Stochastic models

Voter model

In the mathematical theory of probability, the voter model is an interacting particle system introduced by Richard A. Holley and Thomas M. Liggett in 1975. One can imagine that there is a "voter" at each point on a connected graph, where the connections indicate that there is some form of interaction between a pair of voters (nodes). The opinions of any given voter on some issue changes at random times under the influence of opinions of his neighbours. A voter's opinion at any given time can take one of two values, labelled 0 and 1. At random times, a random individual is selected and that voter's opinion is changed according to a stochastic rule. Specifically, for one of the chosen voter's neighbors is chosen according to a given set of probabilities and that individual's opinion is transferred to the chosen voter. An alternative interpretation is in terms of spatial conflict. Suppose two nations control the areas (sets of nodes) labelled 0 or 1. A flip from 0 to 1 at a given location indicates an invasion of that site by the other nation. Note that only one flip happens each time. Problems involving the voter model will often be recast in terms of the dual system of coalescing Markov chains. Frequently, these problems will then be reduced to others involving independent Markov chains. (Wikipedia).

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Linear regression

Linear regression is used to compare sets or pairs of numerical data points. We use it to find a correlation between variables.

From playlist Learning medical statistics with python and Jupyter notebooks

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(ML 13.6) Graphical model for Bayesian linear regression

As an example, we write down the graphical model for Bayesian linear regression. We introduce the "plate notation", and the convention of shading random variables which are being conditioned on.

From playlist Machine Learning

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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

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B27 Introduction to linear models

Now that we finally now some techniques to solve simple differential equations, let's apply them to some real-world problems.

From playlist Differential Equations

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Regression Trees, Clearly Explained!!!

Regression Trees are one of the fundamental machine learning techniques that more complicated methods, like Gradient Boost, are based on. They are useful for times when there isn't an obviously linear relationship between what you want to predict, and the things you are using to make the p

From playlist StatQuest

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Linear Regression using Python

This seminar series looks at four important linear models (linear regression, analysis of variance, analysis of covariance, and logistic regression). A video that explains all four model types is at https://www.youtube.com/watch?v=SV9AxXFWZnM&t=12s This video is on linear regression usin

From playlist Statistics

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Logistic Regression Details Pt1: Coefficients

When you do logistic regression you have to make sense of the coefficients. These are based on the log(odds) and log(odds ratio), but, to be honest, the easiest way to make sense of these are through examples. In this StatQuest, I walk you though two Logistic Regression Examples, step-by-s

From playlist StatQuest

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(ML 13.3) Directed graphical models - formalism (part 1)

Definition of a directed graphical model, or more precisely, what it means for a distribution to respect a directed acyclic graph.

From playlist Machine Learning

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Paper Read Aloud: Fool Me Twice: Entailment from Wikipedia Gamification

I'm reading a paper out loud from start to finish! Read the whole paper here: http://users.umiacs.umd.edu/~jbg//docs/2021_naacl_fm2.pdf Research talk: https://youtu.be/JSI1zTsCFTo Code and data: https://github.com/google-research/fool-me-twice

From playlist Papers Read Aloud

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Strata 2013: Sasha Issenberg, "The Victory Lab"

http://strataconf.com/ Nerds crash the gates of a venerable American institution, shoving aside its so-called wise men and replacing them with a radical new data-driven order. We've seen it in sports, and now in The Victory Lab- which Politico has described as "Moneyball for politics"- Sas

From playlist Strata Conference 2013 (Santa Clara, CA)

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Mod-03 Lec-18 Electoral Competition 1

Game Theory and Economics by Dr. Debarshi Das, Department of Humanities and Social Sciences, IIT Guwahati. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Game Theory and Economics | CosmoLearning.org Economics

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Mod-03 Lec-20 Hotelling Model: Concluding Remarks

Game Theory and Economics by Dr. Debarshi Das, Department of Humanities and Social Sciences, IIT Guwahati. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Game Theory and Economics | CosmoLearning.org Economics

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Courses - R. SUN "Brownian web, Brownian net, and their universality"

The Brownian web is the collection of one-dimensional coalescing Brownian motions starting from every point in space-time. Originally conceived by Arratia in the context of the one-dimensional voter model and its dual coalescing random walks, the Brownian web has since been shown to arise

From playlist T1-2015 : Disordered systems, random spatial processes and some applications

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Introduction to R: ANOVA

This is lesson 26 of a 30-part introduction to the R programming language for data analysis and predictive modeling. Link to the code notebook below: Intro to R: ANOVA https://www.kaggle.com/hamelg/intro-to-r-part-26-ANOVA This lesson covers the ANOVA test for comparing whether the mean

From playlist Introduction to R

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Milan Svolik: Polarization and the Subversion of Democracy in Latin America

Professor Svolik has authored and co-authored articles on the politics of authoritarian regimes and democratization in leading political science journals, including the "American Political Science Review," the "American Journal of Political Science", and the "Journal of Politics." He is th

From playlist The MacMillan Report

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Mod-03 Lec-19 Different Aspects of Hotelling Model

Game Theory and Economics by Dr. Debarshi Das, Department of Humanities and Social Sciences, IIT Guwahati. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Game Theory and Economics | CosmoLearning.org Economics

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3. Iterative deletion and the median-voter theorem

Game Theory (ECON 159) We apply the main idea from last time, iterative deletion of dominated strategies, to analyze an election where candidates can choose their policy positions. We then consider how good is this classic model as a description of the real political process, and how we m

From playlist Game Theory with Ben Polak

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ISPS DEMOCRACY SERIES: “The 2022 Midterm Elections: What Happened and Why?”

A panel of political experts discuss voting patterns in the 2022 midterm elections that offer valuable insights and lessons at all levels of government and for the current state of our democracy. Moderated by ISPS Director Alan Gerber, the panel focuses on understanding what political beha

From playlist The Institution for Social and Policy Studies (ISPS)

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Exponential Growth Models

Introduces notation and formulas for exponential growth models, with solutions to guided problems.

From playlist Discrete Math

Related pages

Ergodic process | Duality (mathematics) | Invariant measure | Borel–Cantelli lemma | Random walk | Sequential dynamical system | Almost surely | Contact process (mathematics) | Probability | Markov chain | Chebyshev's inequality | Interacting particle system