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Many mathematicians and statisticians are undisciplined in the use of these words, using the word "random variable" to refer to any quantity to which a probability distribution is assigned. The number of spades you get in a poker hand from a well shuffled deck is random. The mass of the dwarf planet Pluto may not be random the way a poker hand is, ...


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You state Suppose this rule proves to be a very accurate rule (i.e. when this condition is true, patients almost always have the disease) But that is often not the situation. If the broad boundary is very accurate, and if the detection means almost certainly that the patient has the disease, then this is a very good decision rule. The doctors will be happy ...


2

The model you've presented here looks a lot like an ANOVA. If memory serves me right, ANOVA and many other methods were developed from applications in agriculture, in which plots of land would be given various treatments. In these applications, the plots of land were given treatments randomly and so the estimated $\tau_i$ would be the effect of the ...


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Is this a case of overfitting? Decision trees are prone to do that. Have you got enough data to use a held out test set to validate the model? If so, the doctors might be convinced by the results on the test set. Alternatively, it might be a case where an executive commissions a model, but when it is delivered the in-house experts whose judgement it replaces ...


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Could this be an issue of precision and recall? You are writing "when this condition is true, patients almost always have the disease" and call this accuracy. But usually one/I would not call that accuracy. The English Wikipedia has a large table in the "Precision and recall" article https://en.wikipedia.org/wiki/Precision_and_recall Here ...


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A metric is a measurement and therefore has units: a parameter may not. For example a mole in chemistry is the amount if stuff that has 6*10^23 molecules is atoms or whatever, and is a dimensionless number - a parameter, not a metric - that has no units. A metric space is any set of data where distance between two points is the same in both directions and ...


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I think you are describing Percentages (2) and Percentage points (1). More details here.


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I am confused by the terminology because the term "independent samples" is usually used as a synonym for "unpaired samples". Does this fact mean that unpaired samples are always generated by independent random variables (assuming we have a probability model for our data)? No, 'unpaired data' is not always independent. The answer below ...


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As others have written, this is compositional data analysis. We have a compositional-data tag, so searching for threads carrying, e.g., this tag and the "time-series" one may be helpful. One paper on forecasting compositional time series is Snyder et al. (2017, IJF). Essentially, the idea is to transform the original compositional time series, then ...


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Independence has a formal definition, i.e. $f_{X,Y}(x,y)=f_X(x)f_Y(y)$. On the other hand, I do not think that the term 'unpaired samples' has a formal statistical definition, and, at the risk of sounding snobbish, it is not a term that I ever hear formally trained (bio)statisticians use. Non-statisticians I work with will use that term, and I encounter the ...


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In the generalized linear model (specially meant for classification problem), the source of non-linearity is activation funtion with linear argument of the form $\omega^\top x +\omega_0$. Here, we just need to estimate the parameters $\omega, \omega_0$ only and the activation might be user defined. While, in regression problem, the using least square ...


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You’re talking about making predictions not inference, but in case of inference we talk about practical significance. Statistical significance may help you to detect an effect that “significantly” differs from zero, but the effect may be so small that is has no practical significance, there’s no practical use of it.


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BLACK-BOX MODEL That is the closest that I can think to what you describe. However, a "black-box model" is not necessarily useless. While many applications want to know how the model works, there are some situations where just getting the right answer is the crucial aspect. The name comes from the idea of throwing data into a black box, so that ...


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From practical point of view, how deep learning models are trained, deployed and improved. In the current literature, architecture usually implies a neural network architecture, i.e., choosing layer topology and activation functions. Outside neural networks, architecture makes not much sense, unless they have hierarchy and need of search. The usage of the ...


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Statistics: Texas sharpshooter fallacy The fallacy you describe resembles the Texas sharpshooter fallacy, in which one reverses the order of sampling data and fitting one's hypothesis so that the observation confirms it. From the linked Wikipedia article: The name comes from a joke about a Texan who fires some gunshots at the side of a barn, then paints a ...


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The best I know of at the moment is by an article by Rufilanchas in 2017 [1]: in it, he says that Pearson, the first person to use the word (not the first who used such a diagram), used it in relation to how he believed that the vertical alignment of columns to represent frequency distributions is preferable to it aligned horizontally: "...Pearson, who ...


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The Fallacy is not statistical. It is related to determinism. old science was deterministic and also stiff . So the butterfly effect was a logical consequence: you change something just a little bit and the future is completely different as a result. This is not how science is understood today. Determinism is gone, and even In stiff systems we are finding ...


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The universe and mankind The fact that we observe the unlikely event of a universe, solar system and planet that is able generate intelligent life, is a type of survival bias. (and as Mehmet mentions in the comments, this could be seen as a cherry picking fallacy) We see the unlikely event because without it we wouldn't have lived to see the absence of the ...


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I think the fallacies in this argument tend to be different than what you're calling out. After all, $(3,4)$ is an arbitrary point on the dartboard, but some (if not all) of the aspects of the universe called out in fine-tuning arguments (particular masses, coupling constants, etc.) are genuinely non-arbitrary, perhaps even special properties. So the counter ...


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You are probably thinking of a component cause, part of the sufficient component causal model. It is described briefly here.


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I believe one more answer, specifically addressing your points as they currently stand (Revision 11) and comments is warranted. Is Wikipedia's page on the sigmoid function incorrect? No. In some communities, specifically Machine Learning, some (maybe even most?) people use the term "sigmoid function" in a different, more limited sense, as a ...


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It's an expression that is often used as short-hand or conventional jargon. Anyone who finds it puzzling should feel that way! Some people say "accounts for" instead as a usage supposedly a little softer. What is meant by explanation any way? This is a long-standing topic in philosophy (epistemology and philosophy of science) going back at least to ...


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