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.
2 votes
2 answers
409 views

Why check for normality of data in a sample?

from what I understand the assumption of normality (that must be assumed if one wants to use parametric tests) refers to the sampling distribution of the mean. It does not imply that the distriubtion ...
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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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Including random effects or not including them, that is the question

My problem I would like to infer the relative importance of "habitat connectivity" compared to "habitat quality" to explain tits breeding success in a urban area (more details ...
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 ...
2 votes
1 answer
185 views

Computing posterior variance at noisy training samples using Gaussian Process regression

Sorry for a possible naive question but this has been unclear to me for awhile... Consider the data model $y = f(x) + \epsilon, \;\; \epsilon \sim \mathcal{N}(0, \sigma_v^2)$. They show in Rasmussen ...
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1 answer
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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: ...
6 votes
2 answers
194 views

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 ...
4 votes
1 answer
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Unbiased estimator for $\mu_1/\mu_2$

Let $X_1,X_2,\ldots,X_n$ and $Y_1,Y_2,\ldots,Y_n$ be independent random samples from $N(\mu_1,1)$ and $N(\mu_2,1)$ populations respectively with $\mu_2\neq0$. I need to find an unbiased estimator for $...
7 votes
1 answer
330 views

How to make Bayesian-style inference for a Poisson process?

I am working on a fleet management software recently. Normally, the arrival of merchant request is a Poisson process. That is to say, on average we have a new merchant request every 10 minutes, but ...
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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1 answer
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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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Inverse problem that involves derivatives of unknown function [duplicate]

I am trying to solve an inverse problem where I try to approximate a function $f(x)$ that fulfills the following equation $\ddot{z}_m = \frac{\sigma^2}{2} \frac{\partial^2 f(z_m)}{\partial z^2} + \...
1 vote
1 answer
242 views

How can I use linear/logistic regression for inference with colinear variables and a smallish dataset?

I have a dataset of around 120 observations, with 30 calculated variables and I am trying to predict a continuous response (result of an experiment) using those 30 variables. Ideally the smallest ...
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A question about "control groups" in IV regression

I am doing an analysis which covers the electricity market in the US. The dataset that I use contains 39 states, which 15 of them has a value other (higher) than zero for the regressor. This makes the ...
1 vote
1 answer
106 views

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 ...
2 votes
1 answer
543 views

Profile likelihood

I am considering a normal distribution with mean $\beta_1 + \beta_2\exp(-\phi x)$ and variance $\sigma^2$, i.e. $y \sim N(\beta_1 + \beta_2\exp(-\phi x), \sigma^2) $. My aim is to calculate the ...
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Interpreting Mediation Analysis Results obtained using R [duplicate]

I ran a mediation analysis using R and I got the following result : As you can see ACME and ADE are not significant but the Total effect is significant, how should I interpret this? please include ...
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Moving from Sample data to population

I have a data sampling set of success/failure data so I have classified it as discrete binomial data. ie. failure rate sampling 0/10 1/10 1/10 0/10 and therefore I can use the binomial distribution on ...
2 votes
1 answer
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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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1 answer
277 views

Find Conditional probability distribution given conditions - Bayes Network

I'm taking a course on bayesian statistics and I'm having trouble with one assigment, it goes like this: Construct an example in which two variables have a common effect, and the presence of one of ...
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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 ...
1 vote
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Link between cross-validation and inference

Let's consider for instance Linear Regression and let's say we obtained some $t$-stats and confidence intervals for the coefficient estimates. Let's suppose we also split the datasets into $K$ Folds ...
5 votes
1 answer
259 views

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. ...
1 vote
1 answer
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Matchit - Distance between 2 Propensity scores for findings specific pairs

I'm trying to find "spare" controls in case of drop-out in my primary control. I took my primary control sample (n=29), and ran Optimal match for find secondary match sample (N=350 optional ...
1 vote
1 answer
371 views

Causal impact R - Is it possible to model multiple the pre and post periods? Indivudally for participants

I would like to use the causal impact algorithm, however, not in the context of marketing, but in medicine. The problem is that the intervention does not take place at the same time, but on an ...
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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 (...
1 vote
1 answer
533 views

Statistical comparison of numerous nonlinear model parameters

I have 84 data sets (n=3) corresponding to 28 conditions (sample composition and temperature) and have fit my data set to the following nonlinear model using MATLAB nonlinear curve fitting: $$y = \...
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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 ...
13 votes
3 answers
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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 ...
2 votes
1 answer
347 views

How to fit a superimposed distribution (\eg a Gaussian distribution + a Uniform distribution)

Suppose we have a set of independent observations of a random variable X, which is a Superimposition of two mutual independent random variables (i.e. X = Y + Z), Y follows a uniform distribution, ...
3 votes
0 answers
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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 ...
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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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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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 ...
2 votes
1 answer
36 views

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 ...
4 votes
1 answer
724 views

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 ...
2 votes
1 answer
223 views

How does one recover the true solution to underdetermined equations when one has some prior or data about how the solution should look like?

I was interested in recovering the solution $x$ to a linear system underdetermined $N < D$: $$ Ax = y$$ as accurately as possible to the true $x$. Obviously, this system has infinite number of ...
1 vote
2 answers
72 views

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 ...
1 vote
1 answer
296 views

Variable Importance for Logistic regression with categorical data?

If I run the logistic regression with X variables containing categorical data. (I do one-hot encoding on categorical data) How do I evaluate the variable importance? Is there any methods or literature ...
3 votes
1 answer
90 views

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 ...
1 vote
0 answers
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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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