scholarly journals Functional Quantization Based Stratified Sampling Methods

2010 ◽  
Author(s):  
Gilles Pages ◽  
Sylvain Corlay
Keyword(s):  
Sampling Methods ◽  
Stratified Sampling ◽  
Functional Quantization

scholarly journals Functional quantization-based stratified sampling methods

2015 ◽  
Vol 21 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Sylvain Corlay ◽  
Gilles Pagès
Keyword(s):  
Variance Reduction ◽  
Sampling Methods ◽  
Brownian Bridge ◽  
Reduction Factor ◽  
Stratified Sampling ◽  
Lipschitz Continuous ◽  
Infinite Dimensional ◽  
Path Dependent ◽  
Functional Quantization ◽  
Continuous Functionals

AbstractIn this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and the variance reduction that can be achieved with stratified sampling. We first put the emphasis on the consistency of quantization for partitioning the state space in stratified sampling methods in both finite and infinite-dimensional cases. We show that the proposed quantization-based strata design has uniform efficiency among the class of Lipschitz continuous functionals. Then a stratified sampling algorithm based on product functional quantization is proposed for path-dependent functionals of multi-factor diffusions. The method is also available for other Gaussian processes such as Brownian bridge or Ornstein–Uhlenbeck processes. We derive in detail the case of Ornstein–Uhlenbeck processes. We also study the balance between the algorithmic complexity of the simulation and the variance reduction factor.

scholarly journals A Stratified Sampling Approach for Improved Sampling from a Calibrated Ensemble Forecast Distribution

2016 ◽  
Vol 17 (9) ◽  
pp. 2405-2417 ◽  
Author(s):  
Yiming Hu ◽  
Maurice J. Schmeits ◽  
Schalk Jan van Andel ◽  
Jan S. Verkade ◽  
Min Xu ◽  
...  
Keyword(s):  
Sampling Methods ◽  
Skill Score ◽  
Predictive Distribution ◽  
Ensemble Forecast ◽  
Stratified Sampling ◽  
Dependence Structure ◽  
Ensemble Forecasts ◽  
Empirical Copula ◽  
Space Dependence ◽  
Better Than

Abstract Before using the Schaake shuffle or empirical copula coupling (ECC) to reconstruct the dependence structure for postprocessed ensemble meteorological forecasts, a necessary step is to sample discrete samples from each postprocessed continuous probability density function (pdf), which is the focus of this paper. In addition to the equidistance quantiles (EQ) and independent random (IR) sampling methods commonly used at present, the stratified sampling (SS) method is proposed. The performance of the three sampling methods is compared using calibrated GFS ensemble precipitation reforecasts over the Xixian basin in China. The ensemble reforecasts are first calibrated using heteroscedastic extended logistic regression (HELR), and then the three sampling methods are used to sample calibrated pdfs with a varying number of discrete samples. Finally, the effect of the sampling method on the reconstruction of ensemble members with preserved space dependence structure is analyzed by using EQ, IR, and SS in ECC for reconstructing postprocessed ensemble members for four stations in the Xixian basin. There are three main results. 1) The HELR model has a significant improvement over the raw ensemble forecast. It clearly improves the mean and dispersion of the predictive distribution. 2) Compared to EQ and IR, SS can better cover the tails of the calibrated pdfs and a better dispersion of calibrated ensemble forecasts is obtained. In terms of probabilistic verification metrics like the ranked probability skill score (RPSS), SS is slightly better than EQ and clearly better than IR, while in terms of the deterministic verification metric, root-mean-square error, EQ is slightly better than SS. 3) ECC-SS, ECC-EQ, and ECC-IR all calibrate the raw ensemble forecast, but ECC-SS shows a better dispersion than ECC-EQ and ECC-IR in this study.

Absorptive Capacity, Innovativeness and the Performance of Micro-enterprises in Malaysia

2017 ◽  
Vol 21 (3) ◽  
pp. 243-249 ◽  
Author(s):  
Abdullah Al Mamun ◽  
Nik Maheran Nik Muhammad ◽  
Mohammad Bin Ismail
Keyword(s):  
Absorptive Capacity ◽  
Sampling Methods ◽  
Peninsular Malaysia ◽  
Complete Data ◽  
Stratified Sampling ◽  
Significant Positive Effect ◽  
Cross Sectional ◽  
Cross Sectional Design ◽  
Positive Effect ◽  
Micro Enterprises

This study examines the effect of the entrepreneur’s innovativeness and absorptive capacity on micro-enterprise innovativeness and the performance of micro-enterprises owned and managed by women micro-entrepreneurs in Peninsular Malaysia. This study adopted a cross-sectional design and stratified sampling methods, and collected complete data from 417 micro-entrepreneurs. Findings of this study reveal that women micro-entrepreneurs’ innovativeness and absorptive capacity have a significant positive effect on micro-enterprise innovativeness and the performance of micro-enterprises. The development programmes and policies on innovation and SMEs should therefore emphasize on promoting innovativeness and improving the absorptive capacity among the women micro-entrepreneurs to improve the performance of micro-enterprises.

Brachytherapy dose-volume histogram computations using optimized stratified sampling methods

2002 ◽  
Vol 29 (3) ◽  
pp. 424-432 ◽  
Author(s):  
K. Karouzakis ◽  
M. Lahanas ◽  
N. Milickovic ◽  
S. Giannouli ◽  
D. Baltas ◽  
...  
Keyword(s):  
Sampling Methods ◽  
Stratified Sampling ◽  
Dose Volume Histogram ◽  
Dose Volume

scholarly journals Computationally effient geostatistical simulation for uncertainty propagation in models with spatially distributed parameters

2017 ◽  
Author(s):  
Στυλιανός Λιοδάκης
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Sampling Methods ◽  
Uncertainty Propagation ◽  
Stratified Sampling ◽  
Spatial Context ◽  
Flow And Transport ◽  
Model Predictions ◽  
Spatially Distributed

Uncertainty is endemic in geospatial data due to the imperfect means of recording, processing, and representing spatial information. Propagating geospatial model inputs inherent uncertainty to uncertainty in model predictions is a critical requirement in each model's impact assessment and risk-conscious policy decision-making. It is still extremely difficult, however, to perform in practice uncertainty analysis of model outputs, particularly in complex spatially distributed environmental models, partially due to computational constraints.In the field of groundwater hydrology, the "stochastic revolution" has produced an enormous number of theoretical publications and greatly influenced our perspective on uncertainty and heterogeneity; it has had relatively little impact, however, on practical modeling. Monte Carlo simulation using simple random (SR) sampling from a multivariate distribution is one of the most widely used family of methods for uncertainty propagation in hydrogeological flow and transport model predictions, the other being analytical propagation.Real-life hydrogeological problems however, consist of complex and non-linear three dimensional groundwater models with millions of nodes and irregular boundary conditions. The number of Monte-Carlo runs required in these cases, depends on the number of uncertain parameters and on the relative accuracy required for the distribution of model predictions. In the context of sensitivity studies, inverse modelling or Monte-Carlo analyses, the ensuing computational burden is usually overwhelming and computationally impractical. These tough computational constrains have to be relaxed and removed before meaningful stochastic groundwater modeling applications are possible.A computationally efficient alternative to classical Monte Carlo simulation based on SR sampling is Latin hypercube (LH) sampling, a form of stratified random sampling. The latter yields a more representative distribution of model outputs (in terms of smaller sampling variability of their statistics) for the same number of input simulated realizations. The ability to generate unbiased LH realizations becomes critical in a spatial context, where random variables are geo-referenced and exhibit spatial correlation, to ensure unbiased outputs of complex models. On this regard, this dissertation offers a detailed analysis of LH sampling and compares it with SR sampling in a hydrogeological context. Additionally, two alternative stratified sampling methods, here named stratified likelihood (SL) sampling and minimum energy (ME) sampling, are examined (proposed in a spatial context) and their efficiency is further compared to SR and LH in a hydrogeological context; also accounting for the uncertainty related to the particular model at hand via a two step sampling method. All three stratified sampling methods (accounting for model sensitivity in the second case study) were found in this work to be more efficient than simple random sampling.Additionally, this thesis proposes a novel method for the expansion of the application domain of LH sampling to very large regular grids which is the common case in environmental (hydrogeological or not) models. More specifically, a novel combination of Stein's Latin Hypercube sampling with a Monte Carlo simulation method applicable over high discretization domains is proposed, and its performance is further validated in 2D and 3D hydrogeological problems of flow and transport in a mid-heterogeneous porous media, both consisting of about $1$ million nodes. Last, an additional novel extension of the proposed LH sampling on large grids is adopted for conditional high discretized problems. In this case too, the performance of the proposed approach is evaluated in a 3D hydrogeological model of flow and transport. Results indicate that both extensions (conditional and not) of LH sampling on large grids facilitate efficient uncertainty propagation with fewer model runs due to more representative model inputs. Overall, it could be argued that all the proposed methodological approaches could reduce the time and computer resources required to perform uncertainty analysis in hydrogeological flow and transport problems. Additionally, since it is the first time that stratified sampling is performed over high discretization domains, it could be argued that the proposed extensions of LH sampling on large grids could be considered a milestone for future uncertainty analysis efforts. Moreover, all the proposed stratified methods could contribute to a wider application of uncertainty analysis endeavors in a Monte Carlo framework for any spatially distributed impact assessment study.

scholarly journals Competitive intelligence as an important contributor to the growth of banks: A Zimbabwean perspective

2014 ◽  
Vol 3 (3) ◽  
pp. 81-95
Author(s):  
Alexander Maune
Keyword(s):  
Strategic Planning ◽  
Research Methodology ◽  
Banking Sector ◽  
Sampling Methods ◽  
Business Environment ◽  
Stratified Sampling ◽  
Competitive Intelligence ◽  
Cross Sectional ◽  
Important Contributor

This paper explores how competitive intelligence has been an important contributor of growth in banks in Zimbabwe and how the banks are making use of competitive intelligence for such growth. The paper used a descriptive cross-sectional research methodology. Data was collected through questionnaires and interviews. Purposive and stratified sampling methods were used. The paper found that most Zimbabwean banks have undertaken competitive intelligence in one way or another for strategic planning and better understanding the competitive business environment and competitors. The findings from this research will assist the entire banking sector and will be of great academic value.

The Use of APL in Forest Sampling and Mensuration

1981 ◽  
Vol 57 (2) ◽  
pp. 71-76
Author(s):  
Stephen J. Titus
Keyword(s):  
Programming Language ◽  
Sampling Methods ◽  
Stratified Sampling ◽  
Random Point ◽  
Stand Volume ◽  
Variable Radius ◽  
Direct Definition

Use of the APL programming language in solving selected problems in forest sampling and mensuration topics is illustrated using "direct definition" APL functions. Mensuration topics include the crown competition factor and log, tree, and stand volume. Simple random, point (variable radius plot), and stratified sampling methods are discussed.

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