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An Illustrated Guide to Mobile Technology
An Illustrated Guide to Mobile Technology

Cellular phone technology – its historical origins, impact on business, technical architecture of cellular systems

2015

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Stories

Published in

Towards Data Science

·Sep 12

The Markov and the Bienaymé–Chebyshev Inequalities

A deep dive into the meaning of the two bounds and into the remarkable series of happenings that led to their discovery — It’s not often that the universe tells you that something simply cannot be done. It doesn’t matter how smart you are or how lavishly bank-rolled you are or what corner of the universe you call your own. When the universe says “Not possible”, there are no two ways around it…

Andrey Markov

17 min read

The Markov and the Bienaymé–Chebyshev Inequalities
The Markov and the Bienaymé–Chebyshev Inequalities
Andrey Markov

17 min read


Published in

Towards Data Science

·Jul 12

Unraveling the Law of Large Numbers

The LLN is interesting as much for what it does not say as for what it does — O n August 24, 1966, a talented playwright by the name Tom Stoppard staged a play in Edinburgh, Scotland. The play had a curious title, “Rosencrantz and Guildenstern Are Dead.” Its central characters, Rosencrantz and Guildenstern, are childhood friends of Hamlet (of Shakespearean fame). The play opens with Guildenstern…

The Law Of Large Numbers

15 min read

Unraveling the Law of Large Numbers
Unraveling the Law of Large Numbers
The Law Of Large Numbers

15 min read


Published in

Towards Data Science

·Jun 17

A Deep Dive into the Science of Statistical Expectation

How we come to expect something, what it means to expect anything, and the math that gives rise to the meaning. — It was the summer of 1988 when I stepped onto a boat for the first time in my life. It was a passenger ferry from Dover, England to Calais, France. I didn’t know it then, but I was catching the tail end of the golden era of Channel crossings by…

Statistical Expectation

29 min read

A Deep Dive into the Science of Statistical Expectation
A Deep Dive into the Science of Statistical Expectation
Statistical Expectation

29 min read


Published in

Towards Data Science

·May 12

The Aspiring Statistican’s Introduction to Random Variables

When it comes to yelling “Surprise!”, the universe never gets tired. — In this article, we’ll take a contemplative walk across the land of chance. We’ll learn about random walks, about discrete and continuous random variables, and about their probability distributions. We’ll understand why it’s meaningless to assign a probability to a continuous random variable’s value. And in doing so, we’ll unearth…

Random Variables

31 min read

The Aspiring Statistican’s Introduction to Random Variables
The Aspiring Statistican’s Introduction to Random Variables
Random Variables

31 min read


Mar 13

A Tutorial On Solving a System of Linear Regression Equations

How to fit a system of regression equations using Python and Statsmodels — In this article, we’ll walk through a tutorial on how to fit a system of linear regression models using the Generalized Least Squares (GLS) technique. We’ll use the term ‘regression model’ and ‘regression equation’ more or less interchangeably. This tutorial assumes that you already know the concepts and theory behind…

Regression Equations

14 min read

A Tutorial On Solving a System of Linear Regression Equations
A Tutorial On Solving a System of Linear Regression Equations
Regression Equations

14 min read


Dec 9, 2022

An Illustrated Introduction to Systems of Regression Equations

How to fit a mesh of inter-dependent regression models using techniques such as GLS. — In this article, we’ll study a very interesting topic in statistical modeling, namely, how to fit a system of inter-dependent regression models. At first glance, this topic may appear a bit esoteric, but systems of interconnected regression models pop up surprisingly often in real life. In the rest of this…

System Of Equations

25 min read

An Illustrated Introduction to Systems of Regression Equations
An Illustrated Introduction to Systems of Regression Equations
System Of Equations

25 min read


Nov 20, 2022

A Tutorial on Generalized Least Squares Regression Using Python and Statsmodels

We’ll learn how to use the GLS estimator to fit a linear model on a real world data set — The Generalized Least Squares (GLS) estimator is an effective alternative to the Ordinary Least Squares (OLS) estimator for fitting linear models on data sets that exhibit heteroskedasticity (i.e., non-constant variance) and/or auto-correlation. In a previous article, we had detailed out the motivation for the GLS estimator and described how it…

Generalized Least Squares

10 min read

A Tutorial on Generalized Least Squares Regression Using Python and Statsmodels
A Tutorial on Generalized Least Squares Regression Using Python and Statsmodels
Generalized Least Squares

10 min read


Published in

Towards Data Science

·Nov 1, 2022

A Deep-Dive into Generalized Least Squares Estimation

A detailed look at how to fit a robust GLS model on heteroskedastic, auto-correlated data sets — Generalized Least Squares (GLS) estimation is a generalization of the Ordinary Least Squares (OLS) estimation technique. GLS is especially suitable for fitting linear models on data sets that exhibit heteroskedasticity (i.e., non-constant variance) and/or auto-correlation. …

Generalized Least Squares

15 min read

A Deep-Dive into Generalized Least Squares Estimation
A Deep-Dive into Generalized Least Squares Estimation
Generalized Least Squares

15 min read


Published in

Towards Data Science

·Oct 6, 2022

A Tutorial on White’s Heteroskedasticity Consistent Estimator Using Python and Statsmodels

How to use the White’s heteroskedasticity consistent estimator using Python and statsmodels — In this article, we shall learn how to employ the HC estimator to perform statistical inference that is robust to heteroskedasticity. This article is PART 2 of the following two part series: PART 1: Introducing White’s Heteroskedasticity Consistent Estimator PART 2: A tutorial on White’s Heteroskedasticity Consistent Estimator using Python and…

Linear Regression

8 min read

A Tutorial on White’s Heteroskedasticity Consistent Estimator Using Python and Statsmodels
A Tutorial on White’s Heteroskedasticity Consistent Estimator Using Python and Statsmodels
Linear Regression

8 min read


Published in

Towards Data Science

·Sep 27, 2022

Introducing the White’s Heteroskedasticity Consistent Estimator

An introduction to the HC estimator, and its importance in building regression models in the face of heteroskedasticity — In this article, we’ll bring together two fundamental topics in statistical modeling, namely the covariance matrix and heteroskedasticity. Covariance matrices are the work horses of statistical inference. They are used for determining if regression coefficients are statistically significant (i.e. different from zero), and for constructing confidence intervals for each coefficient…

Heteroskedasticity

13 min read

Introducing the White’s Heteroskedasticity Consistent Estimator
Introducing the White’s Heteroskedasticity Consistent Estimator
Heteroskedasticity

13 min read

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In-depth explanations of statistical models. Get the intuition behind the equations.

Following
  • TDS Editors

    TDS Editors

  • JJ Lim, PhD

    JJ Lim, PhD

  • Ben Huberman

    Ben Huberman

  • Caitlin Kindig

    Caitlin Kindig

  • Ludovic Benistant

    Ludovic Benistant

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