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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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

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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Different modes of statistics [closed]

What is the difference between descriptive statistics ,prescriptive statistics ,and predictive statistics ? And do they follow bayesian or frequentist approach?( Is predictive more of bayesian and ...
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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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Controlling a nonrandom sample [closed]

I have a large nonrandom sample and a small random sample from the same population. I wish to control the first by the second. In particular, I want to estimate both a linear regression and a binary ...
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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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Interpreting group averages to inform selection of covariates in linear model

I am trying to understand the point of an exercise I found in an old problem set. The question provides a dataset with two categorical covariates $X$ and $Z$, the first having 5 possible levels, and ...
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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 ...
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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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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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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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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 ...
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Standard deviation of multiple two point samples

I am currently optimizing the acquisition time of an experimental Physics setup. To achieve our goal, we need to be able to properly estimate the error bars of each of the 200-time domain points of an ...
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relationship of Standard error and t test

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 ...
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Estimating covariance between two random forests

I'm building two random forests in R, one using a "treatment" dataset, $\hat{f}_1$, and the other using a "control" dataset, $\hat{f}_2$, so ...
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Likelihood a datapoint belongs to a given non-normal distribution

This problem is encountered by me lot of times. Let's say I have a set of data points (x1, x2,....,xn) whose mean and standard deviation can be calculated. However these data points are non-normally ...
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Testing for Trends in Sales Data, of 2 Products(Independent data of each Product)

The Data is structured as: Date of Sale | Order Amt | Price of product | Qty. Product A was sold independent of Product B(thus, 2 datasets), so dates do not match at certain instances, and entries are ...
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5 votes
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Practical implication of failing to reject a null hypothesis

Consider a scenario where you are trying to measure a dosage of a medicine. The machine is calibrated to fill a mean dosage of 50mg. But for a reason you believe that machine's calibration is off. For ...
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How to check if improvement in search results is significant

I'm implementing a search engine in two different ways A and B, and I am comparing their accuracies. Accuracy of system A is measured as follows: Given a query, I check if system A gives me the result ...
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How to assess the most important features and their statistical significance without a supervised learning model

There is a task that doesn't appear to make much sense to me in a textbook. I have a dataset of categorical variables (the features and target are categorical) . I am asked to determine what are the ...
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2 answers
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Why do we find evidence against null hypothesis in hypothesis testing?

Why do you make the claim that you want to prove ( or have a hunch to be true) to be alternative hypothesis? One might argue that it has to do with the way hypothesis testing is set up. That you find ...
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How to compute variance of predicted values from a model that uses superlearner?

In addition to obtaining predicted values, is there a way to obtain the variance of predicted values from a model that uses superlearner? For instance, one may want to make inference about the ...
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Applied Bayesian Statistics - Textbooks

I understand the bayesian statistics, but I don't see many textbooks approaching the bayesian statistics in a practical way. Some book recommendations on Bayesian Practical Applications would be great....
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Is this version of null hypothesis definition wrong?

Would it wrong to say that the definition of null hypothesis is as follows: Null hypothesis is a statistical hypothesis that usually asserts that nothing special is happening with respect ...
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Repeated measures covariants in linear model and not outcome

I have a dataset which contains a categorical outcome, 2 repeated measures over time for the same subject and several covariates ...
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Modify Bayesian Average for Multiple Quarters

I am currently calculating a bayesian average using Q1 data using the following equation: I would like to incorporate data from other quarters for several years back, i.e. Q4 2021, Q3 2021, Q2 2021, ...
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Understanding error in bayesian inference

Let us say we have: Data $X$ Parameter that we are trying to estimate is $\Theta$ The Bayesian estimation method is to Assume a prior on $\Theta$ Sample $x$ from $X$ Use Bayes theorem. Compute the ...
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