scholarly journals Unbiased Simulation of Rare Events in Continuous Time

2021 ◽  
Author(s):  
James Hodgson ◽  
Adam M. Johansen ◽  
Murray Pollock
Keyword(s):  
Continuous Time ◽  
Rare Events ◽  
Splitting Method ◽  
Rare Event ◽  
Unbiased Estimation ◽  
Proof Of Concept ◽  
Numerical Examples ◽  
Event Simulation ◽  
Sample Paths ◽  
Practical Feasibility

AbstractFor rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and $$\varepsilon$$ ε -strong simulation of diffusions, which can be used to almost surely constrain sample paths to a given tolerance, suggests one way to do this. We specify how such algorithms can be combined with the classical multilevel splitting method for rare event simulation. This provides unbiased estimations of the probability in question. We discuss the practical feasibility of the algorithm with reference to existing $$\varepsilon$$ ε -strong methods and provide proof-of-concept numerical examples.

scholarly journals RARE EVENT SIMULATION

2005 ◽  
Vol 20 (1) ◽  
pp. 45-66 ◽  
Author(s):  
Agnès Lagnoux
Keyword(s):  
Confidence Interval ◽  
Branching Processes ◽  
Splitting Method ◽  
Rare Event ◽  
Fast Simulation ◽  
Rare Event Simulation ◽  
Event Simulation ◽  
Sample Paths ◽  
Simulation Based ◽  
Multiple Copies

This article deals with estimations of probabilities of rare events using fast simulation based on the splitting method. In this technique, the sample paths are split into multiple copies at various stages in the simulation. Our aim is to optimize the algorithm and to obtain a precise confidence interval of the estimator using branching processes. The numerical results presented suggest that the method is reasonably efficient.

A multi-level splitting algorithm based on differential evolution

2018 ◽  
Vol 09 (02) ◽  
pp. 1850021
Author(s):  
Liping Wang ◽  
Wenhui Fan
Keyword(s):  
Differential Evolution ◽  
Rare Event ◽  
Sampling Strategy ◽  
Splitting Algorithm ◽  
Algorithm Efficiency ◽  
Event Simulation ◽  
Sample Paths ◽  
Level Splitting ◽  
Key Factor ◽  
Multi Level

Multi-level splitting algorithm is a famous rare event simulation (RES) method which reaches rare set through splitting samples during simulation. Since choosing sample paths is a key factor of the method, this paper embeds differential evolution in multi-level splitting mechanism to improve the sampling strategy and precision, so as to improve the algorithm efficiency. Examples of rare event probability estimation demonstrate that the new proposed algorithm performs well in convergence rate and precision for a set of benchmark cases.

scholarly journals Rare Event Simulation for Stochastic Dynamics in Continuous Time

2019 ◽  
Vol 176 (5) ◽  
pp. 1185-1210 ◽  
Author(s):  
Letizia Angeli ◽  
Stefan Grosskinsky ◽  
Adam M. Johansen ◽  
Andrea Pizzoferrato
Keyword(s):  
Continuous Time ◽  
Stochastic Dynamics ◽  
Rare Event ◽  
Rare Event Simulation ◽  
Event Simulation

scholarly journals A Two-Step Branching Splitting Model Under Cost Constraint for Rare Event Analysis

2009 ◽  
Vol 46 (2) ◽  
pp. 429-452 ◽  
Author(s):  
Agnès Lagnoux-Renaudie
Keyword(s):  
Transition Probabilities ◽  
Splitting Method ◽  
Rare Event ◽  
Event Analysis ◽  
Sample Paths ◽  
Multiple Copies ◽  
Speed Up ◽  
Two Phases ◽  
The Cost

In this paper we consider the splitting method first introduced in rare event analysis. In this technique, the sample paths are split into R multiple copies at various stages to speed up the simulation. Given the cost, the optimization of the algorithm suggests taking all the transition probabilities to be equal; nevertheless, in practice, these quantities are unknown. We address this problem by presenting an algorithm in two phases.

scholarly journals A Comparison of Weighted Stochastic Simulation Methods

2021 ◽  
Author(s):  
Payton J Thomas ◽  
Mohammad Ahmadi ◽  
Hao Zheng ◽  
Chris J. Myers
Keyword(s):  
Stochastic Simulation ◽  
Biological System ◽  
Rare Events ◽  
Rare Event ◽  
Simulation Methods ◽  
Rare Event Simulation ◽  
Event Simulation ◽  
New Methods

1ABSTRACTRare events are of particular interest in biology because rare biochemical events may be catastrophic to a biological system. To estimate the probability of rare events, several weighted stochastic simulation methods have been developed. Unfortunately, the robustness of these methods is questionable. Here, an analysis of weighted stochastic simulation methods is presented. The methods considered here fail to accomplish the task of rare event simulation, in general, suggesting that new methods are necessary to adequately study rare biological events.

scholarly journals A Two-Step Branching Splitting Model Under Cost Constraint for Rare Event Analysis

2009 ◽  
Vol 46 (02) ◽  
pp. 429-452 ◽  
Author(s):  
Agnès Lagnoux-Renaudie
Keyword(s):  
Transition Probabilities ◽  
Splitting Method ◽  
Rare Event ◽  
Event Analysis ◽  
Sample Paths ◽  
Multiple Copies ◽  
Speed Up ◽  
Two Phases ◽  
The Cost

In this paper we consider the splitting method first introduced in rare event analysis. In this technique, the sample paths are split into R multiple copies at various stages to speed up the simulation. Given the cost, the optimization of the algorithm suggests taking all the transition probabilities to be equal; nevertheless, in practice, these quantities are unknown. We address this problem by presenting an algorithm in two phases.

Framework for rare event detection using Artificial Neural Network based context free grammar

2020 ◽  
Vol 39 (6) ◽  
pp. 8463-8475
Author(s):  
Palanivel Srinivasan ◽  
Manivannan Doraipandian
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Event Detection ◽  
Performance Metrics ◽  
Rare Events ◽  
Rare Event ◽  
Video Stream ◽  
Context Free Grammar ◽  
Artificial Neural ◽  
Context Free

Rare event detections are performed using spatial domain and frequency domain-based procedures. Omnipresent surveillance camera footages are increasing exponentially due course the time. Monitoring all the events manually is an insignificant and more time-consuming process. Therefore, an automated rare event detection contrivance is required to make this process manageable. In this work, a Context-Free Grammar (CFG) is developed for detecting rare events from a video stream and Artificial Neural Network (ANN) is used to train CFG. A set of dedicated algorithms are used to perform frame split process, edge detection, background subtraction and convert the processed data into CFG. The developed CFG is converted into nodes and edges to form a graph. The graph is given to the input layer of an ANN to classify normal and rare event classes. Graph derived from CFG using input video stream is used to train ANN Further the performance of developed Artificial Neural Network Based Context-Free Grammar – Rare Event Detection (ACFG-RED) is compared with other existing techniques and performance metrics such as accuracy, precision, sensitivity, recall, average processing time and average processing power are used for performance estimation and analyzed. Better performance metrics values have been observed for the ANN-CFG model compared with other techniques. The developed model will provide a better solution in detecting rare events using video streams.

Rare event simulation

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Rare Event ◽  
Path Sampling ◽  
Rapid Progress ◽  
Computationally Efficient ◽  
Transition Path ◽  
Transition Path Sampling ◽  
Event Simulation ◽  
Reaction Coordinates ◽  
Simulation Techniques ◽  
Transition Interface

The development of techniques to simulate infrequent events has been an area of rapid progress in recent years. In this chapter, we shall discuss some of the simulation techniques developed to study the dynamics of rare events. A basic summary of the statistical mechanics of barrier crossing is followed by a discussion of approaches based on the identification of reaction coordinates, and those which seek to avoid prior assumptions about the transition path. The demanding technique of transition path sampling is introduced and forward flux sampling and transition interface sampling are considered as rigorous but computationally efficient approaches.

scholarly journals Unbiased estimation of the solution to Zakai’s equation

2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra
Keyword(s):  
Continuous Time ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Linear Filtering ◽  
Multilevel Monte Carlo ◽  
Zakai Equation ◽  
Unbiased Estimators ◽  
First Order ◽  
Multilevel Monte Carlo Method ◽  
Filtering Problem

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

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