Sampling (statistics)

Gy's sampling theory

Gy's sampling theory is a theory about the sampling of materials, developed by Pierre Gy from the 1950s to beginning 2000s in articles and books including: * (1960) Sampling nomogram * (1979) Sampling of particulate materials; theory and practice * (1982) Sampling of particulate materials; theory and practice; 2nd edition * (1992) Sampling of Heterogeneous and Dynamic Material Systems: Theories of Heterogeneity, Sampling and Homogenizing * (1998) Sampling for Analytical Purposes The abbreviation "TOS" is also used to denote Gy's sampling theory. Gy's sampling theory uses a model in which the sample taking is represented by independent Bernoulli trials for every particle in the parent population from which the sample is drawn. The two possible outcomes of each Bernoulli trial are: (1) the particle is selected and (2) the particle is not selected. The probability of selecting a particle may be different during each Bernoulli trial. The model used by Gy is mathematically equivalent to Poisson sampling. Using this model, the following equation for the variance of the sampling error in the mass concentration in a sample was derived by Gy: in which V is the variance of the sampling error, N is the number of particles in the population (before the sample was taken), q i is the probability of including the ith particle of the population in the sample (i.e. the first-order inclusion probability of the ith particle), m i is the mass of the ith particle of the population and a i is the mass concentration of the property of interest in the ith particle of the population. It is noted that the above equation for the variance of the sampling error is an approximation based on a linearization of the mass concentration in a sample. In the theory of Gy, correct sampling is defined as a sampling scenario in which all particles have the same probability of being included in the sample. This implies that q i no longer depends on i, and can therefore be replaced by the symbol q. Gy's equation for the variance of the sampling error becomes: where abatch is the concentration of the property of interest in the population from which the sample is to be drawn and Mbatch is the mass of the population from which the sample is to be drawn. It has been noted that a similar equation had already been derived in 1935 by Kassel and Guy. Two books covering the theory and practice of sampling are available; one is the Third Edition of a high-level monograph and the other an introductory text. (Wikipedia).

Video thumbnail

(PP 6.1) Multivariate Gaussian - definition

Introduction to the multivariate Gaussian (or multivariate Normal) distribution.

From playlist Probability Theory

Video thumbnail

What is a Sampling Distribution?

Intro to sampling distributions. What is a sampling distribution? What is the mean of the sampling distribution of the mean? Check out my e-book, Sampling in Statistics, which covers everything you need to know to find samples with more than 20 different techniques: https://prof-essa.creat

From playlist Probability Distributions

Video thumbnail

Statistics: Sampling Methods

This lesson introduces the different sample methods when conducting a poll or survey. Site: http://mathispower4u.com

From playlist Introduction to Statistics

Video thumbnail

Purposive Sampling

What is purposive (deliberate) sampling? Types of purposive sampling, advantages and disadvantages. Check out my e-book, Sampling in Statistics, which covers everything you need to know to find samples with more than 20 different techniques: https://prof-essa.creator-spring.com/listing/sam

From playlist Sampling

Video thumbnail

(ML 16.7) EM for the Gaussian mixture model (part 1)

Applying EM (Expectation-Maximization) to estimate the parameters of a Gaussian mixture model. Here we use the alternate formulation presented for (unconstrained) exponential families.

From playlist Machine Learning

Video thumbnail

Non Probability Sampling

Overview of non probability sampling; advantages and disadvantages, types. Check out my e-book, Sampling in Statistics, which covers everything you need to know to find samples with more than 20 different techniques: https://prof-essa.creator-spring.com/listing/sampling-in-statistics

From playlist Sampling

Video thumbnail

Multi-ethnic GWAS study of aorta diameter and polygenic risk prediction for thoracic aortic disease

Dr. Catherine Tcheandjieu, Stanford University 2020 Stanford.Berkeley.UCSF Next Generation Faculty Symposium

From playlist 2020 Stanford.Berkeley.UCSF Next Generation Faculty Symposium

Video thumbnail

The Power of Sampling by Peter W. Glynn

Infosys-ICTS Turing Lectures The Power of Sampling Speaker: Peter W. Glynn (Stanford University, USA) Date: 14 August 2019, 16:00 to 17:00 Venue: Ramanujan Lecture Hall, ICTS Bangalore Sampling-based methods arise in many statistical, computational, and engineering settings. In engine

From playlist Infosys-ICTS Turing Lectures

Video thumbnail

Anup Rao : Communication Complexity and Information Complexity - 4

The study of efficient communication communication using tools from information theory has led to many interesting results for basic problems in the last few decades. In this mini-course, we shall learn the basic concepts of communication complexity and see some its applications to distrib

From playlist Nexus Trimester - 2016 -Tutorial Week at CIRM

Video thumbnail

Perception, Action, and Experience: Retying the Golden Braid

Intuitively, our mental life involves, as Andy Clark evocatively puts it, “a seamless unfolding of perception, action and experience: a golden braid in which each element twines intimately with the rest.” Cognitive science is widely held to have decisively unraveled these strands, inspirin

From playlist Whitney Humanities Center

Video thumbnail

Intro to Sample Proportions

An overview and introduction to understanding sampling distributions of proportions [sample proportions] and how to calculate them

From playlist Unit 7 Probability C: Sampling Distributions & Simulation

Video thumbnail

JUDGMENT and SNOWBALL Non-random Sampling (12-6)

Judgment sampling (a.k.a., expert sampling, authoritative sampling, purposive sampling, judgmental sampling) is a technique in which the sample is selected based on the researcher’s (or other experts’) existing knowledge or professional judgment. It may provide highly accurate findings wit

From playlist Sampling Distributions in Statistics (WK 12 - QBA 237)

Video thumbnail

Jennifer Listgarten: "Structured Populations in Genetics"

Computational Genomics Summer Institute 2016 "Structured Populations in Genetics" Jennifer Listgarten, Microsoft Research Institute for Pure and Applied Mathematics, UCLA July 21, 2016 For more information: http://computationalgenomics.bioinformatics.ucla.edu/

From playlist Computational Genomics Summer Institute 2016

Video thumbnail

05c Data Analytics: Distribution Transform

A short discussion on the topic of distribution transforms, e.g. transforming your data to the parametric Gaussian distribution.

From playlist Data Analytics and Geostatistics

Video thumbnail

Distinguished Visitor Lecture by Xihong Lin Scalable Analysis of Large Multi Ethic Biobanks and ...

Scalable Analysis of Large Multi Ethic Biobanks and Whole Genome Sequencing Studies Xihong Lin Harvard University, USA

From playlist Distinguished Visitors Lecture Series

Video thumbnail

Bruno Klingler - 3/4 Tame Geometry and Hodge Theory

Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic. On the other hand, according to both the Hodge conjecture and the Grothendie

From playlist Bruno Klingler - Tame Geometry and Hodge Theory

Video thumbnail

Invariant Measures for Non-autonomous systems.... by Sergey Kryzhevich

PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.

From playlist Smooth And Homogeneous Dynamics

Video thumbnail

filter / edges - CS50 Walkthroughs 2019

*** This is CS50, Harvard University's introduction to the intellectual enterprises of computer science and the art of programming. *** HOW TO SUBSCRIBE http://www.youtube.com/subscription_center?add_user=cs50tv HOW TO TAKE CS50 edX: https://cs50.edx.org/ Harvard Extension School: ht

From playlist CS50 Walkthroughs 2019

Video thumbnail

C. Soulé - Arithmetic Intersection (Part4)

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic intersection number of ¯L and ¯M. We shall explain the definition and the basic properties of

From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes

Video thumbnail

Sampling Distributions and Confidence Intervals (Part 1 of Intro to Statistics)

Intro to Statistics Part 1. This is part one of a short course on foundations of statistics. If you've never taken a statistics class before (or even if you have), this course will walk you through what you need to know. Check out my e-book, Sampling in Statistics, which covers everythin

From playlist Intro to Statistics

Related pages

Variance | Poisson sampling | Sampling error | Correct sampling | Linearization