Combining Nested Sampling and Normalizing Flows
In order to validate our understanding of the world around us, we want to compare theoretical models to data we have actually observed. Often, these models are functions of parameters, and we want to know the values of those parameters such that the models most closely represent the world. For example, we may believe the concentration of one molecule in a chemical reaction should decrease exponentially with time. However, we also want to know the rate constant, the parameter in the model that multiplies time in the exponential, such that the model exponential curve actually resembles a specific reaction that we observe. This is the problem of parameter inference, for which we often turn to Bayesian methods, especially when working with complex models and/or many parameters..
Assurance, a Bayesian Approach in Reliability Demonstration Testing for Quality Technology
Title: Assurance for Sample Size Determination in Reliability Demonstration Testing Authors & Year: Kevin Wilson & Malcolm Farrow (2021) Journal: Technometrics [DOI: 10.1080/00401706.2020.1867646] Why Reliability Demonstration Testing? Ensuring high reliability is critical for hardware products, especially those involved in safety-critical functions such as railway systems and nuclear power reactors. To build trust, manufacturers use reliability demonstration tests (RDT) where a sample of products is tested and failures are observed. If the test meets specific criteria, it demonstrates the product’s reliability. The RDT design varies based on the type of hardware product being tested, whether it is failure on demand or time to failure. Traditionally, sample sizes for RDT have been determined using methods that consider the power of a hypothesis test or risk criteria. Various approaches, such as Bayesian methods and risk criteria evaluation, have been developed over the decades in order to enhance the effectiveness of RDT. These measures…
MathStatBites at SCMA8: Astro Image Processing is BLISS?
In June 2023, astronomers and statisticans flocked to “Happy Valley’” Pennsylvania for the eighth installment of the Statistical Challenges in Modern Astronomy, a bidecadal conference. The meeting, hosted at Penn State University, marked a transition in leadership from founding members Eric Feigelson and Jogesh Babu to Hyungsuk Tak, who led the proceedings. While the astronomical applications varied widely, including modeling stars, galaxies, supernovae, X-ray observations, and gravitational waves, the methods displayed a strong Bayesian bent. Simulation based inference (SBI), which uses synthetic models to learn an approximate function for the likelihood of physical parameters given data, featured prominently in the distribution of talk topics. This article features work presented in two back-to-back talks on a probabilistic method for modeling (point) sources of light in astronomical images, for example stars or galaxies, delivered by Prof. Jeffrey Regier and Ismael Mendoza from the University of Michigan-Ann Arbor.