Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models

Quantile is an important quantity in reliability analysis, as it is related to the resistance level for defining failure events. This study develops a computationally efficient sampling method for estimating extreme quantiles using stochastic black box computer models. Importance sampling has been widely employed as a powerful variance reduction technique to reduce estimation uncertainty and improve computational efficiency in many reliability studies. However, when applied to quantile estimation, importance sampling faces challenges, because a good choice of the importance sampling density relies on information about the unknown quantile. We propose an adaptive method that refines the importance sampling density parameter toward the unknown target quantile value along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove some convergence properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through numerical examples and wind turbine case study.     

Exact expected values of variance estimators for simulation

We formulate exact expressions for the expected values of selected estimators of the variance parameter (that is, the sum of covariances at all lags) of a steady‐state simulation output process. Given in terms of the autocovariance function of the process, these expressions are derived for variance estimators based on the simulation analysis methods of nonoverlapping batch means, overlapping batch means, and standardized time series. Comparing estimator performance in a first‐order autoregressive process and the M/M/1 queue‐waiting‐time process, we find that certain standardized time series estimators outperform their competitors as the sample size becomes large. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A note on a variance bound for the multinomial and the negative multinomial distribution

We prove a Chernoff‐type upper variance bound for the multinomial and the negative multinomial distribution. An application is also given.Copyright © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 179–183, 2014     

Optimal pricing and inventory control policy in periodic‐review systems with fixed ordering cost and lost sales

This paper studies a periodic‐review pricing and inventory control problem for a retailer, which faces stochastic price‐sensitive demand, under quite general modeling assumptions. Any unsatisfied demand is lost, and any leftover inventory at the end of the finite selling horizon has a salvage value. The cost component for the retailer includes holding, shortage, and both variable and fixed ordering costs. The retailer's objective is to maximize its discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We show that, under a mild assumption on the additive demand function, at the beginning of each period an (s,S) policy is optimal for replenishment, and the value of the optimal price depends on the inventory level after the replenishment decision has been done. Our numerical study also suggests that for a sufficiently long selling horizon, the optimal policy is almost stationary. Furthermore, the fixed ordering cost (K) plays a significant role in our modeling framework. Specifically, any increase in K results in lower s and higher S. On the other hand, the profit impact of dynamically changing the retail price, contrasted with a single fixed price throughout the selling horizon, also increases with K. We demonstrate that using the optimal policy values from a model with backordering of unmet demands as approximations in our model might result in significant profit penalty. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

小样本三维正态分布整体检验射击精度方法研究

讨论了小样本三维同方差正态分布整体检验射击精度问题.给出了n=3,4,5的不同显著水平α的检验OC曲线.计算出了与第一类错误和第二类错误相联系的有关重要物理参数.模拟表明该方法检验效果良好.     

The Un-Holy Russo-Chinese alliance

ABSTRACT

This essay argues that a Sino-Russian alliance has come into being over many years of the two states’ evolutionary policies. Although Vladimir Putin has emphasised that this is a multi-faceted relationship, this essay focuses exclusively on its military dimension. It comprises extensive inter-ministerial and inter-governmental cooperation, arms sales, joint exercises, and shared political orientation. While it may not be a formal alliance like NATO research, e.g. by Alexander Korolev, indicates that in general experts argue that what they have achieved is even better than an alliance.