# 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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### consistency of Huber m-estimator [closed]

Let X1, . . . , Xn be a sample from a strictly positive density that is symmetric about some point. Show that the Huber M-estimator for location is consistent for the symmetry point.
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### Curve of Moment Generating Function [closed]

Let Mx(t) be the m.g.f of any distribution. is it possible to draw a curve (generalized curve, that will be valid for any distribution) of m.g.f if i do not assume any specific distribution?
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1 vote
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### F statistic for 3 nested models

Given models M1 and M2, the first with q parameters and the second with p>q parameters, and assuming that M1 is nested in M2, then we can test the hypothesis that the smaller model is adequate by ...
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### How can I estimate causality or the causal effect between any two variables using any statistical techniques in Python?

I am new to the idea of causal inference or causality in statistic and in Python. I have a dataframe test which looks as follows: ...
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### Is it true that currently we cannot compute p-values or confidence intervals for the coefficients from a Lasso regression problem? [duplicate]

I found a textbook online that had the following to say regarding the Lasso, "Computing the p-values or confidence intervals for the coefficients of a model fitted with lasso, remains an open ...
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1 vote
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### Adjusting for unconfounding in DAG context?

I am reading Cox's Case-Control Studies(2014) pg 6 of Preamble chapter. The book uses DAGs but it seems that it deviates from DAGs. I am not sure whether the following statement should hold in DAGs ...
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### Is it better to have more degrees of freedom or less?

The concept of degrees of freedom appears in many places in statistics. Yet I still don't understand what is the role of degrees of freedom. Why can we just use sample size (and we need to decrease it ...
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### How do you interpret a predictor in logistic regression when not all individuals qualify? [duplicate]

As a really simplified example, for instance, I wanted to find out what predictors are associated with kids being able to run over a mile as binary outcome. Ex.1 One of the predictors is ballet ...
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1 vote
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### Can we apply hypothesis testing to not-actively sampled groups?

For argument's sake, in the below please assume that the hypothesis test we'd be considering would be a simple z-test to check whether an observed difference between two groups' means or proportions ...
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### statistical vs set/category theoretic "equivalence"?

Equivalence is basic to mathematics, e.g. https://en.wikipedia.org/wiki/Equivalence_relation. "Equivalence tests" are common in statistics, e.g. https://en.wikipedia.org/wiki/...
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### P-Values from Robust Linear Mixed Models?

I'm running a study which is is investigating how different types of smiles (two levels) are processed in different situational contexts (three levels). I currently have a robust linear mixed model, ...
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### How to use auxiliary factors as weights in a Portfolio

(1) I am looking to form a Market Neutral Portfolio based off possibly 2 factors. Factor1 is the Primary factor, I rank all the stocks (say 1000 stocks) based off the Factor1 value, and pick top 100 ...
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### Nested factorial design for three factors [closed]

I want to design an experiment with three factors. Factor 1 shall have two levels (say, A and B), factor 2 has two levels (say, C and D) and factor 3 has two levels (say, E and F). By design, factor 2 ...
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### How can I fit distribution for data which "almost fits"?

I have a sample for events occurring at certain continuous distances (kilometers), let's suppose emergency calls to hospitals. I have 200k observations, coming from 500 hospitals for an entire month. ...
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### What is design-based validation and what is the difference to CV?

In Wadoux et al. 2021 I came across two modes of statistical inference, design-based and model-based. I get the difference between the two modes and I know what that means regarding a sampling scheme (...
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### Doubt in modes of reasoning [duplicate]

Is it correct to say that probability is deductive reasoning and statistics is inductive reasoning?
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### Statistic tests in "table 1" - which to choose?

I have made a table overall comparing two cohorts - a "table 1". The table includes gender, age and 2 different scores from the two cohorts. I would like to test if gender, age and the 2 ...
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1 vote
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### How to derive g-computation for a longitudinal experiment from sequential conditional exchangeability?

We have a longitudinal experiment, with interventions $\bar{A}=\{A_1,A_2,\ldots,A_K\}$ and outcomes $\bar{Y}=\{Y_1,Y_2,\ldots,Y_K\}$. Using some sequential conditional exchangeability assumptions, it ...
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### Statistical Inference Casella & Berger Exercise 7.11 [duplicate]

I'm self studying statistics using Casella & Berger Statistical Inference and I'm confused about a detail in solution to exercise 7.11. Here's the problem I'm try to solve: Let $X_1, ..., X_n$ be ...
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### Policy announcement as a treatment variable (causal inference)

I am using data from sub-reddits like [this][1] or [this][2], where users discuss their thoughts on the Federal government unemployment insurance and its fairness. Specifically, I wonder if it makes ...
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### How to Perform Statistical Testing to determine best student in class?

I have a dataset of marks of 6 students - A, B, C, D, E, F, G for 30 subjects each. Subjects Student A Student B Student C .... Subject 1 marks... Subject 2 Subject 3 ... 30 subjects The marks ...
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### Reparametrizing a Uniform Prior Distribution to Multivariate Standard Normal

Problem Description I have a posterior distribution $$p(\theta\mid y) \propto p(y \mid \theta) p(\theta)$$ with a uniform prior $p(\theta)= \mathcal{U}([a, b]^n)$, which is bounded. However, for my ...
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### Efron Hastie CASI exercise 4.3

This is an exercise from Computer Age Statistical Inference by Efron and Hastie, student edition of the book. Draw a schematic graph of $\dot{l}_{x}(\theta)$ versus $\theta$. Use it to justify (4.25) ...
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### Finding causality using text data

I have read several recent papers on new machine learning methods to find causality using textual unstructured data. Here are some famous examples, and I am still not sure if we can hold the SUTVA ...
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### What is "power cut"?

I am reading Yudi Pawitan's In All Likelihood chapter 7 section 5. He mentioned the following in sequential design using likelihood approach with justification of stopping rule not affecting ...
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### Validating ranking based on custom score

For a certain problem, where we need to create a score on some malicious activities of user, I have created a custom scoring mechanism. The scores are generated for each user. The problem statement is ...
1 vote
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### Ridge Regression/Lasso

I have a dataset where I am trying to identify what group of people (i.e the predictors) are most likely to do X. I have ~25 predictors, ~5k cases and a binary outcome Y. The predictors are ...
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### Dowhy causal inference estimates equal from two different models - why?

I am using a python package based on judea pearls book of why. I Tried two different models which i have depicted below, these structures would go in the digraph section of the code below. After ...
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1 vote
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### Bayesian inference with a binary and a continuous variable

I am studying the link between a linguistic feature (the specifics doesn't really matter but for any given language there are two options, the language either has the feature or it doesn't) and gender ...
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### Sufficient statistic and the maximum likelihood estimator of the probability of having an infectious disease when people are grouped and tested

Suppose N students arriving at a college are all equally likely to have a particular disease with an unknown probability p. The disease status (affected / not affected) of all students are independent....
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1 vote
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### Can posterior become tractable if we know p(x)?

In the VAE framework where x is an input data (a vector) and z is a vector of continuous latent variables, the posterior ...
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### inference for indicator from biased sample

I would like to develop an indicator. I was able to research 33 values from a population of about 1000 objects. It is now easy to calculate the mean value and a confidence interval. Is this a ...
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### Can I use a One-Sample T-Test to compare Employee Turnover for a period against an industry Benchmark?

I have collected employee turnover rates over the year. The attrition rates are as such: Month Attrition Rate Jan 2.23% Feb 1.40% Mar 2.99% Apr 1.43% May 1.72% Jun 1.15% Jul 1.64% Aug 1.60% ...
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### What is the difference between Variational Inference and Variational EM?

I have been reading about variational inference and it is relation to Bayesian regression. It seems there are two versions The first version is discussed here. The second version is discussed here. ...
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### choice between zero inflated poisson and zero inflated negative binomial

For count data with excessive number of zeros, there are two choices of models, zero inflated poisson and zero inflated negative binomial. Q1: How does one make appropriate choice between the two from ...
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### How to quantify impact of one data on another?

I work with an airline company trying to quantify if google search do lead to ticket booking. I have two dataset: (1) Search data = basically date of search, fly-date for search (2) Booking data = ...
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### Comparing efficiency between estimators

Suppose that $\hat \theta_1, \hat \theta_2$ are two estimators of $\theta$. Furthermore, assume that \begin{align} \sqrt{n}(\hat \theta_1-\theta)\overset{d}{\to}N(0,V_1)\\ \sqrt{n}(\hat \theta_2-\...
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### How can I use KL divergence to discriminate between two similar distributions?

Let us say we have two similar distriubtions(ex:laplace and normal or weibull and gamma) and we wish to discriminate between these two distributions. One of the most common method to do so is ratio of ...
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### How does the EM algorithm work in Bayesian regression? [closed]

I have problem distinguishing between the latent variables $z_i$ and the parameters $\theta_i$ in EM algorithm. Suppose we have the hierarchical priors \begin{aligned} \beta|\tau,\omega &\sim \...
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### Reasonable to incorporate sample size into beta-binomial?

Setup: The relationship between the beta and binomial distributions is well known. \frac{\pi^{\alpha - 1} (1 - \pi)^{\beta - 1}}{B(\alpha, \beta)} \leftrightarrow {{n}\choose{x}}\pi^{x} (1 - \pi)^{n-...
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1 vote
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### How to meaningfully interpret coefficients in an OLS model made by other people?

I'm a political sciences undergraduate student working on a study of the activity of the Upper Chambers in the UK and other former British colonies. I came across a 2008 study by Russell and Sciara ...
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### How to evaluate likelihood in MCMC for arbitrarily shaped distributions?

I'm very confused with the use of MCMC to estimate distributions that have a complex shape, like multiple peaks, or that aren't generated from a known distribution. In particular, when calculating the ...
I know that t-value can be calculated by $(sample mean-population mean)/sem$ and that the standard error (SE) means the t value is calculated according to the sample size. What I do not understand ...