Nonparametric Uncertainty Quantification for Stochastic Gradient Flows

This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce a stochastic matrix whose generator is a discrete approximation to the backward Kolmogorov operator of the underlying dynamics. The eigenvectors of this stochastic matrix, which we will refer to as the diffusion coordinates, are discrete approximations to the eigenfunctions of the Kolmogorov operator and form an orthonormal basis for functions defined on the data set. Using this basis, we consider the projection of three uncertainty quantification (UQ) problems (prediction, filtering, and response) into the diffusion coordinates. In these coordinates, the nonlinear prediction and response problems reduce to solving systems of infinite-dimensional linear ordinary differential equations. Similarly, the continuous-time nonlinear filtering problem reduces to solving a system of infinite-dimensional linear stochastic differential equations. Solving the UQ problems then reduces to solving the corresponding truncated linear systems in finitely many diffusion coordinates. By solving these systems we give a model-free algorithm for UQ on gradient flow systems with isotropic diffusion. We numerically verify these algorithms on a 1-dimensional linear gradient flow system where the analytic solutions of the UQ problems are known. We also apply the algorithm to a chaotically forced nonlinear gradient flow system which is known to be well approximated as a stochastically forced gradient flow.Comment: Find the associated videos at: http://personal.psu.edu/thb11

Milkshake Prices, International Reserves, and the Mexican Peso

Menu prices from 13 international restaurant franchises that operate in both El Paso and Ciudad Juarez are utilized to examine the behavior over time of the peso/dollar exchange rate. Parametric and non-parametric tests indicate that the price ratio alone provides a biased estimator of the exchange rate. In addition to the multi-product price ratio, the empirical analysis also incorporates interst rate prity and balance of payment variables. The combination of unique microeconomic sample data with national macroeconomic variables illustrates one manner in which border economies provide information regarding the interplay of financial markets between Mexico and the United States.Prices; exchange rates; border economics

Decentralization and Local Governments’ Performance: How Does Fiscal Autonomy Affect Spending Efficiency?

In Italy, as in other countries around the world, recent reforms share the goal of increasing the fiscal autonomy of lower tiers of governments, from Regions to Municipalities, in order to align spending with funding responsibilities and increase the efficiency in the provision of essential public services. The purpose of this paper is to assess spending efficiency of local governments and to investigate the effects of tax decentralization, focusing on the role played by incumbent politicians’ accountability. The analysis relies on a sample of Italian municipalities and exploits both parametric (SFA) and nonparametric (DEA) techniques to study spending inefficiency and its main determinants. Consistently with modern fiscal federalism theories, our results show that more fiscally autonomous municipalities exhibit less inefficient behaviours. We also find that the shorter is the distance from new elections, the higher is excess spending, thus giving further support to the traditional “electoral budget cycle” agument. Other political features of governing coalition, such as age and gender of the mayor, do not seem to exert any significant impact on inefficiency levels.Local governments, Fiscal autonomy, Political accountability, Spending efficiency, Parametric and nonparametric frontiers

Development of a quantitative health index and diagnostic method for efficient asset management of power transformers

Power transformers play a very important role in electrical power networks and are frequently operated longer than their expected design life. Therefore, to ensure their best operating performance in a transmission network, the fault condition of each transformer must be assessed regularly. For an accurate fault diagnosis, it is important to have maximum information about an individual transformer based on unbiased measurements. This can best be achieved using artificial intelligence (AI) that can systematically analyse the complex features of diagnostic measurements. Clustering techniques are a form of AI that is particularly well suited to fault diagnosis. To provide an assessment of transformers, a hybrid k-means algorithm, and probabilistic Parzen window estimation are used in this research. The clusters they form are representative of a single or multiple fault categories. The proposed technique computes the maximum probability of transformers in each cluster to determine their fault categories. The main focus of this research is to determine a quantitative health index (HI) to characterize the operating condition of transformers. Condition assessment tries to detect incipient faults before they become too serious, which requires a sensitive and quantified approach. Therefore, the HI needs to come from a proportionate system that can estimate health condition of transformers over time. To quantify this condition, the General Regression Neural Network (GRNN), a type of AI, has been chosen in this research. The GRNN works well with small sets of training data and avoids the needs to estimate large sets of model parameters, following a largely non-parametric approach. The methodology used here regards transformers as a collection of subsystems and summarizes their individual condition into a quantified HI based on the existing agreed benchmarks drawn from IEEE and CIGRE standards. To better calibrate the HI, it may be mapped to a failure probability estimate for each transformer over the coming year. Experimental results of the research show that the proposed methods are more effective than previously published approaches when diagnosing critical faults. Moreover, this novel HI approach can provide a comprehensive assessment of transformers based on the actual condition of their individual subsystems

Stochastic expansions using continuous dictionaries: L\'{e}vy adaptive regression kernels

This article describes a new class of prior distributions for nonparametric function estimation. The unknown function is modeled as a limit of weighted sums of kernels or generator functions indexed by continuous parameters that control local and global features such as their translation, dilation, modulation and shape. L\'{e}vy random fields and their stochastic integrals are employed to induce prior distributions for the unknown functions or, equivalently, for the number of kernels and for the parameters governing their features. Scaling, shape, and other features of the generating functions are location-specific to allow quite different function properties in different parts of the space, as with wavelet bases and other methods employing overcomplete dictionaries. We provide conditions under which the stochastic expansions converge in specified Besov or Sobolev norms. Under a Gaussian error model, this may be viewed as a sparse regression problem, with regularization induced via the L\'{e}vy random field prior distribution. Posterior inference for the unknown functions is based on a reversible jump Markov chain Monte Carlo algorithm. We compare the L\'{e}vy Adaptive Regression Kernel (LARK) method to wavelet-based methods using some of the standard test functions, and illustrate its flexibility and adaptability in nonstationary applications.Comment: Published in at http://dx.doi.org/10.1214/11-AOS889 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Development of a quantitative health index and diagnostic method for efficient asset management of power transformers

Power transformers play a very important role in electrical power networks and are frequently operated longer than their expected design life. Therefore, to ensure their best operating performance in a transmission network, the fault condition of each transformer must be assessed regularly. For an accurate fault diagnosis, it is important to have maximum information about an individual transformer based on unbiased measurements. This can best be achieved using artificial intelligence (AI) that can systematically analyse the complex features of diagnostic measurements. Clustering techniques are a form of AI that is particularly well suited to fault diagnosis. To provide an assessment of transformers, a hybrid k-means algorithm, and probabilistic Parzen window estimation are used in this research. The clusters they form are representative of a single or multiple fault categories. The proposed technique computes the maximum probability of transformers in each cluster to determine their fault categories. The main focus of this research is to determine a quantitative health index (HI) to characterize the operating condition of transformers. Condition assessment tries to detect incipient faults before they become too serious, which requires a sensitive and quantified approach. Therefore, the HI needs to come from a proportionate system that can estimate health condition of transformers over time. To quantify this condition, the General Regression Neural Network (GRNN), a type of AI, has been chosen in this research. The GRNN works well with small sets of training data and avoids the needs to estimate large sets of model parameters, following a largely non-parametric approach. The methodology used here regards transformers as a collection of subsystems and summarizes their individual condition into a quantified HI based on the existing agreed benchmarks drawn from IEEE and CIGRE standards. To better calibrate the HI, it may be mapped to a failure probability estimate for each transformer over the coming year. Experimental results of the research show that the proposed methods are more effective than previously published approaches when diagnosing critical faults. Moreover, this novel HI approach can provide a comprehensive assessment of transformers based on the actual condition of their individual subsystems

Milkshake Prices, International Reserves, and the Mexican Peso

Menu prices from 13 international restaurant franchises that operate in both El Paso and Ciudad Juarez are utilized to examine the behavior over time of the peso/dollar exchange rate. Parametric and non-parametric tests indicate that the price ratio alone provides a biased estimator of the exchange rate. In addition to the multi-product price ratio, the empirical analysis also incorporates interst rate prity and balance of payment variables. The combination of unique microeconomic sample data with national macroeconomic variables illustrates one manner in which border economies provide information regarding the interplay of financial markets between Mexico and the United States

Incidence and impact of land conflict in Uganda

While there is a large, though inconclusive, literature on the impact of land titles in Africa, little attention has been devoted to the study of land conflict, despite evidence on increasing incidence of such conflicts. The authors use data from Uganda to explore who is affected by land conflicts, whether recent legal changes have helped to reduce their incidence, and to assess their impact on productivity. Results indicate that female-headed households and widows are particularly affected and that the passage of the 1998 Land Act has failed to reduce the number of pending land conflicts. The authors also find evidence of a significant and quantitatively large productivity-reducing impact of land conflicts. This suggests that, especially in Africa, attention to land-related conflicts and exploration of ways to prevent and speedily resolve them would be an important area for policy as well as research.Environmental Economics&Policies,Municipal Housing and Land,Land and Real Estate Development,Real Estate Development,Agricultural Knowledge&Information Systems,Real Estate Development,Agricultural Knowledge&Information Systems,Environmental Economics&Policies,Municipal Housing and Land,Land and Real Estate Development

Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study

Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced