# 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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### Is it acceptable to run two linear models on the same data set?

For a linear regression with multiple groups (natural groups defined a priori) is it acceptable to run two different models on the same data set to answer the following two questions? Does each group ...
212 views

### Reverse birthday problem with multiple collisions

Assume you had an alien year with an unknown length N. If you have a random sample of said aliens and some of them share birthdays, can you use this data to estimate the length of the year? For ...
168 views

### Measuring some of the patients more than once

I'm conducting a clinical study where I determine an anthropometrical measure of the patients. I know how to handle the situation where I have one measure per patient: I make a model, where I have a ...
500 views

### How is prior knowledge possible under a purely Bayesian framework?

This is more of a philosophical question, but from a purely Bayesian standpoint how does one actually form prior knowledge? If we need prior information to carry out valid inferences then there seems ...
3k views

### Mixture Models and Dirichlet Process Mixtures (beginner lectures or papers)

In the context of online clustering, I often find many papers talking about: "dirichlet process" and "finite/infinite mixture models". Given that I've never used or read about dirichlet process or ...
960 views

### Understanding the Behrens–Fisher problem

This section of this article says: Ronald Fisher in 1935 introduced fiducial inference in order to apply it to this problem. He referred to an earlier paper by W. V. Behrens from 1929. Behrens and ...
7k views

### Interpret Regression Coefficients After various Differencing

There are few explanations I can find that describe how to interpret linear regression coefficients after differencing a time series (to eliminate a unit root). Is it just so simple that there is no ...
2k views

### Is there a test/technique/method for comparing principal components decompositions between samples?

Is there any methodical way to compare the directions, magnitudes, etc of PCA results for different samples drawn from the same population? I'm leaving the nature of the test deliberately vague ...
2k views

### Complete sufficient statistic

I've recently started studying statistical inference. I've been working through various problems and this one has me completely stumped. Let $X_1,\dots,X_n$ be a random sample from a discrete ...
120 views

### What are the recent works and research scope in asymptotic inference (large sample theory)?

What are some current significant theoretical work that has been done in the field of asymptotic inference / large sample theory? What is the research scope in this field right now? Is there any open ...
4k views

### Complete statistic for $\sigma^2$ in a $N(\mu,\sigma^2)$

I would like to know if the statistic $$T(X_1,\ldots,X_n)=\frac{\sum_{i=1}^n (X_i-\bar{X}_n)^2}{n-1}$$ is complete for $\sigma^2$ in a $N(\mu,\sigma^2)$ setting. Does this depend on whether $\mu$ is ...
598 views

### Choosing non-informative priors

I am working on a model relying on an ugly parametrized function acting as a calibration function on a part of the model. Using a Bayesian setting, I need to get non-informative priors for the ...
993 views

### Bayesian inference on a sum of iid real-valued random variables

Let $X_1$, $X_2$, ..., $X_n$ be iid RV's with range $[0,1]$ but unknown distribution. (I'm OK with assuming that the distribution is continuous, etc., if necessary.) Define $S_n = X_1 + \cdots + X_n$...
923 views

### Why is the marginal likelihood difficult/intractable to estimate?

I have a generally basic question to ask here that has been troubling to me for a while. Through most of my reading of bayesian statistics, it stated matter-of-factedly that the marginal likelihood is ...
826 views

### What is probabilistic programming?

For the past year, I've been hearing a lot about Probabilistic Programming (PP) frameworks like PyMC3 and Stan, and how great PP is. And today, someone shared this link with me: Pyro: a Deep ...
953 views

### What is the difference using a Fisher's Exact Test vs. a Logistic Regression for $2 \times 2$ tables?

For a $2 \times 2$ table, two ways to do inference on the table is through Fisher's Exact Test and also a Logistic Regression. I was told that using a Fisher's Exact Test, we are only interested in ...
539 views

### 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 ...
1k views

### Is confirmatory vs exploratory statistics “induction vs deduction”?

This webpage says: Inferential Statistics - Deductive Approach Descriptive Statistics - Inductive Approach But I doubt it. If I understand correctly, Inferential Statistics is "given some ...
2k views

### Is there a GLM bible?

Is there consensus in the field of statistics that one book is the absolute best source and completely covering every aspect of GLM - detailing everything from estimation to inference?
1k views

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### Differences between prior distribution and prior predictive distribution?

While studying Bayesian statistics, somehow I am facing a problem to understand the differences between prior distribution and prior predictive distribution. Prior distribution is sort of fine to ...
I would like to find a way to show whether the sample quantile is an unbiased estimator of the true quantiles. Let $F$ be strictly increasing with density function $f$. I will define the $p$-th ...