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 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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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 ...