Alejandro Morales' Blog
Alejandro Morales' Blog
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Numerical methods
Estimating variance: should I use n or n - 1? The answer is not what you think
Estimates of population parameters based on samples are not exact: there is always some error involved. In principle, one can estimate a population parameter with any estimator, but some will be better than others.
Last updated on Sep 1, 2019
8 min read
Numerical methods
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R
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Statistics
Maximum likelihood estimation from scratch
Maximum likelihood estimates of a distribution Maximum likelihood estimation (MLE) is a method to estimate the parameters of a random population given a sample. I described what this population means and its relationship to the sample in a previous post.
Last updated on Aug 26, 2019
13 min read
R
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Numerical methods
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Statistics
Beyond normality: the bootstrap method for hypothesis testing
tl;dr: Parametric bootstrap methods can be used to test hypothesis and calculate p values while assuming any particular population distribution we may want. Non-parametric bootstrapping methods can be used to test hypotheses and calculate p values without having to assume any particular population as long as the sample can be assumed to be representative of the population and one can transform the data adequately to take into account the null hypothesis.
Aug 18, 2019
151 min read
R
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Statistics
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Numerical methods
Where do p-values come from? Fundamental concepts and simulation approach
tl;dr: P-values are tail probabilities calculated from the sampling distribution of a sample-based statistic. This sampling distribution will depend on the size of the sample, the statistic being calculated and assumptions about the random population from which the data could have been sampled.
Aug 10, 2019
11 min read
R
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Statistics
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Numerical methods
Automatic Differentiation with Dual Numbers
tl;dr: Given any model that maps inputs to outputs, Dual Numbers can be used to calculate the exact derivative of any output with respect to any input without requiring the user to calculate these derivatives.
Aug 4, 2019
8 min read
Julia
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Numerical methods
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