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 ...
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 ...
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: ...
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 ...
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 ...
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' ...
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 ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 ...
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 ...
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 ...
98 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 ...
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 ...
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 ...
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 ...
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 ...
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() ...
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 ...
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 ...
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 ...
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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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 ...
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 ...
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 ...
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 ...
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, ...
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) means in laymans term?
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 ...
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 ...
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 ...
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 ...
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 $D_\theta$ ...
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 ...
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. ...
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, $\gamma$. ...