# 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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### Adjusting OverAll Time Performance using sectional Times

Assume I have two runners, Runner_1 is the average runner and Runner_2 is Usain Bolt. We let the two runners compete in 3 different races on a 100m distance. We assume that the benchmark time for 50m ...
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### The performance of EM algorithm at different local maximas

Setup: Say I have a problem (any problem that can be modeled by a probabilistic model) to solve, this problem involves some unknown parameters to estimate. I model this problem in a probabilistic ...
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### How do you compute the confidence interval for the product of two separate A/B tests?

I am trying to find the confidence interval of the end result of two A/B tests. As an example, lets assume that for test 1 I am looking at the click-through rate of a page and have a control and ...
26 views

### Testing multiple hypotheses multiple times

I estimate a linear model consisting of one dependent and four independent variables. I want to test wether each of the independent variables has a significant impact on the dependent variable, i.e. I ...
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### If two sample means of $X$ differ significantly and $X$ predicts $Y$, can it be inferred that the samples differ in their $Y$?

In the following model: $Y = \beta_0 + \beta_1 X + \epsilon$ $X$ is found to be significantly related to $Y$. Now, I observe $X$ within two groups. I compare the two means and find that the $X$ ...
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### t-test to compare weighted means

I have an unbalanced panel of paired differences. That is, my panel consists of 100 firm time series of paired differences with varying length. I have tested wether the unweighted mean is different ...
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### Most Efficient Estimator and Uniformly minimum variance unbiased estimator

I am studying Estimation theory from "Introduction to theory of statistics" by "Mood and Graybill". After completing I thought I understood UMVUE (uniformly minimum variance ...
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### What statistical test to discriminate between within and between category with 2-dimensional data?

Let's say I have a multidimensional data with one axis indicating factors of a customer base (eg. income), and another axis could show some options (eg. fashion store A, fashion store B, fashion store ...
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### Is there a formula for the expectation and variance of a ratio of sampling variances?

I know the formulas for the expectation and variance of the sample variance, difference between two sample means and proportions. Sample Variance $E(S^2) = σ^2$ $V(S^2) = 2\sigma^4/(n-1)$ Difference ...
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### How does pymc3 posterior simulation work in this simple case without having the full conditional distributions?

I'm trying to estimate the posterior distribution of the gamma parameters alpha and beta given that my data comes from a gamma distribution and the priors I chose come from two uniform distributions. ...
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### proof of Cramer-Rao lower bound

I am trying to understand the proof for this theorem from the book Casella and Berger (2nd ed.) page 336. $W(X)$ if any estimator for samples $X_1,\ldots,X_n$ on distribution $f(X|\theta)$. I notice ...
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### How to normalize data which has started at different time periods?

So I have to review our business producers and have a long list of ones which have been signed up since 2017 with the company. We have continually hired more producers throughout the past three years. ...
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### Variance estimator using mixture of scaled and unscaled data

Given two datasets: $X_1, \dots, X_n \sim N(1, \sigma^2)$ and $X_{n+1}, \dots, X_N \sim N(1, 2\sigma^2)$ My proposed estimator for $\sigma^2$ is simply a scaled combination of both classical ...
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### Question about probability vs inferential statistics

I'm currently struggling with a question involving probability and statistics. I have this dataset of sales, and I was trying to make a probability of sales based on that dataset and the data that it ...
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### How to obtain equation for evidence given equation for joint density of latent and observed variables (Variational Inference)

I am working through the following review paper: https://arxiv.org/pdf/1601.00670.pdf and would like to gain some insight into arriving at the formulae for joint density of latent and observed ...
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### Causal Inference of Between-Group Differences in Time Series Data

I'm relatively new to time series data/causal inference (am working my way through Mostly Harmless Econometrics as we speak). Though, I'm still not sure how to appropriately test between-group ...
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### Comparing countries with different proportions of available data and missing values

I have 200 countries, and each country has various subcategories with different number of data points and missing values. For example, I have a country with 100 data points, 40% of which are missing ...
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### Does it make sense to build 2 models - one for prediction and one for inference?

I am considering using a Generalised Additive model for prediction and a Generalised Mixed effects model for inference to explain the relationship between variables, so I can play to the strengths of ...
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### How to estimate differences between two normal means when variances are tested to be unequal

Let $X_1 X_2...X_n, Y_1 Y_2...Y_n$ be $\sim N(\mu_x$, $\sigma_x^2$), $\sim N(\mu_y, \sigma_y^2$). I want to estimate ($\mu_x - \mu_y$) and have used F-test to see that $\sigma_x^2$ $\neq$ $\sigma_y^2$ ...
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### What are the worst (commonly adopted) ideas/principles in statistics?

In my statistical teaching, I encounter some stubborn ideas/principles relating to statistics that have become popularised, yet seem to me to be misleading, or in some cases utterly without merit. I ...