# 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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### Do likelihood ratios and Bayesian model comparison provide superior & sufficient alternatives to null-hypothesis testing?

In response to a growing body of statisticians and researchers that criticize the utility of null-hypothesis testing (NHT) for science as a cumulative endeavour, the American Psychological Association ...
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### Is frequentist conditional inference still being used in practice?

I've recently reviewed some old papers by Nancy Reid, Barndorff-Nielsen, Richard Cox and, yes, a little Ronald Fisher on the concept of "conditional inference" in the frequentist paradigm, which ...
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### Can a trend stationary series be modeled with ARIMA?

I have a question / confusion about stationary series required for modeling with ARIMA(X). I am thinking of this more in terms of inference (effect of an intervention), but would like to know if ...
962 views

### Are independent variables necessarily “independent” and how does this relate to what's being predicted?

I'm fairly new to statistics. I'm not clear on the meaning of independent and dependent variables and the relationship to what's being predicted. In my text, as an example there is a data set ...
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### Why I should use Bayesian inference with uninformative prior? [duplicate]

I am a Ph.D. student and currently I am studying Bayesian inference concerning vector autoregressive models. A lot of researchers when talking about uninformative prior, conclude that the results of ...
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### In Bayesian inference, why are some terms dropped from the posterior predictive?

In Kevin Murphy's Conjugate Bayesian analysis of the Gaussian distribution, he writes that the posterior predictive distribution is $$p(x \mid D) = \int p(x \mid \theta) p(\theta \mid D) d \theta$$ ...
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### Formula for 95% confidence interval for $R^2$

I googled and searched on stats.stackexchange but I cannot find the formula to calculate a 95% confidence interval for an $R^2$ value for a linear regression. Can anyone provide it? Even better, let'...
686 views

### Behrens–Fisher problem

Is there a good published expository account, with mathematical details, of the various approaches that have been taken to the Behrens–Fisher problem?
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### If a tennis match was a single large set, how many games would give the same accuracy?

Tennis has a peculiar three tier scoring system, and I wonder if this has any statistical benefit, from the point of view of a match as an experiment to determine the better player. For those ...
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### Researcher 1 runs 1000 regressions, researcher 2 runs only 1, both get same results — should they make different inferences?

Imagine a researcher is exploring a dataset and runs 1000 different regressions and he finds one interesting relationship among them. Now imagine another researcher with the same data runs just 1 ...
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### 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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### Inference on fixed effects in a mixed effects model

I have correlated data and am using a logistic regression mixed effects model to estimate the individual level (conditional) effect for a predictor of interest. I know that for standard marginal ...
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### Maximum likelihood parameters deviate from posterior distributions

I have a likelihood function $\mathcal{L}(d | \theta)$ for the probability of my data $d$ given some model parameters $\theta \in \mathbf{R}^N$, which I would like to estimate. Assuming flat priors on ...
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### How would you explain statistical significance to people with no statistical background?

Background: I had to perform a data analysis for a client (some kind of lawyer) who was an absolute beginner in statistics. He asked me what the term "statistical significance" means and I really ...
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### Maximum Likelihood estimator - confidence interval

How can I construct an asymptotic confidence interval for a real parameter, starting from the MLE for that parameter?
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### Why aren't “error in X” models more widely used?

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{...
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### Estimating probability of success, given a reference population

Suppose you have the following situation: You observed over time 1000 bowling players, who each played a relatively small number of games (say 1 to 20). You noted the strike percentage for each of ...
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### What does “variational” mean?

Does the use of "variational" always refer to optimization via variational inference? Examples: "Variational auto-encoder" "Variational Bayesian methods" "Variational renormalization group"
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### Neg Binomial and the Jeffreys' Prior

I'm trying to obtain the Jeffreys' prior for a negative binomial distribution. I can't see where I go wrong, so if someone could help point that out that would be appreciated. Okay, so the situation ...
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### In general, is doing inference more difficult than making prediction?

My question comes from the following fact. I have been reading posts, blogs, lectures as well as books on machine learning. My impression is that machine learning practitioners seem to be indifferent ...
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### Are bayesian methods inherently sequential?

Ie, to do sequential analysis (you don't know ahead of time exactly how much data you will collect) with frequentist methods requires special care; you can't just collect data until the p-value gets ...
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### Hypothesis Testing and the Scientific Method

Reading the answers to this thread, I started wondering about how Hypothesis Testing relates to the Scientific Method. While I have a good understanding of both, I am having a hard time drawing the ...
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### What is the difference between VAE and Stochastic Backpropagation for Deep Generative Models?

What is the difference between Auto-encoding Variational Bayes and Stochastic Backpropagation for Deep Generative Models? Does inference in both methods lead to the same results? I'm not aware of any ...
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### Should degrees of freedom corrections be used for inference on GLM parameters?

This question is inspired by Martijn's answer here. Suppose we fit a GLM for a one parameter family like a binomial or Poisson model and that it is a full likelihood procedure (as opposed to say, ...
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### Why is using cross-sectional data to infer / predict longitudinal changes a Bad Thing?

I'm looking for a paper which I hope exists, but don't know if it does. It could be a set of case studies, and / or an argument from probability theory, about why using cross-sectional data to infer / ...
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### Why is an estimator considered a random variable?

My understanding of what an estimator and an estimate is: Estimator: A rule to calculate an estimate Estimate: The value calculated from a set of data based on the estimator Between these two terms, ...
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### The concept of 'proven statistically'

When the news talk about things been 'proven statistically' are they using a well-defined concept of statistics correctly, using it wrong, or just using an oxymoron? I imagine that a 'statistical ...
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### Implications of current debate on statistical significance

In the past few years, various scholars have raised a detrimental problem of scientific hypothesis testing, dubbed "researcher degree of freedom," meaning that scientists have numerous choices to make ...
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### How to interpret Cochran-Mantel-Haenszel test?

I'm testing the independence of two variables, A and B, stratified by C. A and B are binary variables and C is categorical (5 values). Running Fisher's exact test for A and B (all strata combined), I ...
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