of erasing loops we contract them. The full algorithm bears similarities with the celebrated Wilson's algorithm to generate uniform spanning trees and can be seen as a certain limit of the original Wilson's algorithm. ;Comment: 47 pages, many figures, 2 simulations Continued on ES/IODE ➡️ https://etcse.fr/WbLU9 ------- If you find this interesting, feel free to follow, comment and share. We need your help to enhance our visibility, so that our platform continues to serve you.