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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Measuring mutual dependencies between variables. The most fundamental relation

One has a simple dataset of 3 independent variables, e.g., x, y, z. Now: y and z are logically connected (this is known a priori) and indeed a nice & tight correlation (small scatter) between ...
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Does the posterior necessarily follow the same conditional dependence structure as the prior?

One of the assumptions in a model is the conditional dependence between random variables in the joint prior distribution. Consider the following model, $$p(a,b|X) \propto p(X|a,b)p(a,b)$$ Now suppose ...
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Data distributions extrapolation

Is there a way to extrapolate (according to variance or other statistics) distributions from data? In other words, I have a gene expression matrix in which rows are genes while columns are samples (i....
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On estimators that do not converge to a constant

Say one had constructed an estimator $\hat{\mu}_n$ for a parameter $\mu$ and that such estimator had the property that $$\hat{\mu}_n \xrightarrow {d} X$$ where $X$ is a random variable with an ...
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Does Normality Imply Randomness?

I have data indicating the number of counts per minute (so 60 rows in total - one for each minute - and # of events in that minute). I have ran the Shapiro - Wilk test which implies the data does not ...
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Bayesian estimation of weighted proportion

Having bayesian estimates of a proportion is relatively easy. You model that proportion as a binomial variable, you choose a beta-binomial prior and by using the likelihood you obtain a beta-binomial ...
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What is the meaning of × in statistics?

What is the meaning of the symbol × in an ANOVA context? More specifically what is the meaning of × in the following table? ...
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In the fully supervised case, provided we have contingency matrices, is Bayesian inference the optimal method?

BACKGROUND Imagine that we have contingency matrices, i.e., counts or frequencies, linking the features (say, columns) and targets (rows). One could then compute the posterior probabilities, i.e., ...
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Machine learning: is the effect of one predictor adjusted for the others?

In machine learning - notably ensemble methods such as random forest, gradient boosting, extreme gradient boosting etc - can we say that the effect obtained for one predictor is ADJUSTED for all other ...
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How can I get the 95% simultaneous confidence interval for four proportions?

300 male high school students are surveyed on their smoking frequencies, the results are following: Frequency (1)never smoke (2) 1-4/day (3) 5-10/day (4)more than 10/day Number of people ...
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Inferring random variables from their sum

Suppose I have a large set of receipts that list the items I bought, but only list the total cost. One day I might have bought Milk, Butter, and Eggs. A different day I might have bought Bread, Milk,...
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How to Use Chi-Squared Test for Inference about Three-way independence

If I recall correctly, three random variables X, Y, and Z are three-way independent iff these two statements are met: P(X∩Y∩Z) = P(X)P(Y)P(Z) X, Y, and Z are all pairwise independent of each other. ...
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Calculate risk between classes

I am doing some exercises about logistic regression with SAS and I need to calculate and interpret odds. For calculating the individual probabilities I use those formulas: While later, the Professor,...
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How time series structure can affect the independence of residuals condition for MLR?

I am going through all four conditions for Multiple Linear Regression and stick with this question: what happens with the independence if we have time series data structure?
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How to compare two statistical distributions with unavailability measurements?

I have two different measuring instruments to evaulate if an electronic device is working or not. These instruments provide a working/not-working reading each day and at the end of the month I compute ...
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Generalizing Bayesian methods by assuming a “distribution of distributions” instead of a prior

Bayesian methods assume a prior distribution with several hyperparameters. Unfortunately, this is asymptotically incorrect, because distributions in the real world are never exact. For example, the ...
This question is a follow-up/extension to this post. Suppose I have four regressions. $y_i=x_i\beta_i+\epsilon_i,\quad i=1,2,3,4$ I want to test whether $(\beta_1-\beta_2)-(\beta_3-\beta_4)>0$....
When we calculate the standard error of a regression coefficient, we do not account for the randomness in the design matrix $X$. In OLS for instance, we calculate $\text{var}(\hat{\beta})$ as \$\text{...