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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is the $Var(\hat{\beta_1}|X)$ same as the variance of $Var(\hat{\beta_1})$ in simple linear regression?

Here are two captures from different videos on youtube, one obtains $Var(\hat{\beta_1})$, the other obtains $Var(\hat{\beta_1}|X)$ but they yields the same equations when the second capture further ...
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Systematized way to analyze "nested" data

I would like to analyze a dataset that looks like the following: ...
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What is the test statistic in this example?

I have a sample from a country's population. I am trying to figure out what is the test statistic for a certain question. The data contains 1400 people.. with ages, consumes alcohol or not, and wages. ...
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What test can I use to compare experimental group 1 to placebo and to experimental group 2 but not compare experimental group 2 to the placebo group?

The aim of this study is to examine the difference between two different polyphenol supplements on exercise recovery (measurements taken at pre, immediately post, 1 week and 2 weeks post-) The study ...
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Inference for parameters in stable distribution case

I performed a fit of some SP500 returns with two heavy tailed distributions, using MATLAB. These are like two guess about what distribution has generated the data. This is the output In both cases ...
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Product of two independent Student distributions

What is the product of two independent student t distributions? In which case does this product product result in another t distribution?
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Question regarding the Bayes estimator of a parameter $\theta$ which has a continuous distribution

Let $c > 0$ and \begin{equation} L(\theta,a)=\left\{ \begin{array}{@{}ll@{}} c|\theta-a|, & \text{if}\ \theta < a \\ |\theta-a|, & \text{if}\ \theta \ge a \quad. \end{array}\...
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Testing for significant trend factors

I'm currently working on a project to improve my company's methods for frequency and severity trend selection in a few models. At the moment, given a series of points in time, we take a ...
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Analysing Likert scale responses

I have a dataset consisting of Learner's response for Likert scale questions. The data consists of questions from different courses, therefore not all questions belonging to any particular group. ...
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What is the difference between MVB UMVUE and MVUE.?

Cramer Rao inequality gives MVB and if MVB exist it is MLE. Rao Blackwell gives UMVUE, but isn’t when we have MVB estimator for unbiased it is UMVUE? Then what is MVUE? MVB minimum variance bound ...
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Interpreting boxplot VS stacked histogram in example

I understand what a boxplot and histogram are supposed to show, but I'm a bit confused on how it is being presented in this graphic printout from R. The picture is taken from Beyond Multiple Linear ...
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Unbiased estimator of population variance for sampling without replacement

What I wrote below only apply to the situation where we have finite population. I saw many of my friends used sample variance with Bessel's correction $\frac{\sum_i^n (X_i - \bar{X})^2}{n-1}$ to ...
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Bayesian Model(Write out likelihood and prior)

I am working with a dataset regarding transmission rate for a disease spreading among cattle at different farms during a 5-month period. The goal is to estimate the transmission parameter $\alpha$ ...
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Applications of "Dose Response" Outside of Biostatistics?

I was reading about a class of models called "Dose Response Models" (https://cran.r-project.org/web/packages/drda/vignettes/drda.pdf) - in the traditional sense, these are typically used to ...
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Does the "type" of standard error affect the relationship between the standard errors of standardized vs. unstandardized estimates?

While previous answers explain how to convert between standardized and unstandardized coefficients and their standard errors, it is not clear if this formula applies across different types of standard ...
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Issue with bounded in probability

I have tried to prove the following problem that I read in the lecture and it seems not transparent to me. Suppose that $Y_{i}$ be independent random variables (with $i=1,2,3, \dotsc$). Each has the ...
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Post analysis using raw data or SHAP values in Machine learning

Let's say I have SHAP value returned in dataframe for input variables like below ...
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When does a difference in means not capture the true treatment effects vs a regression with pre-treatment controls?

A question from Gelman - Regression & Other Stories... In answer to my own question...my understanding is that a difference in means should not capture the treatment effect when there are pre-...
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Bayesian model comparison with systematic error

Two parameters $(x,y)$ were measured for 3 different objects, wielding the following results: $$\{ (x,y) \}= \{ (1,3), (3,5), (5,9) \}$$ Knowing that the error in the estimation of the values $y$ is ...
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Can somebody help me understand the sentences in more readable expresions?

I was reading a paper about "bayesSimIG" and I have problem in understand the following paragraph.I have read it many times and did a lot of research for it and have understood what each ...
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Confidence Intervals and Hyptothesis testing

Iam currently reading up on basic statistics and Iam somewhat confused about the computation/inference of confidence intervals and hypothesis tests. As far as I have understood there are several ...
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How to test a product of a OLS estimators?

I estimated a vector $\beta $ using OLS $\hat \beta =(\hat e_1 \hat e_2 \hat e_3)$ and I have the covariance matrice $\hat v(\hat \beta )$. How can I test this null hypothesis $H_0 : \hat e_1 \hat ...
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Fisher's exact test when resampling from the population

I am using different ML classifiers for making predictions related to a binary classification. I would like to compare two groups. Let's call them A and B. The already trained and tested classifier ...
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is nrmse scale-dependent?

Im trying to evaluate my regression models using a normalised version of the RMSE, nrmse = rmse(y, y_pred)/rmse(y, y_mean) where y_mean is the array of the same len as y filled with the mean value of ...
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Chi square for three categorical variables

Can I use chi square test with three variables ? The variables are organizational climate (11 dimensions), job satisfaction (7 dimensions) and customer satisfaction (5 dimensions). Likert scale. any ...
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Should you clean your data after or before selecting a sample?

Assuming a 500k dataset. For statistical modeling purposes (selecting up to 10% of 500k as a sample). Should I clean the 500k dataset first before selecting a sample or select the sample first and ...
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When I have population data do I need probability and can I infere? [duplicate]

Say I have data about a population and I want to analyze them, then in my understanding the "sample" is the population. And then do I need probability, like p-values, confident intervalls ...
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How can I calculate Posterior Distribution, analytically with given information?

The image below shows that the posterior distribution is as follows with given information: I wonder how the posterior has been calculated, analytically.
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sufficient, minimal, complete

Are all complete statistics functions of each other? For example if I have T and S complete statistics Can you always write T in terms of S and S in terms of T?
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variance of the difference of two independent variables is the sum of variances

It is said that variance of the difference of two independent variables is the sum of variances (topic - Confidence intervals. Two means. Independent samples) I tried to experiment with small dataset ...
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Data Set With Variable Start Dates for Churn Modeling (New customers from business acquisition)

I have dataset representing to specific region of the country. Its purchase data which is how much costumer is placing with associated dates of order, amount etc. I want to do churn modeling for this ...
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2 answers
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I have a graph which appears to be random but there seems to be a pattern hidden in it. How do I analyze it?

The below graph seems to be random but I think the peaks seem to repeat after a certain period. Are there any statistical tools I can use to analyze this? Edit: I am adding the plot of its ...
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Meaning of endpoints of ONE confidence interval

From wiki, we should understand the confidence interval by: in large repeated samples, 95% of the realized confidence intervals (computed from samples) can cover the true value of the population ...
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Testing equality of coefficients from two different samples

I have the regression statistics for the same regression run on two different samples, and am asked to explain whether it is possible to test for equality of the coefficents, $\beta_1$and $\beta_2$ ...
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Fisher matrix for a discrete distribution

Let $\mathbf{X} = \{X_1, \ldots, X_n\}$ be a sample of i.i.d. variables following a discrete distribution with parameters $\mathbf{p}^T = (p_1, p_2, p_3)$. How can I find the Fisher information matrix ...
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Uniformly most powerful test

Suppose we have Xi~Exp(λ), and we want to construct a most powerful test for H0 : λ = λ0, H1 : λ = λ1 I then proceed to use the Neyman Pearson lemma : reject H0 when the likelihood ratio L(λ1;X)/L(...
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confidence interval formula of gamma distribution? [closed]

i want a help can someone tell me the formula for confidence interval of gamma distribution? for alpha and beta Parameters i couldent find them? and there also this problem i dont know which pdf of ...
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Likelihood-ratio gradient estimator in linear dynamical system in python (Jax)

TL;DR I am trying to implement the likelihood-ratio gradient estimator in a linear dynamical system (LDS) with Gaussian transition noise and Gaussian observation noise I am currently using python and ...
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2 votes
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Logistic regression - One model trained on different groups

I have a logistic regression model that trains a set of binary independent variables (X) on a binary response variable (Y). The data was gathered from different individuals for who also e.g. socio-...
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Calculate posterior distribution given two normal distributed measurements

I have two measurements $m_x$ and $m_y$ from two sensors $X$ and $Y$. $m_x$ can be approximated by $m_x \sim \mathcal{N}(m_x|m, 2)$ and $m_y$ can be approximated by $m_y \sim \mathcal{N}(m_y|3m, 5)$. ...
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Meaning of multiple exposures in a DAG

I am working with DAGs as a way to do some causal modeling. I am using dagitty - both the website and the R package. I feel like I have a good grasp of most things related to confounding, adjustment ...
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Single-sample self-normalized importance weighting

Self-normalizing sampling schemes (https://artowen.su.domains/mc/Ch-var-is.pdf) seem to require at least two samples to give non-trivial weightings under an importance sampling distribution. Is there ...
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Confused about interpretation and intuition behind Mcnemar's Test [duplicate]

I've always been under the impression that Mcnemar's Test is for paired categorical data, just like paired t-tests are for paired continuous data. However, I was looking at the Wikipedia article for ...
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Constructing a time dummy variable in DiD fixed effects model

I am using a Diff-in-Diff regression design to evaluate the impact of a county-level tax hike (i.e. treatment variable) on tobacco sales (i.e. outcome variable) in a given county, relative to counties ...
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Question on solution of Casella and Berger Exercise 9.10: Showing that $Q(t,\theta)$ is a pivot

My question concerns Exercise 9.10 of Statistical Inference by Casella and Berger: On page 428 the authors say In general, suppose the pdf of a statistic $T$, $f(t|\theta)$, can be expressed in the ...
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How to prove change in a time series when the population is growing?

I have a small dataset with data on the number of heart and liver donors from deceased patients each year (from 2012 to 2021). I would like to find out if there has been a change in the number of ...
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MCMC "for dummies" || how to estimate parameters and what limitations should I consider?

I'm interested in parameter estimation. In a nutshell, I have an expression, e.g., $$f(x,y,w,z; t) = \frac{x\cdot\,y}{w\cdot\,z} \, \frac{k_1}{k_2}\,\frac{j_1}{j_2}\,t$$ in which I know variables $x,y,...
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Why is SATE different to Treatment effect (difference in means)?

A question from Gelman - Regression & Other Stories. This one has me a bit stumped, I've reread sections of the chapter and I'm still not understanding why this is the case. I think the answer is ...
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The exact distribution of the conditional distribution of the OLS estimator

This is the problem that I have tried figuring it out for a while, and I still need some advice because there is no explicit derivation in the textbook that I have seen so far. The problem looks easy ...
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Causal Inference for experiment

I'm working through a textbook (Regression and Other Stories) and have come across a particular problem that I am having difficulty convincing myself I understand. I am specifically interested in part ...
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