# 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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### Sufficient statistics for $\mu_1 - \mu_2$

If $X_1, ..., X_n$ is a random sample from $X \sim N(\mu_1, \sigma^2)$ and $Y_1,..., Y_n$ is a random sample from $Y \sim N(\mu_2, \sigma^2),$ if the samples are independent and $\sigma^2$ is known,...
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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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### What is the difference between a "population," a "sample space," an "underlying probability distribution? and a "model"?

I'm trying to understand an overview of the topic of statistical inference. I have learnt bits and pieces of many of the probability and statistics involved in it but before learning it rigorously it ...
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### Can an asymptotically efficient estimator be biased?

In "Theory of point estimation" by Lehmann and Casella (1998) there is the following definition: It is also said that So terms of the asymptotically normal sequence of estimators can be ...
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### How to make Bayesian-style inference for a Poisson process?

I am working on a fleet management software recently. Normally, the arrival of merchant request is a Poisson process. That is to say, on average we have a new merchant request every 10 minutes, but ...
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### Let $X_1,X_2,\dots,X_n$ be random sample from Poisson($\theta$). Find MVUE of $e^{-2\theta}$

Question: Let $X_1,X_2,\dots,X_n$ be random sample from Poisson($\theta$). Find MVUE of $e^{-2\theta}$ My attempt has been by modifying the answer from this question: The Poisson distribution is a one-...
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### How to show a UMVUE exists only if $g(p)$ is a polynomial of degree at most $n$?

Let $X\sim Bin(n,p)$. The problem is to show that a UMVUE can exist for $g(p)$ only if $g(p)$ is a polynomial in $p$ of degree at most $n$. For the case when $g(p) = \frac{1}{p}$ we can show that it ...
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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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### Deductive reasoning and artificial intelligence

AI has proven to be extraordinary effective for solving certain types of intellectual problems that we thought before only our brains could solve. The number of applications is tremendous: engineering,...
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### What Statistical principles are being violated by comparing specific Trainer Fatality Rates to Race Track Fatality rates?

A Hall of Fame Trainer of Thoroughbred Racehorses has been banned from a Race Track because 7 horses under his care have have been injured while training or racing in the past year. Critics cite a ...
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### Determine statistical difference of slopes of quadratic relationship in a Poisson regression

I'm looking for a statistical or mathematical way to test the difference between two slopes. Others have asked related questions but my problem is quite particular. I'm running a Poisson regression ...