# 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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### Dealing with dependent data in a Bayesian model

Background: Consider a series of dependent data points, $$y_1,y_2,y_3,\cdots,y_N.$$ In cases where the dependence is well described by an exponentially decaying auto-correlation function, it is ...
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### Effects of model selection and misspecification testing on inference: Probabilistic Reduction approach (Aris Spanos)

This question is about pre-test bias, inference after model selection and data snooping within the Probabilistic Reduction (PR) methodology by Aris Spanos (which is related to the Error Statistics ...
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### Sampling distribution of sample trimmed (truncated) mean

It is elementary probability theory that the sample mean of an i.i.d. sample follows normal distribution, if the background distribution is normal. But what about the trimmed mean? Is there any result ...
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### How to do inference over two steps in a graphical model simultaneously?

I have observed data $D$ about a physical object described by $M$. I would like to determine the posterior distribution of $M$ given $D$, or $p(M|D)$. Now I can't infer this directly because unknown ...
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### Who invented train/validation/Test method and when?

I can't seem to find here or in other places the earliest source for this method. it seems the holdout method was separately proposed by Highleyman in 1962, and cross validation was separately ...
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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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### Before using CV-selected Regression model for Inference, shouldn't model performance be evaluated on unused test set?

I just came across a biokinesiology paper that used some Machine Learning methods, but I think there is a flaw in their methodology. The authors had data on stroke patients and used Lasso regression ...
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### How much of a problem is inference after model selection when few models are manually compared?

tl;dr: I found a better model than the one I first thought of while inspecting the data and performed a few steps of variable selection/model fine-tuning. I assume that this is a (mild) case of ...
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### use and misuse of Winsorization

I am doing research on Winsorization (and trimming), which has been broadly applied in many fields, but I think many researchers didn't do it in a "rigorous" way. Or maybe even worse, they misuse it. ...
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### Existence of UMVUE of $\theta$ for sample from $\small{\frac{\ln\theta}{\theta-1}\theta^x\,\mathbf1_{0<x<1}}$?

Suppose $X_1,X_2,\ldots,X_n$ is a random sample drawn from a distribution with pdf $$f_{\theta}(x)=\small\frac{\ln\theta}{\theta-1}\theta^x\,\mathbf1_{0<x<1}\quad,\,\theta>1$$ Does there ...
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### Finding the UMVUE of $\theta^2$ where $f_X(x\mid\theta) =\frac{x}{\theta^2}e^{-x/\theta}I_{(0,\infty)}(x)$

Let $X_1, X_2, . . . , X_n$ be iid random variables having pdf $$f_X(x\mid\theta) =\frac{x}{\theta^2}e^{-x/\theta}I_{(0,\infty)}(x)$$ where $\theta >0$. Give the UMVUE of ${\theta^2}$ I ...
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### Survival model for an epidemic — can the observations be treated as independent?

I've been thinking about ways to tackle an epidemic modelling problem I've been working on, and I've come up against a conceptual difficulty over the way survival analysis works. Here's a really ...
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### Fit data based on generating function

Suppose I have iid data generated from a discrete random variable $X_i \sim D(\lambda)$, and I would like to infer the parameter $\lambda$. Unfortunately, I do not know the likelihood function for $D$,...
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### Confidence and credible interval: cases

I am having difficulties in understanding these two approaches. Let's say given the data I compute both confidence and credible interval, then what is the intuition/interpretation of having: Big CI ...
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### In a simple hypothesis vs composite hypothesis test, are the p-values the same?

In a simple hypothesis test, we have something like $H_0 = 5$ and $H_A = 10$ while in a composite hypothesis test we have something like $H_0 = 5$ and $H_A >5$. Since the p-value is defined to be ...
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### Expectation-Maximization with dependent latent variables

Deriving the equations for a Expectation Maximization over my model, I end up with a posterior for the latent variables (E-step) that prevents me from going on. Generative model I assume my data is ...