Questions tagged [intuition]

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

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Intuitive explanation of Friedman's H-statistic

What is the cleanest, easiest way to explain someone, a non-STEM person the concept of Friedman's H-statistic? What does it intuitively mean? While exploring feature interaction I went through ...
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Intuition for hypothesis testing [duplicate]

I'm in the process of building an intuition for how hypothesis testing works and why we should use it. I'm not new to the topic — I've taken the usual introductory course in probability theory and ...
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Intuitive understanding of least squares slope formula

One formula for the least squares linear regression line with independent variable $X$ and response variable $Y$ is: $\hat{\beta} = \frac{Cov(X, Y)}{Var(X)}$ This formula screams deeper intuition but ...
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Why does the bootstrap method work to estimate a statistic? [duplicate]

I am a novice at statistics and recently learned about the bootstrap method. I am curious about why such a method works. Intuitively it feels like we are cheating since we are not collecting new ...
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1answer
29 views

Intuitively Assert Consistency

Consider a model $$\mathbf y=\beta_0+\mathbf x_1\beta_1+\mathbf x_2\beta_2+\mathbf e$$ and assume $\mathbb E[\mathbf e\mid\mathbf X]=0$. Under this scenario, the OLS estimator is a consistent ...
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Bayesian Probability of Zero?

I've been reading a few different philosophical papers/books which have mentioned a "Bayesian belief". Within these texts I've been basically inferring that within the Bayesian theorem, ...
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39 views

intuition behind asymmetry of Poisson distribution

Today I've learned that the probability of the number of independent random events occurring in a fixed interval of time can be modeled with the Poisson distribution. When thinking about it my ...
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Intuition behind Vapnik-Chervonenkis Symmetrization lemma

I am trying to get a good understanding of what Vapnik-Chervonenkis Symmetrization Lemma really says, since it comes up quite often. First, we consider the empirical process : $$f\mapsto ({\mathbb {P}...
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Covariance vs Correlation Definition [duplicate]

I am having a tough time understanding the difference between both terms. Could someone please clear up what both terms mean and in the process of doing so, explain the difference between them?
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1answer
38 views

Probability on different time scales

I just finished reading "Fooled by Randomness" by Nassim Taleb. He, inter alia, gives the following example to prove one of his points: A 15% return with 10% volatility per annum translates ...
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Intuitive interpretation of the covariance matrix

I am trying to get a "feel" for the covariance matrix. I know that $v_iCov(X)v_j$ gives the covariance between $X$ projected along $v_i$ and $v_j$. I'm curious if there's a similar intuitive ...
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Intuition of Condition of (weak) Stationarity in multivariate case

This may be a duplicate. I am trying to get an intuitive idea about the condition for stationarity. I think I got a fair idea of stationarity as a concept (from this and other sources on internet) but ...
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Intuition for Hotelling's T^2 Test

I have been learning about Hotelling's $T^2$ test from Multivariate Statistics: Old School. The test is given by $T^2 = \nu\cdot\text{trace}(\bf{W}^{-1}\bf{B})$. The author shows that in the case of ...
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Intuition behind the degrees of freedom in ridge regression

I'm reading through the ESL book and I'm on the part of ridge regression where the effective degrees of freedom are defined $$ df(\lambda) = tr(X(X'X + \lambda I)^{-1}X') = \sum_{j=1}^p{\frac{d_j^2}{...
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Intuition behind Nadaraya-Watson kernel estimate

I'm looking through the Nadaraya-Watson kernel smoothing estimate and I'm trying to understand how and why does it work. The Nadaraya-Watson kernel smoothing estimate is defined as $$ \hat{f}(x_0) = \...
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Why does consistency of cluster robust standard error depend on the number of clusters?

I've seen many hand wavy explanations about it, but when I read White's book for the original reference, the math is too dense. Could someone help me derive this result in terms of the asymptotic ...
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1answer
47 views

Econometrics meaning of structural versus regression model

I want to make sure my understanding is correct. Particularly in econometrics, when authors write down a model: $Y_i = \beta_0 + \beta_1 X_i + \epsilon$ Can I think of this as a 'structural model'- or ...
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44 views

Assumption of linearity between variables and log odds in logistic regression

I know that in logistic regression we assume a linear relationship between the independent variables and the logits. Can you explain why is this a reasonable assumption?
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9 views

Question about consistent estimators and asymptotic distributions

Lets say you have an estimator that is consistent, and you do not have any information on the asymptotic distribution, what can you do with such an estimator? Also when using aysmptotic distribtuions, ...
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1answer
63 views

Understanding maximum likelihood estimation

I am told the method of maximum likelihood says we should use the model that assigns the greatest probability to the data we have observed; formally, the maximum likelihood estimator is found by ...
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2answers
113 views

Interpretation of multivariate conditional gaussian function form?

I've been reading over this Multivariate Gaussian conditional proof, trying to make sense of how the mean and variance of a gaussian conditional was derived. I've come to accept that unless I allocate ...
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3answers
300 views

Why does a function being smoother make it more likely?

I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following: Given this training ...
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1answer
139 views

Is it really appropriate to say “standard deviation” is variation or dispersion

Question I have been struggling to convince myself that SD (standard deviation) is about variation or dispersion. Standard deviation From Wikipedia, the free encyclopedia In statistics, the standard ...
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A new strain of covid-19 is 70% more infectious/transmissible. What does that mean and how has it been estimated/measured? [closed]

70% in the media https://www.dailymail.co.uk/news/article-9070683 Prime Minister Boris Johnson told a Downing Street briefing that early analysis showed the new strain could increase the reproductive ...
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Fixed effects vs the dummy variables themselves: structural vs practical equation

I have a question about if there is a substantive difference between a fixed effect and the way we estimate them (e.g., dummy variables). Are the estimated dummy variables the fixed effect, or do they ...
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Intuitive understanding of instrumental variables for natural experiments

I am wondering if my understanding of Instrumental vairables to exploit natural experiments is correct, or if I am misunderstanding something. Is the logic as follows: by using an instrument, you are ...
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Understanding rate of convergence for realized estimators

I'm a Econ student currently taking a small course on realized measures/estimators. I'm a bit confused about the meaning behind rate of convergence for each type of estimator. I'll give some ...
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397 views

Does zero Spearman's rho imply zero Covariance?

To the question of the title I would "intuitively" answer yes, by the following informal argument: Covariance "measures the strength of linear association" (when scaled by the ...
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Intuition behind the inverse of the copula density $\frac{1}{c(u,v)}$

If the inverse of a probability $\frac{1}{p(x)}$ represents the unpredictability or surprisal of a sample from random variable $X$, then what is the intuition behind the point-wise inverse of the ...
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Example where $X$ and $Z$ are correlated, $Y$ and $Z$ are correlated, but $X$ and $Y$ are independent

$X,Y,Z$ are random variables. How to construct an example when $X$ and $Z$ are correlated, $Y$ and $Z$ are correlated, but $X$ and $Y$ are independent?
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In GLIM, how do I understand “the link maps mu to the entire real line, from −∞ to +∞”?

I always read in generalised linear model that the link function has to have a 1-1 correspondence from the range of mu to (-infinity, infinity). But, when we look at log link, for instance, it is not ...
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Intuition behind sampling from a covariance matrix in gaussian processes

I am trying to grasp an intuition here. Say we have a prior covariance matrix defined by a RBF function, if we do a contour plot based on that, we have these characteristic diagonal matrix with unit ...
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Simple poisson regression for a death rate [duplicate]

I am trying to regress the death rate for a particular cause of death for 25-30 year olds. My dependent variable of interest is the crude rate, i.e., y = number of deaths of 25-30 year olds/number of ...
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Jacobian for transformation of discrete random variables (intuition)

I am reading Blitzstein's introduction to probability. He states that, while a transformation of continuous r.v.s needs a Jacobian (or derivative), a transformation of discrete r.v.s does not. Is ...
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29 views

permutation test sampling

In statistical inference, specifically while conducting hypothesis testing, we use permutation test, is there any reason why resampling is done without replacement (shuffle), what difference does it ...
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1answer
53 views

Intuition behind memoryless process and geometric series

I was reading this problem (Page 6, THE BASKETBALL PROBLEM, MEMORYLESS PROCESSES AND THE GEOMETRIC SERIES) and stumbled upon the solution using the memoryless property. I cannot understand the ...
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1answer
60 views

Naive benchmarks for scoring rules

I am a non-mathematical R programmer who is completely new to the idea of scoring rules. I would like to start using them instead of classification evaluation measures like accuracy and recall, which ...
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24 views

Non-mathematical explanation of how to interpret and evaluate scoring rules in R

I am a non-mathematical R programmer who is completely new to the idea of scoring rules. I would like to start using them instead of classification evaluation measures like accuracy and recall, which ...
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1answer
56 views

Intuition Standard Error of the Mean

Trying to understand the intuition behind the standard error of the mean. Starting from this formula: $Var(\bar{X}) = Var(\frac{\bar{X}_1+\bar{X}_2+...+\bar{X}_n}{n})$ The formula talks about a ...
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1answer
53 views

Intuition behind the Endogeneity Test (the Hausman Test)

Suppose we have the following simple regression model (time series framework)" $$y_1=\beta_0+\beta_1 y_2+\beta_2 z_1 +\beta_3 z_2 +u,$$ where $z_1$ and $z_2$ are exogenous and $y_2$ is either ...
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1answer
28 views

the interpretation of high likelihood ratio test statistic

In wikipedia, In wikipedia, the interpretation of high likelihood ratio test statistic is: High values of the statistic mean that the observed outcome was nearly as likely to occur under the null ...
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How to explain instrumental variables to your friends?

Is there an even simpler way of explaining IV than described here? I was recently talking to my friend about my research and was wondering how to convey the intuition of instrumental variables to ...
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23 views

Understanding leverage and influence

there is a reference to the $i^{th}$ diagonal entry in $H$ where $H=X(X^TX)^{-1}X^T$ in the definitions of leverage and cook's distance. See: https://en.wikipedia.org/wiki/Leverage_(statistics) and ...
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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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1k views

Why isn't bootstrapping done in the following manner?

I'm under the impression that when you bootstrap, your final results are the original statistic from your sample data, and the standard errors from the bootstrapped trials. However, it seems more ...
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2answers
49 views

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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20 views

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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44 views

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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28 views

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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