Posts Tagged ‘ mathematics ’

Monotonicity of EM Algorithm Proof

April 19, 2014
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Here the monotonicity of the EM algorithm is established. $$ f_{o}(Y_{o}|\theta)=f_{o,m}(Y_{o},Y_{m}|\theta)/f_{m|o}(Y_{m}|Y_{o},\theta)$$ $$ \log L_{o}(\theta)=\log L_{o,m}(\theta)-\log f_{m|o}(Y_{m}|Y_{o},\theta) \label{eq:loglikelihood} $$ where \( L_{o}(\theta)\) is the likelihood under the observed data and \(L_{o,m}(\theta)\) is the likelihood under the complete data. Taking the expectation of the second line with respect to the conditional distribution of \(Y_{m}\) given \(Y_{o}\) and […] The post Monotonicity of EM Algorithm Proof appeared first on Lindons Log.

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Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Applies to the Sample Mean

Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Applies to the Sample Mean

Having taught and tutored introductory statistics numerous times, I often hear students misinterpret the Central Limit Theorem by saying that, as the sample size gets bigger, the distribution of the data approaches a normal distribution.  This is not true.  If your data come from a non-normal distribution, their distribution stays the same regardless of the […]

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Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

In an earlier video, I introduced the definition of the hazard function and broke it down into its mathematical components.  Recall that the definition of the hazard function for events defined on a continuous time scale is . Did you know that the hazard function can be expressed as the probability density function (PDF) divided by the […]

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Useful for referring—2-25-2014

February 25, 2014
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Useful for referring—2-25-2014

Interview with Nick Chamandy, statistician at Google You and Your Research +  video Trustworthy Online Controlled Experiments: Five Puzzling Outcomes Explained A Survival Guide to Starting and Finishing a PhD Six Rules For Wearing Suits For Beginners Why I Created C++ More advice to scientists on blogging Software engineering practices for graduate students Statistics Matter […]

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Statistical politicians

February 23, 2014
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Statistical politicians

Last week we had the pleasure of Professor Stephen Pollock (University of Leicester) visiting our Department, best known in academic circles for his work on time series filtering (see his papers, and his excellent book). But he has another career as a member of the UK House of Lords (under the name Viscount Hanworth — he is a hereditary peer). It made me wonder how many other politicians have PhDs…

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R: Fun with surf3D function

February 19, 2014
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R: Fun with surf3D function

There is one package that I've been longing. A package that will give me the power to manipulate and do any 3D stuffs in R. I tried persp and wireframe, but I find them difficult to use especially on complicated mathematical functions, like doing param...

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R: Animating 2D and 3D plots

February 13, 2014
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R: Animating 2D and 3D plots

One great package in R is the animation made by Yihui Xie. And just for fun, we are going to explore that. Our aim is to create simple animated 2D and 3D plots. Here is the first one, 2D of courseThe code,It's a piece of cake right? The function we use...

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Video Tutorial: Breaking Down the Definition of the Hazard Function

Video Tutorial: Breaking Down the Definition of the Hazard Function

The hazard function is a fundamental quantity in survival analysis.  For an event occurring at some time on a continuous time scale, the hazard function, , for that event is defined as , where is the time, is the time of the occurrence of the event. However, what does this actually mean?  In this Youtube […]

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Rectangular Integration (a.k.a. The Midpoint Rule) – Conceptual Foundations and a Statistical Application in R

Rectangular Integration (a.k.a. The Midpoint Rule) – Conceptual Foundations and a Statistical Application in R

Introduction Continuing on the recently born series on numerical integration, this post will introduce rectangular integration.  I will describe the concept behind rectangular integration, show a function in R for how to do it, and use it to check that the distribution actually integrates to 1 over its support set.  This post follows from my […]

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Use standard deviation (not mad about MAD)

January 19, 2014
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Use standard deviation (not mad about MAD)

Nassim Nicholas Taleb recently wrote an article advocating the abandonment of the use of standard deviation and advocating the use of mean absolute deviation. Mean absolute deviation is indeed an interesting and useful measure- but there is a reason that standard deviation is important even if you do not like it: it prefers models that […] Related posts: Don’t use correlation to track prediction performance What does a generalized linear…

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