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A simple solution is commonly encountered in epidemiology. It's based on the fact that causation and time go hand in hand. For a variable $A$ to "feedback" to itself, time must be involved. In this way feedback can be accounted for if we incorporate time into an acyclic graph. For example, the following simple diagram demonstrates how a variable $A$ at ...


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I want to start of by thanking @amoeba says Reinstate Monica & ttnphns for their contributions that have greatly helped me! I'm so grateful in fact, I'd want to buy them a drink or be able to return the favor somehow. The only thing I'm going to add to their reply is my python implementation of drawing these Decision boundaries, I think it'll help ...


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Looks like it's "Methods of Multivariate Statistics" by Muni S. Srivastava, Wiley 2002. It's available on Amazon.com in the U.S., with used copies going for $10-$15


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A nice review of some algorithms, with linked papers and packages, here: https://causalml.readthedocs.io/en/latest/about.html This is only a small subset of the broader research field, but still useful. For more general reviews see also: Machine learning: An applied econometric approach ICML Causal Inference tutorial


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Joe Berkson coined the phrase. To my knowledge, it first shows up in 1963 in Edwards, Lindman, and Savage's "Bayesian Statistical Inference for Psychological Research" in Psychological Review, 70(3): The preceding paragraph illustrates a procedure that statisticians of all schools find important but elusive. It has been called the interocular traumatic ...


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If you agree that a logistic regression is a special case of a neural network, then the answer is D. R. Cox, who invented logistic regression.[1] A neural network with zero hidden layers and a single sigmoid output and trained to maximize the binomial likelihood (equiv. minimize cross-entropy) is logistic regression. Minimizing a binomial cross-entropy is ...


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Don't let the perfect be the enemy of the good Many of the issues you have raised are perfectly reasonable concerns. Having said that, it is important to distinguish between cases where reported data is wrong, versus cases where reported data is correct, but is limited in its usage due to the omission of other relevant information. The latter case is ...


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If more information is available, you may wish to incorporate it into assigning a missing data point. For example, a study of players historical rankings over time, including those who were unranked for a period, might suggest a more meaningful value (derived from their average rank) than using just a team average value. Losing data is not usually the ...


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Mulaik, S. A. (2009). Linear Causal Modeling with Structural Equations. Chapman and Hall/CRC. This seems to be a mathematically thorough treatment of the subject.


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Efron has a book "Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing and Prediction" that turned out be exactly what I was looking for. The assumptions are very clearly laid out.


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