Questions tagged [inference]

Drawing conclusions about population parameters from sample data. See https://en.wikipedia.org/wiki/Inference and https://en.wikipedia.org/wiki/Statistical_inference

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How to interpret a QQ plot

I am working with a small dataset (21 observations) and have the following normal QQ plot in R: Seeing that the plot does not support normality, what could I infer about the underlying distribution? ...
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110 votes
7 answers
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T-test for non normal when N>50?

Long ago I learnt that normal distribution was necessary to use a two sample T-test. Today a colleague told me that she learnt that for N>50 normal distribution was not necessary. Is that true? If ...
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100 votes
9 answers
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Understanding "variance" intuitively

What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their child how would one go about it? It's a concept that I ...
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95 votes
12 answers
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Who Are The Bayesians?

As one becomes interested in statistics, the dichotomy "Frequentist" vs. "Bayesian" soon becomes commonplace (and who hasn't read Nate Silver's The Signal and the Noise, anyway?). In talks and ...
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69 votes
8 answers
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What is a good, convincing example in which p-values are useful?

My question in the title is self explanatory, but I would like to give it some context. The ASA released a statement earlier this week “on p-values: context, process, and purpose”, outlining various ...
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67 votes
32 answers
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What are the worst (commonly adopted) ideas/principles in statistics?

In my statistical teaching, I encounter some stubborn ideas/principles relating to statistics that have become popularised, yet seem to me to be misleading, or in some cases utterly without merit. I ...
64 votes
3 answers
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Testing equality of coefficients from two different regressions

This seems to be a basic issue, but I just realized that I actually don't know how to test equality of coefficients from two different regressions. Can anyone shed some light on this? More formally, ...
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63 votes
13 answers
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Two-tailed tests... I'm just not convinced. What's the point?

The following excerpt is from the entry, What are the differences between one-tailed and two-tailed tests?, on UCLA's statistics help site. ... consider the consequences of missing an effect in the ...
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58 votes
6 answers
61k views

Rule of thumb for number of bootstrap samples

I wonder if someone knows any general rules of thumb regarding the number of bootstrap samples one should use, based on characteristics of the data (number of observations, etc.) and/or the variables ...
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50 votes
7 answers
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Why would someone use a Bayesian approach with a 'noninformative' improper prior instead of the classical approach?

If the interest is merely estimating the parameters of a model (pointwise and/or interval estimation) and the prior information is not reliable, weak, (I know this is a bit vague but I am trying to ...
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46 votes
4 answers
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What are the factors that cause the posterior distributions to be intractable?

In Bayesian statistics, it is often mentioned that the posterior distribution is intractable and thus approximate inference must be applied. What are the factors that cause this intractability?
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46 votes
6 answers
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Why do we need multivariate regression (as opposed to a bunch of univariate regressions)?

I just browsed through this wonderful book: Applied multivariate statistical analysis by Johnson and Wichern. The irony is, I am still not able to understand the motivation for using multivariate (...
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42 votes
3 answers
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How do DAGs help to reduce bias in causal inference?

I have read in several places that the use of DAGs can help to reduce bias due to Confounding Differential Selection Mediation Conditioning on a collider I also see the term “backdoor path” a lot. ...
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37 votes
2 answers
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Should we address multiple comparisons adjustments when using confidence intervals?

Suppose we have a multiple comparisons scenario such as post hoc inference on pairwise statistics, or like a multiple regression, where we are making a total of $m$ comparisons. Suppose also, that we ...
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34 votes
8 answers
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Intuitive explanation of "Statistical Inference"

What is the cleanest, easiest way to explain someone the concept of Inference? What does it intuitively mean? How would you go to explain it to the layperson, or to a person who has studied a very ...
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34 votes
7 answers
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Inference vs. estimation?

What are the differences between "inference" and "estimation" under the context of machine learning? As a newbie, I feel that we infer random variables and estimate the model parameters. Is my this ...
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34 votes
2 answers
2k views

Performing a statistical test after visualizing data - data dredging?

I'll propose this question by means of an example. Suppose I have a data set, such as the boston housing price data set, in which I have continuous and categorical variables. Here, we have a "quality"...
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34 votes
2 answers
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How to derive the standard error of linear regression coefficient

For this univariate linear regression model $$y_i = \beta_0 + \beta_1x_i+\epsilon_i$$ given data set $D=\{(x_1,y_1),...,(x_n,y_n)\}$, the coefficient estimates are $$\hat\beta_1=\frac{\sum_ix_iy_i-n\...
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33 votes
4 answers
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What is the fiducial argument and why has it not been accepted?

One of the late contributions of R.A. Fisher was fiducial intervals and fiducial principled arguments. This approach however is nowhere near as popular as frequentist or Bayesian principled arguments. ...
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32 votes
3 answers
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Why does basic hypothesis testing focus on the mean and not on the median?

In basic under-grad statistics courses, students are (usually?) taught hypothesis testing for the mean of a population. Why is it that the focus is on the mean and not on the median? My guess is that ...
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32 votes
3 answers
979 views

Accommodating entrenched views of p-values

Sometimes in reports I include a disclaimer about the p-values and other inferential statistics I've provided. I say that since the sample wasn't random, then such statistics would not strictly apply....
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28 votes
8 answers
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Why are hypothesis tests still used when we have the bootstrap and central limit theorem?

Why are hypothesis tests still used when we have the bootstrap and central limit theorem? To give context to my question, I briefly go over the central limit theorem and illustrate a simulation ...
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28 votes
3 answers
9k views

What if your random sample is clearly not representative?

What if you take a random sample and you can see it is clearly not representative, as in a recent question. For example, what if the population distribution is supposed to be symmetric around 0 and ...
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27 votes
2 answers
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Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution?

My understanding is that when using a Bayesian approach to estimate parameter values: The posterior distribution is the combination of the prior distribution and the likelihood distribution. We ...
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27 votes
2 answers
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Why is the Fisher Information matrix positive semidefinite?

Let $\theta \in R^{n}$. The Fisher Information Matrix is defined as: $$I(\theta)_{i,j} = -E\left[\frac{\partial^{2} \log(f(X|\theta))}{\partial \theta_{i} \partial \theta_{j}}\bigg|\theta\right]$$ ...
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26 votes
4 answers
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Kullback-Leibler divergence WITHOUT information theory

After much trawling of Cross Validated, I still don't feel like I'm any closer to understanding KL divergence outside of the realm of information theory. It's rather odd as somebody with a Math ...
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25 votes
3 answers
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Inference after using Lasso for variable selection

I'm using Lasso for feature selection in a relatively low dimensional setting (n >> p). After fitting a Lasso model, I want to use the covariates with nonzero coefficients to fit a model with no ...
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25 votes
2 answers
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How does the inverse transform method work?

How does the inversion method work? Say I have a random sample $X_1,X_2,...,X_n$ with density $f(x;\theta)={1\over \theta} x^{(1-\theta)\over \theta}$ over $0<x<1$ and therefore with cdf $F_X(x)=...
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25 votes
2 answers
8k views

Why is the posterior distribution in Bayesian Inference often intractable?

I have a problem understanding why Bayesian Inference leads to intractable problems. The problem is often explained like this: What I don't understand is why this integral has to be evaluated in the ...
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24 votes
2 answers
2k views

What does "fiducial" mean (in the context of statistics)?

When I Google for "fisher" "fiducial" ...I sure get a lot of hits, but all the ones I've followed are utterly beyond my comprehension. All these hits do seem to ...
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23 votes
2 answers
3k views

What non-Bayesian methods are there for predictive inference?

In Bayesian inference a predictive distribution for future data is derived by integrating out unknown parameters; integrating over the posterior distribution of those parameters gives a posterior ...
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23 votes
3 answers
4k views

Using regularization when doing statistical inference

I know about the benefits of regularization when building predictive models (bias vs. variance, preventing overfitting). But, I'm wondering if it is a good idea to also do regularization (lasso, ...
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23 votes
1 answer
5k views

How many times must I roll a die to confidently assess its fairness?

(Apologies in advance for use of lay language rather than statistical language.) If I want to measure the odds of rolling each side of a specific physical six-sided die to within about +/- 2% with a ...
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22 votes
3 answers
5k views

Comparison between MaxEnt, ML, Bayes and other kind of statistical inference methods

I'm in no way a statistician (I've had a course in mathematical statistics but nothing more than that), and recently, while studying information theory and statistical mechanics, I met this thing ...
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22 votes
3 answers
10k views

Neyman-Pearson lemma

I have read the Neyman–Pearson lemma from the book Introduction to the Theory of Statistics by Mood, Graybill and Boes. But I have not understood the lemma. Can anyone please explain the lemma to ...
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21 votes
6 answers
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What is the difference between descriptive and inferential statistics?

My understanding was that descriptive statistics quantitatively described features of a data sample, while inferential statistics made inferences about the populations from which samples were drawn. ...
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21 votes
2 answers
2k views

If the likelihood principle clashes with frequentist probability then do we discard one of them?

In a comment recently posted here one commenter pointed to a blog by Larry Wasserman who points out (without any sources) that frequentist inference clashes with the likelihood principle. The ...
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20 votes
4 answers
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Flaws in Frequentist Inference

I have problem to understanding the following example. (1) After the next day that the glitch discovered what can tell about the observation? $X_i\nsim N(\mu,1)$ or just $X_i\sim N(\mu_2,1)$. Some ...
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20 votes
3 answers
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Do the pdf and the pmf and the cdf contain the same information?

Do the pdf and the pmf and the cdf contain the same information? For me the pdf gives the whole probability to a certain point(basically the area under the probability). The pmf give the probability ...
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20 votes
2 answers
4k views

Elastic/ridge/lasso analysis, what then?

I'm getting really interested in the elastic net procedure for predictor shrinkage/selection. It seems very powerful. But from the scientific point of view I don't know well what to do once I got the ...
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20 votes
2 answers
533 views

Minimizing bias in explanatory modeling, why? (Galit Shmueli's "To Explain or to Predict")

This question references Galit Shmueli's paper "To Explain or to Predict". Specifically, in section 1.5, "Explaining and Prediction are Different", Professor Shmueli writes: In explanatory ...
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19 votes
3 answers
33k views

What are "coefficients of linear discriminants" in LDA?

In R, I use lda function from library MASS to do classification. As I understand LDA, input $...
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18 votes
7 answers
32k views

MLE vs MAP estimation, when to use which?

MLE = Maximum Likelihood Estimation MAP = Maximum a posteriori MLE is intuitive/naive in that it starts only with the probability of observation given the parameter (i.e. the likelihood function) and ...
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18 votes
4 answers
739 views

War stories where wrong decisions were made based on statistical information?

I think it is fair to say statistics is an applied science so when averages and standard deviations are calculated it is because someone is looking to make some decisions based on those numbers. ...
18 votes
1 answer
10k views

Bayesian network inference using pymc (Beginner's confusion)

I am currently taking the PGM course by Daphne Koller on Coursera. In that, we generally model a Bayesian Network as a cause and effect directed graph of the variables which are part of the observed ...
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17 votes
3 answers
1k views

What is the difference between a "statistical experiment" and a "statistical model"?

I am following A.W. van der Vaart, asymptotic statistics (1998). He talks of statistical experiments, claiming that they are different from a statistical model, but he defines neither. My question: ...
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17 votes
3 answers
951 views

Should "City" be a fixed or a random effect variable?

I am analyzing data on "BloodSugar" level (dependent variable) and trying to find its relation with "age", "gender" and "weight" (independent variables) of ...
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17 votes
3 answers
18k views

Do descriptive statistics have p-values?

I'm being asked to find the p-values for descriptive statistics. However, it's my understanding that p-values are for test statistics. If I'm not mistaken, a p-value is the probability of observing a ...
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17 votes
3 answers
2k views

Good summaries (reviews, books) on various applications of Markov chain Monte Carlo (MCMC)?

Are there any good summaries (reviews, books) on various applications of Markov chain Monte Carlo (MCMC)? I've seen Markov Chain Monte Carlo in Practice, but this books seems a bit old. Are there ...
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17 votes
3 answers
8k views

What does a 'tractable' distribution mean?

For example, in generative adversarial network, we often hear that inference is easy because the conditional distribution of x given latent variable z is 'tractable'. Also, I read somewhere that ...
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