Subset simulation is a method used in reliability engineering to compute small (i.e., rare event) failure probabilities encountered in engineering systems. The basic idea is to express a small failure probability as a product of larger conditional probabilities by introducing intermediate failure events. This conceptually converts the original rare event problem into a series of frequent event problems that are easier to solve. In the actual implementation, samples conditional on intermediate failure events are adaptively generated to gradually populate from the frequent to rare event region. These 'conditional samples' provide information for estimating the complementary cumulative distribution function (CCDF) of the quantity of interest (that governs failure), covering the high as well as the low probability regions. They can also be used for investigating the cause and consequence of failure events. The generation of conditional samples is not trivial but can be performed efficiently using Markov chain Monte Carlo (MCMC). Subset Simulation takes the relationship between the (input) random variables and the (output) response quantity of interest as a 'black box'. This can be attractive for complex systems where it is difficult to use other variance reduction or rare event sampling techniques that require prior information about the system behaviour. For problems where it is possible to incorporate prior information into the reliability algorithm, it is often more efficient to use other variance reduction techniques such as importance sampling. It has been shown that subset simulation is more efficient than traditional Monte Carlo simulation, but less efficient than line sampling, when applied to a fracture mechanics test problem. (Wikipedia).
Math subsets are an important concept to understand. So what is the subset definition in math? What is a subset? We go over that part of set theory in this video as well as some details on the empty set and its subset properties. Enjoy! I hope you find this video helpful, and be sure to a
From playlist Set Theory
This video defines and give the notation used for subsets and proper subsets. http://mathispower4u.com
From playlist Sets
Recorded: Fall 2015 Lecturer: Dr. Erin M. Buchanan This video covers how to subset data in R using logical operators, call functions, and the subsetting function. Lecture materials and assignment available at statisticsofdoom.com. https://statisticsofdoom.com/page/basic-statistics/ Us
From playlist Learn R + Statistics
Formal Definition of a Function using the Cartesian Product
Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Subset Sum Problem | Subset Sum Problem Using Dynamic Programming | Data Structures | Simplilearn
This video aims to solve subset sum problem using dynamic programming. This "subset sum problem" tutorial helps learners to learn data structures and algorithm through a standard problem. This video will cover the following concepts: 00:00 Introduction to Subset Sum Problem 00:41 Problem
From playlist Data Structures & Algorithms [2022 Updated]
In this College Algebra video, Tori explains the definition of a subset and gives a few examples.
From playlist Basics: College Algebra
Introduction to Subsets (new version available)
This video defines and give the notation used for subsets and proper subsets. https://youtu.be/mqBDYTcpAA0 The new version fixed an error in the audio.
From playlist Set Theory
An overview and introduction to understanding sampling distributions of proportions [sample proportions] and how to calculate them
From playlist Unit 7 Probability C: Sampling Distributions & Simulation
Dakshita Khurana - Weakening Assumptions in Quantum Cryptography IV.b Part 2 of 2 - IPAM at UCLA
Recorded 29 July 2022. Dakshita Khurana of the University of Illinois at Urbana-Champaign presents "Weakening Assumptions in Quantum Cryptography IV.b" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: We will discuss how quantum information can be used to r
From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography
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From playlist Adiabatic Quantum Computing Conference 2016
Live CEOing Ep 670: Language Design in Wolfram Language [Index Functions, IntegerChop, and More]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements and features to the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram
From playlist Behind the Scenes in Real-Life Software Design
Nexus Trimester - Yuval Ishai (Technion) 1/2
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From playlist Nexus Trimester - 2016 - Secrecy and Privacy Theme
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From playlist Control Theory and Optimization
Daniela Egas Santander (6/30/21): Nerve theorems for fixed points of neural networks
A fundamental question in computational neuroscience is to understand how the network’s connectivity shapes neural activity. A popular framework for modeling neural activity are a class of recurrent neural networks called threshold linear networks (TLNs). A special case of these are comb
From playlist AATRN 2021
Dimitri Bertsekas: "Distributed and Multiagent Reinforcement Learning"
Intersections between Control, Learning and Optimization 2020 "Distributed and Multiagent Reinforcement Learning" Dimitri Bertsekas - Massachusetts Institute of Technology & Arizona State University Abstract: We discuss issues of parallelization and distributed asynchronous computation f
From playlist Intersections between Control, Learning and Optimization 2020
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Finished Immerman-Szelepcsenyi theorem
From playlist MIT 18.404J Theory of Computation, Fall 2020
Probabilistic techniques for simulating quantum (...) - A. Montanaro - Workshop 2 - CEB T3 2017
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From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
DDPS | Parameter Subset Selection and Active Subspace Techniques for Engineering & Biological Models
Engineering and biological models generally have a number of parameters which are nonidentifiable in the sense that they are not uniquely determined by measured responses. Furthermore, the computational cost of high-fidelity simulation codes often precludes their direct use for Bayesian m
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
(ML 16.7) EM for the Gaussian mixture model (part 1)
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From playlist Machine Learning