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Perceptually uniform colormap

This can be considered a form of honesty, Transparent language.

Graphing colors - for example, area charts showing intensity using the rainbow: not good. Intensity should be shown with luminance, not hue.

IBM did research on this back in the day. There is a collection of perceptually uniform maps at colorcet.com/. Also, Matplotlib adopted a new set of defaults in 2015. Lecture at www.youtube.com/watch?v=xAoljeRJ3lU.

Cool guide: seaborn.pydata.org/tutorial/color_palettes.html

What links here

Created (4 years ago)

#statistics

What links here

(Sorted by recent first)

Created (4 years ago)

Akaike Information Criterion

Bayesian methods, #statistics

Reasons for information criteria can be found in a book Information Theory and Statistics by Kullback. Explains well.

True model yi = 1 + x0.1 - x2 0.2 …

Various models (hundreds, thousands) ∑ …

Choose model by best (smallest) AIC/BIC/DIC/WAIC.

AIC = D train + 2p

AIC is an approximation that is reliable only when: (1) The priors are flat or overwhelmed by the likelihood. (2) The posterior distribution is approximately multivariate Gaussian. (3) The sample size N is much greater than the number of parameters k.

Watanabe-Akaike Information Criterion

Like AIC, you can rank models by WAIC. But a more interpretable measure is an Akaike weight. The weight for a model i in a set of m models is given by

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where dWAIC is the difference between each WAIC and the lowest WAIC, i.e. dWAIC = WAICi - WAICmin.

Leave-one-out cross-validation (LOO-CV)

New kid on the block, around 2020 it was the best (for which situations?).

Created (4 years ago)

Estimator

#statistics

An estimator is a rule for estimating a given quantity based on observed data.

Example estimators: error, MSE, sampling deviation, bias, best linear unbiased estimator (BLUE), minimum-variance unbiased estimator (MVUE), maximum a posteriori (MAP).

A consistent estimator, AKA asymptotically consistent estimator, is one which converges to the correct value even if it has bias initially, with enough samples.

A biased estimator is one where the expected value and true value are different.

If an unbiased estimator converges on any value, it means the estimator must be consistent. In other words, there is no such thing as an unbiased inconsistent estimator, but there are unbiased estimators that do not converge. Schoolbook examples of this are such dead-stupid estimators as x = Xn, which never takes the whole array X1,2,3… into account, only the latest observation and naturally that does not converge to any kind of average, but it unbiasedly estimates the latest observation.

BLUE

Created (4 years ago)
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