Inverse set estimation and inversion of simultaneous confidence intervals

The preimage or inverse image of a predefined subset of the range of a deterministic function, called inverse set for short, is the set in the domain whose image equals that predefined subset. To quantify the uncertainty in the estimation of such a set, we propose data-dependent inner and outer confidence sets that are sub- and super-sets of the true inverse set with a given confidence. Existing methods require strict assumptions, and the predefined subset of the range is usually an excursion set for only one single level. We show that by inverting pre-constructed simultaneous confidence intervals, commonly available for different kinds of data, multiple confidence sets of multiple levels can be simultaneously constructed with the desired confidence non-asymptotically. The method is illustrated on dense functional data to determine regions with rising temperatures in North America and on logistic regression data to assess the effect of statin and COVID-19 on clinical outcomes of in-patients

Real-time Monitoring for the Next Core-Collapse Supernova in JUNO

Core-collapse supernova (CCSN) is one of the most energetic astrophysical events in the Universe. The early and prompt detection of neutrinos before (pre-SN) and during the SN burst is a unique opportunity to realize the multi-messenger observation of the CCSN events. In this work, we describe the monitoring concept and present the sensitivity of the system to the pre-SN and SN neutrinos at the Jiangmen Underground Neutrino Observatory (JUNO), which is a 20 kton liquid scintillator detector under construction in South China. The real-time monitoring system is designed with both the prompt monitors on the electronic board and online monitors at the data acquisition stage, in order to ensure both the alert speed and alert coverage of progenitor stars. By assuming a false alert rate of 1 per year, this monitoring system can be sensitive to the pre-SN neutrinos up to the distance of about 1.6 (0.9) kpc and SN neutrinos up to about 370 (360) kpc for a progenitor mass of 30$M_{\odot}$ for the case of normal (inverted) mass ordering. The pointing ability of the CCSN is evaluated by using the accumulated event anisotropy of the inverse beta decay interactions from pre-SN or SN neutrinos, which, along with the early alert, can play important roles for the followup multi-messenger observations of the next Galactic or nearby extragalactic CCSN.Comment: 24 pages, 9 figure

Bayesian and Frequentist Methods for Uncertainty Quantification and Interpretation in Statistical and Machine Learning Models

Modern statistical and machine learning models excel at capturing complex non-linear relationships between outcomes and predictors, resulting in high accuracy. However, the complexity of these models can impede statistical inference and interpretation. This dissertation confronts and tries to overcome the emerging challenges presented by intricate models and big data.One significant challenge involves modeling and statistical inference for zero-inflated semi-continuous data. Thus, in the first part, we develop a flexible Bayesian semi-parametric mixture model for zero-inflated skewed longitudinal data, generating credible intervals for not only the mean but also any quantiles of the parameters and predictions, aiding population inference of skewed data. The model is applied to evaluate how number of binge drinking episodes changes with neuromaturation using the National Consortium on Alcohol and Neuro-Development in Adolescence data.On the other hand, credible or confidence intervals do not directly address a common question: can we identify a subset of predictions or parameters with true values exceeding a specific threshold with confidence? To tackle this, in the second part, we improve upon the inverse set estimation framework that estimates such sets by developing an approach with fewer assumptions and broader applicability to various data settings. We construct an excursion set map with probability guarantee on the North American Regional Climate Change Assessment Program data using the proposed method. Moreover, we use this new method to discover characteristics of in-patients at high risk for severe outcomes using University of California San Diego hospital data.In the third part, we apply this inverse set estimation inference framework to quantify prediction model uncertainty and develop theories and algorithms that ensure non-conservative coverage rates for a single threshold in non-asymptotic settings in regression problems. We demonstrate the effectiveness of the constructed confidence sets for uncertainty quantification and interpretation in both simulate data and PhysioNet sepsis prediction data

The Effect of Nano-Aluminumpowder on the Characteristic of RDX based Aluminized Explosives Underwater Close-Filed Explosion

In order to investigate the effect of nano-aluminum powder on the characteristic of RDX based aluminized explosives underwater closed-filed explosions, the scanning photographs along the radial of the charges were gained by a high speed scanning camera. The photographs of two different aluminized explosives underwater explosion have been analyzed, the shock wave curves and expand curves of detonation products were obtained, furthermore the change rules of shock waves propagation velocity, shock front pressure and expansion of detonation products of two aluminized explosives were investigated, and also the parameters of two aluminized explosives were contrasted. The results show that the aluminized explosive which with nano-aluminum whose initial shock waves pressure propagation velocity, shock front pressure are smaller than the aluminized explosive without nano-aluminum and has lower decrease rate attenuation of energy

The Effect of Nano-Aluminumpowder on the Characteristic of RDX based Aluminized Explosives Underwater Close-Filed Explosion

In order to investigate the effect of nano-aluminum powder on the characteristic of RDX based aluminized explosives underwater closed-filed explosions, the scanning photographs along the radial of the charges were gained by a high speed scanning camera. The photographs of two different aluminized explosives underwater explosion have been analyzed, the shock wave curves and expand curves of detonation products were obtained, furthermore the change rules of shock waves propagation velocity, shock front pressure and expansion of detonation products of two aluminized explosives were investigated, and also the parameters of two aluminized explosives were contrasted. The results show that the aluminized explosive which with nano-aluminum whose initial shock waves pressure propagation velocity, shock front pressure are smaller than the aluminized explosive without nano-aluminum and has lower decrease rate attenuation of energy

A semi‐parametric Bayesian model for semi‐continuous longitudinal data

Semi-continuous data present challenges in both model fitting and interpretation. Parametric distributions may be inappropriate for extreme long right tails of the data. Mean effects of covariates, susceptible to extreme values, may fail to capture relevant information for most of the sample. We propose a two-component semi-parametric Bayesian mixture model, with the discrete component captured by a probability mass (typically at zero) and the continuous component of the density modeled by a mixture of B-spline densities that can be flexibly fit to any data distribution. The model includes random effects of subjects to allow for application to longitudinal data. We specify prior distributions on parameters and perform model inference using a Markov chain Monte Carlo (MCMC) Gibbs-sampling algorithm programmed in R. Statistical inference can be made for multiple quantiles of the covariate effects simultaneously providing a comprehensive view. Various MCMC sampling techniques are used to facilitate convergence. We demonstrate the performance and the interpretability of the model via simulations and analyses on the National Consortium on Alcohol and Neurodevelopment in Adolescence study (NCANDA) data on alcohol binge drinking