Questions tagged [intuition]

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

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34 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
32 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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47 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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0answers
37 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
21 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
58 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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19 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
46 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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0answers
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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0answers
40 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 ...
4
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1answer
180 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
23 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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33 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
94 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
98 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
59 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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17 views

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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0answers
33 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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0answers
24 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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0answers
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
25 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
57 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
158 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
109 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
66 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
55 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
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 ...
4
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1answer
105 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
170 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
21 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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0answers
39 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 ...
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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: $...
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1answer
159 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 ...
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2answers
3k 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 ...
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0answers
52 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
106 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 ...
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0answers
73 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, ...
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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?
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3answers
318 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 ...
35
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2answers
796 views

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

This message in a Reuter's article from 25.02.2019 is currently all over the news: Evidence for man-made global warming hits 'gold standard' [Scientists] said confidence that human activities ...
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21 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 ...
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0answers
39 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 ...
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1answer
168 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 $D_\theta$ ...
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0answers
48 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 ...
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4answers
113 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. ...
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2answers
159 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, $\gamma$. ...