随机观测误差对水环境评价的影响

水环境评价既存在模糊性，又不可避免随机性。以往评价大多只考虑了实测指标的物理权重的影响，而很少考虑指标实测过程中不可避免的随机观测误差的影响。本文先应用了最大熵原理来确定在给定约束条件(即已知信息)下，实测指标最小偏差的先验概率分布。在此基础上，应用蒙特卡罗法构造算例，进一步讨论了单一模糊模型和基于最大熵原理的相对隶属度模糊优化评价模型Ⅰ与Ⅱ，分为方差不均一和方差均一两种情况，分别研究了随机观测误差对上述水环境评价模型的影响。结果表明：随机观测误差对水环境评价的影响不容忽视，有时甚至直接改变评价等级；当观测精度有差异，尤其差异较大时，这种影响也随之加大，此时，评价结果只取决于某一(几)项随机观测误差最小的指标。     

倒边盖挖逆作法基坑支护结构可靠性分析

为了解决采用标准Monte Carlo法计算复杂基坑工程上常见小概率失效,导致计算效率低的问题,以南京市湖南路地下商业街工程为工程背景,首先,将随机响应面法与基坑工程三维模型相结合,求解极限功能函数的响应面方程,并用标准Monte Carlo法计算失效概率和可靠指标,探讨采用倒边盖挖逆作法作为基坑支护结构施工方法的可行性;其次,基于该响应面方程,以土体的弹性模量为随机变量参数,采用马尔可夫链蒙特卡罗子集模拟法(MCMC子集模拟法)计算基坑支护结构的失效概率,并与标准Monte Carlo法结果进行对比分析。结果表明：当支护结构最大侧移控制指标为25 mm时,计算得到的可靠指标均大于4.6,即采用倒边盖挖逆作法施工过程中基坑是安全的;10万次和50万次标准Monte Carlo法计算得到的失效概率均为零,说明对于标准Monte Carlo法,在计算小概率失效问题时10万与50万的样本量是不足的;而MCMC子集模拟法用2.98万个样本计算出的结果与标准Monte Carlo法采用100万个样本计算的结果相对误差仅为1.7%,表明MCMC子集模拟法对于小概率失效问题求解的优势。所提算法在一定...     

A new energy model to capture the behavior of energy price processes

Owing to the vague fluctuation of energy prices from time to time, a new energy model, which considers both the mean-reverting behavior and the long memory property, is proposed in this paper. Since the problem of estimating parameters, in discrete time for this model, plays a central role in forecast inference, the problem of estimating the unknown parameters has been dealt with for the fractional Ornstein–Uhlenbeck process observed discretely. The asymptotic properties of these estimates are also provided. The numerical simulation results confirm the theoretical analysis and show that our method is effective. To show how to apply our approach in realistic contexts, an empirical study of energy in China, namely Daqing crude oil, is presented. The empirical results seem reasonable when compared to the real data.     

Fast delta computations in the swap-rate market model

We develop an efficient algorithm to implement the adjoint method that computes sensitivities of an interest rate derivative to different underlying rates in the co-terminal swap-rate market model. The order of computation per step of the new method is shown to be proportional to the number of rates times the number of factors, which is the same as the order in the LIBOR market model.     

Small-sample Properties of Panel Spatial Autoregressive Models: Comparison of the Bayesian and Maximum Likelihood Methods

Abstract

This article considers autoregressive (SAR) models. We method to estimate the parameters of likelihood (ML) method. Our Bayesian by the Monte Carlo studies. We found the efficient as the ML estimators.     

How effective are heuristic solutions for electricity planning in developing countries

Heuristic algorithms have been widely used to provide computationally feasible means of exploring the cost effective balance between grid versus off grid sources for universal electrification in developing countries. By definition in such algorithms however, global optimality is not guaranteed. We present a computationally intensive but globally optimal mixed integer non-linear programming (MINLP) model for electricity planning and use it in a Monte Carlo simulation procedure to test the relative performance of a widely used heuristic algorithm due to [28]. We show that the overall difference in cost is typically small suggesting that the heuristic algorithm is generally cost effective in many situations. However we find that the relative performance of the heuristic algorithm deteriorates with increasing degree of spatial dispersion of unelectrified settlements, as well as increasing spatial remoteness of the settlements from the grid network, suggesting that the effectiveness of the heuristic algorithm is context specific. Further, we find that allocation of off grid sources in the heuristic algorithm solution is often significantly greater than in the MINLP model suggesting that heuristic methods can overstate the role of off-grid solutions in certain situations.     

Estimation employing a priori information within mass appraisal and hedonic pricing models

Both statistical appraisal and hedonic pricing models decompose houses into a set of individual characteristics. Regression estimates yield the contribution of each characteristic to total value. Unfortunately, straightforward application of OLS may produce untenable results such as implausible coefficient magnitudes or incorrect signs. Often the suspected cause is multicollinearity. This article examines the effect on estimation efficiency of differing levels of multicollinearity, R², and a priori information in the form of sub-market cost data, by comparing inequality restricted least squares (IRLS) with OLS in a series of Monte Carlo experiments. The IRLS procedure investigated here hybridizes the statistical market approach implemented by OLS, and the more traditional cost approach. The experiments show dramatic gains in estimation efficiency from exploiting a priori information through IRLS.     

Bias in estimates of discrimination and default in mortgage lending: The effects of simultaneity and self-selection

The common practices of estimating single-equation models of mortgage rejection to test for discrimination in mortgage markets or single-equation ex ante mortgage default equations to validate underwriting criteria produce biased and inconsistent parameter estimates. This is due to problems of simultaneous equations bias which arise because, in a world of imperfect information, mortgage terms are not exogenous to the rejection or default decision. In addition, mortgage default estimates are also subject to selection bias. Monte Carlo experiments are used to study the nature and extent of likely bias in single-equation estimation results. We find that rejection equation estimates indicate discrimination when none exists and that estimated coefficients of mortgage terms, such as the loan-to-value ratio, are also subject to significant bias in both rejection and default equations.     

MC's for MCMC'ists

We develop a minimum amount of theory of Markov chains at as low a level of abstraction as possible in order to prove two fundamental probability laws for standard Markov chain Monte Carlo algorithms:
1. The law of large numbers explains why the algorithm works: it states that the empirical means calculated from the samples converge towards their "true" expected values, viz. expectations with respect to the invariant distribution of the associated Markov chain (=the target distribution of the simulation).
2. The central limit theorem expresses the deviations of the empirical means from their expected values in terms of asymptotically normally distributed random variables. We also present a formula and an estimator for the associated variance.     

Predicting Variability in a Lake Ontario Phosphorus Model

The prediction of a model always has a degree of uncertainty. Because the level of uncertainty is inversely related to the value of information contained in the prediction, there is a need to quantify the uncertainty. One approach to estimate prediction uncertainty is first-order error analysis. In this method, the error in a characteristic (variable or parameter) is defined by its first nonzero moment (the variance). Errors are propagated through the model using first-order terms in the Taylor series, and the variances are then combined to yield the total prediction uncertainty. An alternative approach to model prediction error analysis is Monte Carlo simulation. In this technique, probability density functions are assigned to each characteristic (variable or parameter), reflecting the uncertainty in that characteristic. Then, values are randomly selected from the distribution for each term and inserted into the model, to calculate a prediction. Repeating this process a number of times produces a distribution of predicted values, which reflects the combined uncertainties. These two approaches (first-order error analysis and Monte Carlo simulation) are applied to Lake Ontario data using a steady state mass balance phosphorus model. Comparisons are made which suggest guidelines for the use of each.