# Questions tagged [intuition]

Questions that seek a conceptual or non-mathematical understanding of statistics.

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### How do we visualize the Decomposition of Variance formula $\text{Var}[y] = \text{Var}_x[\text{E}[y|x]] + \text{E}_x[\text{Var}[y|x]]$?

The Decomposition of Variance formula is $\text{Var}[Y] = \text{Var}_X[\text{E}[Y|X]] + \text{E}_X[\text{Var}[Y|X]]$. This can be described as follows: the variance of y decomposes into the variance ...
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### Why does the autocorrelation of a wide-sense stationary stochastic process only depend on lag? [closed]

$$\mathbf{E}\left[x(t_1)x(t_2)\right] = \mathbf{E}\left[x(t_1+\Delta t)x(t_2+\Delta t)\right] \neq \mathbf{E}\left[x(t_1)x(t_3)\right]$$ $$t_2 = t_1+\tau$$ I'm trying to picture how this is the case ...
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### L2 regularization and its intuition

I am reading about L2 Regularization. As far as I know we add a thing to the loss function that: $$J(w) = LOSS + \lambda w^T w$$ In the book Deep Learning by Goodfellow et al., they stated "...
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### How to develop intuition to reason about models/predictions

I am trying to answer a few questions that I was asked about data science and was wondering what the best way is (from your experience) to develop the qualitative/quantitative intuition behind ...
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### What is the intuition of a dual?

I have been hearing that the Ridge regression is the dual to the GP (Gaussian process regression). What does this mean? Can someone please give an intuition on what 'dual' is. My impression of the '...
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### Intuitive explanation of rules of do-calculus

Do-calculus has 3 rules: https://plato.stanford.edu/entries/causal-models/do-calculus.html I understand them on a mathematical level, but they seem so arbitrary. I can not wrap my head around what the ...
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### Probability Density Function (PDF) Intuition [duplicate]

I know what is Probability Density Function and its application in Machine Learning and Statistics. The problem I faced is that how does it being calculated? For a specific example like the ...
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### Intuitive way to connect gamma and chi-squared distributions

I understand that a chi-squared distribution is a special case of the gamma distribution. However, I find claims of "the math just works out" to be an unhelpful in remembering or ...
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### Intuition for relationship between variance of geometric and exponential distributions

Given that the exponential distribution can be thought of as a continuous version of the geometric, is there an intuitive way to relate their variances? I have some intuition for how the means of ...
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### Intuitive explanation of the paper “Generalized Random Forests” (Athey, Tibshirani, Wager)

This seems like an exciting approach to uplift modelling, but the only resource that I can find is this paper and it is too brief, notation-heavy and dense to be of any use to me. I have an honours ...
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### Intuition behind clustering standard errors

Intuitively, why does a lack of clustering standard errors lead to erroneously smaller standard errors? Looking at the calculations and seeing the difference between SEs that are clustered and not ...
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### Intuition behind projection matrix

I'm new to machine learning and came across projection matrix . In a random thread it was interpreted as The matrix $X(X^\text{T} X)^{-1} X^\text{T}$ is a projection matrix, as it does precisely that:...
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### VAR($p$) estimation

I am bit stumped by this result. Source: Remark on page 46 of Multivariate Time Series Analysis by Rsay. ... one can obtain the GLS estimate of a VAR($p$) model equation by equation. That is, one can ...
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### What is MCRMSE (mean columnwise root mean squared error)?

The MCRMSE evaluation metric was used in the Kaggle Competitions Africa Soil Property Prediction Challenge(6 years ago) and OpenVaccine: COVID-19 mRNA Vaccine Degradation Prediction(On-going) ...
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### Are the following model assumptions on a data stream too restrictive?

Suppose that you were to model a "generic" continuous-time real-world data signal $X$ taking values in a bounded continuum $K\subset\mathbb{R}^d$ (e.g. the body temperature of a patient or ...
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### Intuition on why Gibbs Sampling samples from the posterior distribution

I am new to Gibbs Sampling and I do understand how the algorithm works but I would also like to understand how sampling from the conditional distributions is equivalent to sampling from the joint. ...
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### What does $P(|X_n - X| \geq \epsilon)$ represent intuitively?

I get that $P(|X_n - c| \geq \epsilon)$ represents the probability that the random variable $X_n$ is outside the interval of $(c - \epsilon, c + \epsilon)$ but I am not sure how it works with a random ...
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### Can Principal Component Analysis Be Used Here?

My professor has given us test prep in the form of a scenario essay question (For studying purposes/not graded) I want to see if my method of Principal Component Analysis would be applicable here. I ...
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### Central limit theorem seems counterintuitive given Law of large number

From what I understand, the Central limit theorem says the sample mean is distributed normally when sample number tends to infinity. However, the Law of large number says sample mean converges in ...