![On Maximum Entropy [p]ps-sampling with Fixed Sample Size PDF](https://books.google.com/books/content/images/frontcover/gzautgAACAAJ?fife=w150-h200)
Author: Johan JonassonPublisher:
ISBN:
Category :
Languages : en
Pages : 17
Book Description
On Maximum Entropy [p]ps-sampling with Fixed Sample Size
![On Maximum Entropy [p]ps-sampling with Fixed Sample Size PDF](https://books.google.com/books/content/images/frontcover/gzautgAACAAJ?fife=w80-h100)
Author: Johan JonassonOn Maximum Entropy $ \pi $ Ps-sampling with Fixed Sample Size
Author: J. JonassonEntropy Measures for Environmental Data
Author: Linda AltieriPublisher: Springer Nature
ISBN: 9819725461
Category :
Languages : en
Pages : 172
Book Description
Maximum-Entropy Sampling
Author: Marcia FampaPublisher: Springer Nature
ISBN: 3031130782
Category : Mathematics
Languages : en
Pages : 206
Book Description
This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.
Unequal Probability Sampling and Repeated Surveys
Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
This document is divided into two parts. The first part revolves around the properties of some unequal probability survey sampling designs, and the second part deals with repeated surveys. While the topics developed in these two parts appear to be largely different, they are in fact related. The first part is devoted to the study of properties of two sampling designs with fixed size. In a first chapter we show that maximum entropy sampling with fixed size is more efficient than sampling with replacement. In a second chapter we prove that systematic sampling is a minimum support design. We also give some results on the variance of the Horvitz-Thompson estimator for maximum entropy and for minimum support designs. The second part begins with a case study of the estimation of variance of evolutions in the Swiss panel on value added. In a second chapter, we give covariance estimators for rotating panels with unequal inclusion probabilities. Finally, we describe a coordination method of maximum entropy samples that was developed for the Swiss Federal Statistical Office.
Maximum Entropy Probability Distribution
Author: Jenny FarmerPublisher:
ISBN:
Category :
Languages : en
Pages : 140
Book Description
Given a set of randomly sampled experimental data, a numeric algorithm has been developed to determine a probability distribution function that represents the data. The algorithm is based on the maximum entropy method in information theory, which states that the solution that maximizes entropy while satisfying known constraints is presumed to be the correct solution. The probability distribution function is expressed as an exponential of a series expansion over Chebyshev polynomials where the expansion coefficients are formally Lagrange multipliers and must be determined. The method for finding these Lagrange multipliers is through an iterative trial-and-error approach. After each guess for the coefficients, the trial solution is evaluated according to how well it represents the data. This assessment is performed by using the cumulative distribution function to transform the data to uniformly distributed random data, and then comparing the transformed data to known results for a uniform distribution using binning and ordered statistics. The algorithm is presented in the form of a highly adaptive and flexible tool that does not assume prior knowledge about the data, but provides many documented settings to allow for maximum efficiency in the event the user has more information about the data or has specific requirements. To demonstrate the power and flexibility of this approach, it has been tested and compared against known distributions, many of which have specific properties known to cause standard methods to fail. Each of these examples demonstrates a convergence to the true function as the sample size increases.
Probability Proportional to Size ([pi Sign] Ps) Sampling Using Ranks
![Probability Proportional to Size ([pi Sign] Ps) Sampling Using Ranks PDF](https://books.google.com/books/content/images/frontcover/-6kOvwEACAAJ?fife=w80-h100)
Author: Tommy WrightPublisher:
ISBN:
Category : Sampling (Statistics)
Languages : en
Pages : 17
Book Description
The Mathematical Theory of Communication
Author: Claude E ShannonPublisher: University of Illinois Press
ISBN: 025209803X
Category : Language Arts & Disciplines
Languages : en
Pages : 141
Book Description
Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Author: Ali Mohammad-DjafariPublisher: American Inst. of Physics
ISBN: 9780735403710
Category : Science
Languages : en
Pages : 616
Book Description
The MaxEnt workshops are devoted to Bayesian inference and maximum entropy methods in science and engineering. In addition, this workshop included all aspects of probabilistic inference, such as foundations, techniques, algorithms, and applications. All papers have been peer-reviewed.
Machine Learning in Computer Vision
Author: Nicu SebePublisher: Springer Science & Business Media
ISBN: 1402032757
Category : Computers
Languages : en
Pages : 253
Book Description
The goal of this book is to address the use of several important machine learning techniques into computer vision applications. An innovative combination of computer vision and machine learning techniques has the promise of advancing the field of computer vision, which contributes to better understanding of complex real-world applications. The effective usage of machine learning technology in real-world computer vision problems requires understanding the domain of application, abstraction of a learning problem from a given computer vision task, and the selection of appropriate representations for the learnable (input) and learned (internal) entities of the system. In this book, we address all these important aspects from a new perspective: that the key element in the current computer revolution is the use of machine learning to capture the variations in visual appearance, rather than having the designer of the model accomplish this. As a bonus, models learned from large datasets are likely to be more robust and more realistic than the brittle all-design models.