Questions tagged [intuition]

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

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Intuitive Understanding of the Effect of Correlation on Random Variables in Gaussian Process

So In general covariance matrix in GP provides us with proportionality relation between random variables, in other words $x_1$ and $x_2$ are perfectly correlated if off-diagonal entry has $\rho=\pm 1$:...
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2answers
283 views

Linear and non linear Regression models for single variable

I want to know if there is any regression model for single variable other than simple linear regression. I usually use tree based regression models when there are more than 1 feature and for data with ...
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18 views

AutoEncoder training intuition

I am trying to understand the mechanisms of training an AE and how each of the following components influence the training process: Training data distribution AE architecture Loss function These ...
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20 views

How to understand 'unit roots' in time series data? [duplicate]

What is the meaning of UNIT ROOT in time series modelling? I understand that, for a time series data to be stationary, the mean and standard deviation must be constant throughout the period considered....
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64 views

how to explain canonical correlation to laymen?

Given two sets of variables and the objective of finding correlations among the variables in the two sets, is there any simple examples or explanation, for a group of biologists knowing only basic ...
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1answer
83 views

Advantages/disadvantages of fractional factorial design vs completely randomized design

I'm new to the design of experiments (DoE) and will be running a screening experiment to estimate the effect of a large number of binary independent variables (approximately 10) on a single continuous ...
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78 views

Force directed graphs vs. diffusion maps vs. other dimensionality reduction methods

Can you help me with a conceptual explanation of how force directed graph drawings work compared to other methods in the context of dimensionality reduction for visualization purposes? In particular, ...
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35 views

When computing MLE for linear regression, where does the uncertainty come from?

In my Machine Learning course, when computing MLE for a linear regression problem, we modeled the likelihood function as a Gaussian. I have trouble understanding why. Where does the uncertainty come ...
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1answer
67 views

How to interpret “quantile residuals”

The DHARMa package in R aims to provide scaled (quantile) residuals that, according to the DHARMa vignette, "can be interpreted as intuitively as residuals from ...
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1answer
67 views

What is the intuition behind the factorization theorem? (Sufficient statistics)

By the Fisher's factorization theorem, a statistics is a sufficient statistic if (and only if) the joint density, $$ f(x_1, x_2, x_3, \dots x_n; \theta) $$ can be factorized into two functions, $ g(...
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58 views

Can someone explain Ripley's proof (1996) of the splitting of categorical variables?

Specifically I am referring to this theorem: 1) Suppose there are two classes. For a categorical feature , order the levels in increasing $p(1\mid x = x_i)$. Then a split of the form $\{x_1, ... x_{\...
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6 views

Simple question about the source of variation after fixed effects

Could you please give me the intuition of where does the variation comes from a fixed effects regression? I understand the simpler structures, such as: $y_{it}=\beta_0+\beta_1x_{it}+\alpha_i+\alpha_t+...
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2answers
57 views

Why is the sum of all the elements in a Gaussian-distributed list with zero mean not zero?

If I generate a list of elements which has a Gaussian distribution with zero mean: List = np.random.normal(0, 1, 500) my intuition (why is obviously wrong) tells ...
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61 views

BCA bootstrap intuition

The papers below claims that BCa bootstrap improves bootstrap estimate accuracy over standard quantile bootstrapping, I think by adjusting for the underlying distribution's skew and bias. I am looking ...
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13 views

Intuition about how the formula for “variance of axis of angle $\alpha$ with horizontal axis” works (multiple correspondents analysis)

From the text : Multiple Correspondents Analysis by Brigette LeRoux the following is given (page 32). For the purposes of this post I'm just considering there to be two dimensions that point clouds ...
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2answers
52 views

Intutitive meaning behind the formal definition of sufficient statistic?

According to the definition of sufficiency, a statistic is sufficient for a parameter if the conditional distribution of $X$ given a value of statistic does not depend upon the parameter. What I am ...
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8answers
12k views

Is there a name for the phenomenon of false positives counterintuitively outstripping true positives

It seems very counter intuitive to many people that a given diagnostic test with very high accuracy (say 99%) can generate massively more false positives than true positives in some situations, namely ...
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2answers
100 views

What is the conceptual difference between posterior and likelihood? [duplicate]

I have trouble discerning conceptually between these two notions. I am aware of their formal relations, proprieties and what not, but I just can't wrap my head around what they "mean", if that even ...
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1answer
45 views

Better measure of tail extremity than kurtosis

According to Wikipedia, the only correct interpretation of kurtosis is "tail extremity," the logic being that datapoints within one standard deviation of the mean are raised to the fourth power and ...
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61 views

Simple(st) BI use case for confidence/prediction ellipse visual

I noticed confidence ellipse visuals are not uncommon in scholarly journals, here is one concerning equity premiums. Here is the kind of confidence ellipse that I'm considering for visual reference: ...
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40 views

Making one-sided conclusions from two-sided tests

I'm reading Montgomery's Design and Analysis of Experiments. On page 39, he rejected a two-sided $t$-test against the null hypothesis that modified formulation of some cement mortar doesn't change its ...
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1answer
29 views

why is the level equation in the holt winters triple exponential model different from the other two?

the double exponential model is so simple: level: $s_t = \alpha x_t + (1-\alpha)(s_{t-1}+b_{t-1})$ trend: $b_t = \beta (s_t - s_{t-1}) + (1-\beta)b_{t-1}$ both intuitively weigh the new information ...
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1answer
63 views

Understand neural network in a 'mathematical' way

This is a soft question. But as I read papers/reports about neural network used for pictures. Often there are comments like 'the first layer of the neural network captures the edge/shape information' ...
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29 views

Evaluating a model with Log Loss

I have been looking at alternative ways to intuitively understand the "goodness" of probability predictions from 2-class logistic regression models (and other ML classification models) and came ...
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1answer
47 views

What should a player flipping a coin “expect”?

Thanks for reading. Earlier today, I asked this question on the Math StackExchange: https://math.stackexchange.com/questions/3307837/do-i-break-even-in-a-fair-game If someone were to run a computer ...
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11 views

Difference between spline approximation and models with spline [duplicate]

I am familiar with splines and fitting them. I have recently encountered the possibility to add splines in models (GLM / GAM for exemple). I am under the impression that these notions are ...
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43 views

What's the difference between using a composite null and running a power calculation for minimal effect size?

Probably a weird place to quote, but I just stumbled across this discussion on Reddit, and one of them said (with typos fixed): The effect size in a power calculation has no relationship whatsoever ...
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1answer
225 views

How does Fisher calculate his $p$-value?

After reading a lot of great answers on the topic of Fisherian versus Neyman & Pearson, I still cannot understand how Fisher carries out his test. Here is my understanding of his workflow: ...
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1answer
42 views

Intuition behind difference between specific sequences and sequences with specific properties?

I simply cannot wrap my head around this fact: "A fair coin is no more likely to produce any specific 10-toss sequence than any specific other one, but it is about 250 times as likely to produce one ...
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5k views

When does Fisher's “go get more data” approach make sense?

Quoting gung's great answer Allegedly, a researcher once approached Fisher with 'non-significant' results, asking him what he should do, and Fisher said, 'go get more data'. From a Neyman-Pearson ...
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34 views

Using same sample in two successive hypothesis tests

Quoting On the Problem of the Most Efficient Tests of Statistical Hypotheses (J. Neyman; E. S. Pearson, 1933) Consider, for example, the problem of testing the significance of a difference between ...
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1answer
137 views

How can I understand the complex regression models?

I can understand how it works when there are two variables in the linear regression model(the shaded circles represent the observed variables, and the white ones the latent variables): We can draw ...
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2answers
133 views

Why must a null hypothesis contain equality?

Using the inference of mean as an example, the null and alternative hypothesis could be $$H_0: \mu \le 0 \Leftrightarrow H_1: \mu > 0$$ It is often argued that this makes the calculation of the $...
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1answer
63 views

Why intuitively does $\mathbb E(\frac d {d\theta}\log p_\theta(x))=0$?

Let $p_\theta(x)$ be the probability density function of $x$. Then obviously, $\frac d{d\theta}\mathbb E(1)=0$. But note that $\mathbb E(1)=\int p_\theta(x)dx$, so that $\frac d{d\theta}\mathbb E(1)=\...
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3answers
141 views
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Intuition for nonmonotonicity of coefficient paths in ridge regression

Intuitively, why may some of the slope coefficients in ridge regression increase in magnitude when the penalty parameter $\lambda$ is increased? Or in other words, why are the coefficient paths ...
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34 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 ...
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32 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 ...
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13 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 ...
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1answer
34 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 ...
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2answers
95 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() ...
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2answers
244 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 ...
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1answer
132 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 ...
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1answer
125 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 ...
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1answer
93 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 ...
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15 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{...
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1answer
62 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 ...
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1answer
38 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 ...
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1answer
124 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 ...
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1answer
388 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 ...
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1answer
30 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 ...

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