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Questions tagged [intuition]

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

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1answer
26 views

What are some intuitively pleasing examples of “story”-inspired derivations of a Weibull distribution? [on hold]

What are some intuitively pleasing examples of "story"-inspired derivations of a Weibull distribution?
2
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0answers
31 views

Switching $H_0$ and $H_1$ by replacing $p$ with $1 - p$

I was reading the source code of tseries::adf.test, and it writes ...
0
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0answers
20 views

Reading kernel distribution plot vs typical histogram

Tasked with showing the distribution of a certain data set in a different way, I wanted to try to plot a kernel density. After seeing it however, my co-worker advised against it saying that because ...
0
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0answers
12 views

Changing axes of triangular coordinate planes

Consider a triangular coordinate plane like this: With all three axes in percentage form the readability of the graph is very intuitive, we can trace the gridlines and find the corresponding ...
0
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0answers
7 views

how to calculate entropy on matrix of words, topics

I have been digging in the concept of entropy for a while, now it comes to the implementation part I feel I am confused. Imagine that we have a matrix 20 * 3 standing for 20 words 3 topics (by 20 ...
1
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2answers
40 views

Why does R2 increase with fewer samples using adonis?

I've noticed in a large ecological dataset that when I subsample my data, the R2 'proportion of variance' explained by my categorical grouping (output from adonis() ...
8
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2answers
126 views

What useful properties does the canonical link function have?

So here I am studying generalized linear models. I know this question is quite naive and simple, but I do not exactly know why the link canonical function is so useful. Could someone provide me an ...
8
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1answer
89 views

Intuitively, how does the wild bootstrap work?

I am trying to understand the intuition behind the wild-bootstrap. What is it actually doing? I need to be able to understand what it is trying to do compared to a conventional regression. My data ...
0
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1answer
29 views

Explain Root Mean Square Error to non-technical audience

My company is in the process of switching equipment from one vendor to another. We measured several metrics from the existing and new equipment and compared the time series. The ideal is to have no ...
1
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1answer
41 views

Targeted Maximum Likelihood Estimation for dummies?

I have tried to get my head around the concept of TMLE, but most references seem to be written by people who despise being understood (or maybe I am just hebetudinous). I have tried to read the paper ...
0
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0answers
14 views

Verify that data have property $X$ with hypothesis testing

In data analysis, one usually need to verify that data have property $X$ before applying method $Y$, which takes $X$ as a prerequisite. To illustrate, possible values of $(X, Y)$ include $(\text{...
0
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1answer
58 views

“A property holds if it cannot be rejected”

Most examples in my Time Series Analysis slides and Multivariate Analysis textbook (Applied Multivariate Statistical Analysis, 6th Edition) conduct a hypothesis testing on data's normality, or zero ...
1
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1answer
32 views

Confused about conditional counterparts to traditional probability laws

I'm self-studying probability and have seen the following in various readings. The "conditional counterpart" $$P(x,y|\theta) = P(x|y,\theta)P(y|\theta)$$ to the traditional conditional probability ...
3
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1answer
97 views

Eigenvalues as weighting factors for projection results on corresponding eigenvectors in PCA

In the paper Novel PCA-based Color-to-gray Image Conversion, the authors project the three-dimensional $(R, G, B)$ value of each pixel onto a one-dimensional grayscale space via a curious application ...
1
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1answer
38 views

Difference between covariates and treatment confounders in propensity score matching

Here, I have the definition of a propensity score: Propensity score is defined as the conditional probability of assignment to a treatment given a vector of covariates including the values of all ...
1
vote
1answer
15 views

Intuition / motivation for 2 “measure” values on a bullet chart

I am trying to understand a bit more about the statistical intuition behind bullet charts. This one in particular has two "measure" readouts, one is dark blue one is light blue: For clarity, the gray ...
1
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0answers
30 views

Why is degree of freedom so important? [duplicate]

As far as I'm concerned, the degree of freedom is simply the number of linear equations need to be satisfied. However, it seems closely related to the statistical deduction. For example Dividing by ...
9
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13answers
5k views

If 'B is more likely given A', then 'A is more likely given B'

I am trying to get a clearer intuition behind: "If $A$ makes $B$ more likely then $B$ makes $A$ more likely" i.e Let $n(S)$ denote the size of the space in which $A$ and $B$ are, then Claim: $...
1
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1answer
72 views

why ridge regression only decreases slope and not increases it?

I was following the below example from 'StatQuest with Josh Starmer' youtube channel. The example is pretty simple: red line is the usual 'least squares' (for the red points), and the blue one is ...
1
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2answers
316 views

Intuitive explanation of how UMAP works, compared to t-SNE

I have a PhD in molecular biology. My studies recently started to involve high dimensional data analysis. I got the idea of how t-SNE works (thanks to a StatQuest video on YouTube) but can't seem to ...
1
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0answers
33 views

Intuition behind MA(q) (moving average) time series forecasting model (i.e. 'MA' part of ARIMA) and implementation

The $AR(n)$ part of ARIMA makes sense to me. If $$x_{t+1}=\sum_{i=0}^n a_ix_{t-i}$$ then we are making the intuitive assumption that the next time step will somehow depend on the previous time ...
2
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2answers
94 views

Gaussian Processes: A Crucial Assumption?

I'm reading this paper, and I've come to what seems to be a pretty crucial assumption: Now, the n observations in an arbitrary data set, y = {y1, . . . , yn}, can always be imagined as a single ...
0
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0answers
33 views

Is it fair to consider rolling regression a form of bootstrapping?

The context is time series analysis. A few similarities between rolling regression and boostrapping jump out at me, in that both re-use observations to form new subsamples for estimation. However, ...
0
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0answers
23 views

What does this mean? Can you explain it to me in laymans term? [duplicate]

How to interpret this? What does the ARIMA(0,0,0)(0,1,0)[12] means in laymans term?
4
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3answers
166 views

Why ARIMA is prefered over any other time series analysis method

I am new to time series analysis, and I am self learner. I am using R language to learn how to do time series analysis. I started by studying the concepts and the theory behind such analysis, however ...
24
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1answer
483 views

Evidence for man-made global warming hits 'gold standard': how did they do this?

How should we interpret the $5\sigma$ threshold in this research on climate change? This message in a Reuter's article from 25 february is currently all over the news: They said confidence that ...
1
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0answers
20 views

What scenario corresponds to choosing the “true distribution” $p$ in $\textsf{KL}(p\parallel q)$?

I understand that when you think about changing $q$ in the Kullback-Leibler divergence $\textsf{KL}(p\parallel q)$, this corresponds to trying to find the distribution that minimizes information loss ...
3
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0answers
35 views

Which properties yield the exponential family of distributions?

It seems like every resource that discusses exponential families simply defines the family of distributions, explains why it's useful and then derives some of its properties. I have only seen one ...
4
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1answer
80 views

Intuition behind gradient of expected value and logarithm of probabilities

I recently came across the following curious identity: $$\nabla_\theta \mathbb{E}_{x \sim D_\theta}[f(x)] = \mathbb{E}_{x \sim D_\theta} [ \nabla_\theta \log(D_\theta(x)) f(x)],$$ where $D_\theta$ ...
0
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0answers
37 views

Intuition of variance (in the context of linear regression)

I was studying linear regression lately and checking the assumptions for Ordinary Least Squares method for the regression problem. I was not sure about the intuition behind the difference of squares ...
1
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4answers
65 views

How do I intuitively understand that independence is always symmetric?

Independence between two events, $A$ and $B$, is a symmetric relation, that is, if $P(A \mid B) = P(A)$, then $P(B \mid A) = P(B)$. The proof is very simple and can be found at the ProofWiki. ...
2
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2answers
114 views

Understanding the parameters needed for a distribution in Bayes networks?

Since I have a discriminative mindset hardly can I intuit the so-called parameters needed to specify a distribution in a generative Bayesian Network. I'd like to borrow an example from this blog. If ...
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0answers
9 views

What's a simple explanation for risk and its formula in survival analysis, weibull regression

I have that if the model is $\ln(\mu_i) = \beta_0 + \beta_1 x_1$ where $x_1 \in \{0,1\}$ and represents tired (or anything suitable, sex, etc). The model also has a shape parameter, $\gamma$. ...
0
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0answers
37 views

Idea behind change of basis and how it relates to projecting your points onto principal components

I would like to clarify if my understanding is correct. In the traditional X-Y coordinate system, our choice of basis vectors are $\vec{i} = (1, 0)$ and $\vec{j} = (0, 1)$ and when you I have a point $...
2
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1answer
35 views

Explaining modelling in simple terms

One of the most challenging ideas to describe to non-technical/mathematical people is "modelling". I've used quite a few explanations so far but all of them were around specific modelling techniques. ...
0
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0answers
23 views

Anyone can explain simply targeted learninig? [duplicate]

I am trying to understand Targeted Learning (Mark van der Laan), can anyone explain this method simply, please?
1
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1answer
47 views

Intuition behind the no convergence of the variance of sum of random variables

$$Var[\bar{X}] = \sigma^2/n $$ $$Var [\sum{X}_i] = n\sigma^2$$ $$lim_{n \to \infty} Var[\bar{X}] = 0 $$ wich means at $\infty$ we will always get the same $\bar{X}$ after every simulation. I ...
2
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0answers
41 views

Intuition behind White's Estimators/ Heteroscedasticity-consistent Standard Errors

For a medical study I am trying to understand the intuition behind heteroscedasticity-consistent standard errors. I know that it can be used, when in OLS regression residuals are heteroscedastic. By ...
2
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0answers
38 views

intuitive explanation for expected value of the square of a uniform variable

I'm confused about something that should be simple. Suppose I have a random uniform variable $X$ on $[0,1]$. It's fairly clear that the expected value of $X$ is 1/2. By integrating $x^2$ on $[0,1]$, I ...
4
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3answers
406 views

Explaining multicollinearity in layman's terms

Say we have a study where we want to run a logistic regression on a group of people, and we want to find out whether one attribute of a person makes them more likely to be a smoker. So we have smoker ...
2
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2answers
123 views

Intuitive understanding of variance of sum vs variance of difference

$\newcommand{\Var}{\operatorname{Var}}\newcommand{Cov}{\operatorname{Cov}}$Mathematically, $\Var(X + Y) = \Var(X) + \Var(Y) + 2\Cov(X,Y)$ and $\Var(X - Y) = \Var(X) + \Var(Y) - 2\Cov(X,Y)$ This ...
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0answers
130 views

Is there any intuition behind the writing Jensen-Shannon divergence based on the entropy?

I know that Jensen-Shannon divergence between two distribution $P$ and $Q$ can be written as follow: $JS(P||Q) = H(\frac{P+Q}{2}) - \frac{H(P)}{2} - \frac{H(Q)}{2}$ But is there any intuition behind ...
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0answers
24 views

How to Calculate Percent of Sample mean falls within Population Mean? [closed]

Following screenshot is from Udacity Statistics Tutorial. Klout score which is Social Media popularity score is distributed as shown in picture. Population mean is 37.72 and Standard Deviation is ...
6
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0answers
139 views

What guarantees the existence of a finite representation of the Wold decomposition? Mechanics and Intuition

Every covariance stationary process can be written as a linear, infinite distributed lag of white noise. In other words, every covariance stationary process has a Wold representation. Then we go on to ...
3
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2answers
82 views

What does it mean to model data as binomial?

On Wikipedia it says [T]he binomial distribution with parameters $n$ and $p$ is the discrete probability distribution of the number of successes in a sequence of n independent experiments, ...
7
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2answers
287 views

Uncorrelatedness + Joint Normality = Independence. Why? Intuition and mechanics

Two variables that are uncorrelated are not necessarily independent, as is simply exemplified by the fact that $X$ and $X^2$ are uncorrelated but not independent. However, two variables that are ...
14
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2answers
2k views

Is Cauchy distribution somehow an “unpredictable” distribution?

Is Cauchy distribution somehow an "unpredictable" distribution? I tried doing cs <- function(n) { return(rcauchy(n,0,1)) } in R for a multitude of n values ...
0
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0answers
40 views

Gaussianity and Whitening in ICA - The feeling and intuition behind it

I understand what ICA does at a high level but in the cocktail party problem context. All the examples, articles I have read take a similar problem to explain ICA where the aim is to derive the ...
0
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1answer
39 views

When and when not to use activation function between input layer and hidden layer? [duplicate]

I am beginner to Neural Network and this question might be very basic and stupid. Expecting some intuitive answer.
0
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1answer
85 views

What to conclude for the data-set when the variance for principal components is too low or too high?

I am working on analysing and visualizing a dataset having 12 features and came across PCA. I reduced the dataset to 2 principal components which together explain a variance of 18%. I was able to plot ...