matrices
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254A, Notes 2: The central limit theorem
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Consider the sum of iid real random variables of finite mean and variance for some 0}" title="{\sigma > 0}" class="latex" />. Then the sum has mean and variance , and so (by Chebyshev’s inequality) we expect to usually have size . To put it another way, if we consider the normalised sum ...5 hours ago -
254A, Notes 1: Concentration of measure
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Authority: 116
Suppose we have a large number of scalar random variables , which each have bounded size on average (e.g. their mean and variance could be ). What can one then say about their sum ? If each individual summand varies in an interval of size , then their sum of course varies in an interval of size . However, a ...2 days ago -
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254A, Notes 0a: Stirling’s formula
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In this supplemental set of notes we derive some approximations for , when is large, and in particular Stirling’s formula . This formula (and related formulae for binomial coefficients will be useful for estimating a number of combinatorial quantities in this course, and also in allowing one to analyse ...3 days ago -
254A, Notes 0: A review of probability theory
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In preparation for my upcoming course on random matrices, I am briefly reviewing some relevant foundational aspects of probability theory , as well as setting up basic probabilistic notation that we will be using in later posts. This is quite basic material for a graduate course, and somewhat pedantic in nature, but ...4 days ago -
ToxMiner Software Interface for Visualizing and Analyzing ToxCas...
Science nature & education - science-nature.marc8.com —
Authority: 154
The ToxCast dataset represents a collection of assays and endpoints that will require both standard statistical approaches as well as customized data analysis workflows. To analyze this unique dataset, we have developed an integrated database with Javabased interface called ToxMiner. The software is organized around ...1 week ago -
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Authority: 165
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MIT Linear Algebra, Lecture 3: Matrix Multiplication and Inverse Matrices
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Authority: 464
This is the third post in an article series about MIT’s course “Linear Algebra”. In this post I will review lecture three on five ways to multiply matrices , inverse matrices and an algorithm for finding inverse matrices called Gauss-Jordan elimination . The first lecture covered the geometry of linear ...3 weeks ago -
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