Two Efficient AK-Based Global Reliability Sensitivity Methods by Elaborative Combination of Bayes’ Theorem and the Law of Total Expectation in the Successive Intervals Without Overlapping

2020 ◽  
Vol 69 (1) ◽  
pp. 260-276 ◽  
Author(s):  
Wanying Yun ◽  
Zhenzhou Lu ◽  
Kaixuan Feng ◽  
Xian Jiang ◽  
Pan Wang ◽  
...  
Keyword(s):  
Bayes Theorem ◽  
Reliability Sensitivity ◽  
Global Reliability Sensitivity ◽  
The Law

scholarly journals Market Prices of Risk with Diverse Beliefs, Learning, and Catastrophes

2012 ◽  
Vol 102 (3) ◽  
pp. 141-146 ◽  
Author(s):  
Timothy Cogley ◽  
Thomas J Sargent ◽  
Viktor Tsyrennikov
Keyword(s):  
Bayes Theorem ◽  
The Other ◽  
Information Flows ◽  
Complete Markets ◽  
Learning Dynamics ◽  
Market Prices ◽  
Market Structures ◽  
The Law ◽  
State Learning

We compare market prices of risk in economies with identical patterns of endowments, priors, and information flows, but two different market structures, one with complete markets, another in which consumers can trade only a single risk-free bond. We study how opportunities to speculate, uncommon priors, and learning affect market prices of risk. Two types of consumers have diverse beliefs about the law of motion for a random exogenous endowment. One type knows the true law of motion while the other type learns about it via Bayes' theorem. Less-well-informed consumers are pessimistic, initially overestimating the probability of a catastrophic state. Learning dynamics and the wealth dynamics that they drive contribute to differences in evolutions of market prices of risk across market structures.

Extending the global reliability sensitivity analysis to the systems under double-stochastic uncertainty

2018 ◽  
Vol 22 (3) ◽  
pp. 626-640 ◽  
Author(s):  
Wenxuan Wang ◽  
Hangshan Gao ◽  
Changcong Zhou
Keyword(s):  
Sensitivity Analysis ◽  
Stochastic System ◽  
Dynamic Strength ◽  
Point Estimation ◽  
Coupling Mechanism ◽  
Analysis Method ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Sensitivity Analysis Method ◽  
Global Reliability Sensitivity

Systems with random variables and random excitations exist widely in various engineering problems. Extending the traditional global reliability sensitivity to this double-stochastic system has important guiding significance for its design optimization. However, because there is a certain coupling between the randomness of variables and the randomness of excitation, this coupling mechanism is difficult to determine in practical projects. Therefore, it is difficult to extend the traditional reliability sensitivity analysis method to this double-stochastic system. In this research, it is assumed that there is no correlation between variables and excitations. Then, combining the first-passage method–based dynamic strength formula and the variance-based sensitivity analysis method, an approximate global reliability sensitivity analysis method for this double-stochastic system is proposed. In order to improve the computational efficiency, a nested loop method based on seven-point estimation is proposed for reliability sensitivity analysis. In order to verify the accuracy and efficiency of the proposed method, a Monte Carlo simulation is given as a reference. Three examples are studied and discussed to illustrate the practicality and feasibility of the proposed method.

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