Topic
Hitting time
About: Hitting time is a research topic. Over the lifetime, 1289 publications have been published within this topic receiving 19851 citations.
Papers published on a yearly basis
1 / 2
Papers
Proceedings Article•
26 Apr 2018TL;DR: A very different approach to survival analysis, DeepHit, that uses a deep neural network to learn the distribution of survival times directly and achieves large and statistically significant performance improvements over previous state-of-the-art methods.
Abstract: Survival analysis (time-to-event analysis) is widely used in economics and finance, engineering, medicine and many other areas. A fundamental problem is to understand the relationship between the covariates and the (distribution of) survival times(times-to-event). Much of the previous work has approached the problem by viewing the survival time as the first hitting time of a stochastic process, assuming a specific form for the underlying stochastic process, using available data to learn the relationship between the covariates and the parameters of the model, and then deducing the relationship between covariates and the distribution of first hitting times (the risk). However, previous models rely on strong parametric assumptions that are often violated. This paper proposes a very different approach to survival analysis, DeepHit, that uses a deep neural network to learn the distribution of survival times directly.DeepHit makes no assumptions about the underlying stochastic process and allows for the possibility that the relationship between covariates and risk(s) changes over time. Most importantly, DeepHit smoothly handles competing risks; i.e. settings in which there is more than one possible event of interest.Comparisons with previous models on the basis of real and synthetic datasets demonstrate that DeepHit achieves large and statistically significant performance improvements over previous state-of-the-art methods.
584 citations
TL;DR: A non-linear model to estimate the remaining useful life of a system based on monitored degradation signals is presented and it is revealed that considering nonlinearity in the degradation process can significantly improve the accuracy of remaining usefulLife estimation.
Abstract: Remaining useful life estimation is central to the prognostics and health management of systems, particularly for safety-critical systems, and systems that are very expensive. We present a non-linear model to estimate the remaining useful life of a system based on monitored degradation signals. A diffusion process with a nonlinear drift coefficient with a constant threshold was transformed to a linear model with a variable threshold to characterize the dynamics and nonlinearity of the degradation process. This new diffusion process contrasts sharply with existing models that use a linear drift, and also with models that use a linear drift based on transformed data that were originally nonlinear. Both existing models are based on a constant threshold. To estimate the remaining useful life, an analytical approximation to the distribution of the first hitting time of the diffusion process crossing a threshold level is obtained in a closed form by a time-space transformation under a mild assumption. The unknown parameters in the established model are estimated using the maximum likelihood estimation approach, and goodness of fit measures are applied. The usefulness of the proposed model is demonstrated by several real-world examples. The results reveal that considering nonlinearity in the degradation process can significantly improve the accuracy of remaining useful life estimation.
547 citations
TL;DR: In this article, the authors developed a similar theory for continuous time processes and considered the following types of criteria for geometric convergence: 1. The existence of exponentially bounded hitting times on one and then all suitably "small" sets; 2. The presence of "Foster-Lyapunov" or "drift" conditions on the extended generator of the process.
Abstract: General characterizations of geometric convergence for Markov chains in discrete time on a general state space have been developed recently in considerable detail. Here we develop a similar theory for $\varphi$-irreducible continuous time processes and consider the following types of criteria for geometric convergence: 1. the existence of exponentially bounded hitting times on one and then all suitably "small" sets; 2. the existence of "Foster-Lyapunov" or "drift" conditions for any one and then all skeleton and resolvent chains; 3. the existence of drift conditions on the extended generator $\tilde\mathscr{A}$ of the process. We use the identity $\tilde\mathscr{A}R_\beta = \beta(R_\beta - I)$ connecting the extended generator and the resolvent kernels $R_\beta$ to show that, under a suitable aperiodicity assumption, exponential convergence is completely equivalent to any of criteria 1-3. These conditions yield criteria for exponential convergence of unbounded as well as bounded functions of the chain. They enable us to identify the dependence of the convergence on the initial state of the chain and also to illustrate that in general some smoothing is required to ensure convergence of unbounded functions.
429 citations
TL;DR: In this paper, the authors describe a simple algorithm that simulates exact sample paths of a class of stochastic differential equations and returns the location of the path at a random collection of time instances.
Abstract: We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random collection of time instances. The path can then be completed without further reference to the dynamics of the target process.
363 citations
TL;DR: In this article, a survey of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics is presented, where general results on quasi-stability are given and examples developed in detail.
Abstract: This survey concerns the study of quasi-stationary distributions with
a specific focus on models derived from ecology and population
dynamics. We are concerned with the long time behavior of different
stochastic population size processes when 0 is an absorbing point
almost surely attained by the process. The hitting time of this point,
namely the extinction time, can be large compared to the physical time
and the population size can fluctuate for large amount of time before
extinction actually occurs. This phenomenon can be understood by the
study of quasi-limiting distributions. In this paper, general results
on quasi-stationarity are given and examples developed in detail. One
shows in particular how this notion is related to the spectral
properties of the semi-group of the process killed at 0. Then we
study different stochastic population models including nonlinear terms
modeling the regulation of the population. These models will take
values in countable sets (as birth and death processes) or in
continuous spaces (as logistic Feller diffusion processes or
stochastic Lotka-Volterra processes). In all these situations we study
in detail the quasi-stationarity properties. We also develop an
algorithm based on Fleming-Viot particle systems and show a lot of
numerical pictures.
270 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 8 |
| 2024 | 17 |
| 2023 | 29 |
| 2022 | 89 |
| 2021 | 70 |
| 2020 | 64 |