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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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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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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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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6 votes
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Categorical or Categorial? Is there a difference between the two terms from a statistician's point of view?

I have heard about Categorical distribution and Categorical variables in statistics. But what is a Categorial variable? Can both Categorial and Categorical be used interchangeably? Are there specific ...
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Sample Size Estimation - Default Rating Scales Comparison

I have default data based on the borrower ratings. Data fields: Rating(1-10 scale) | Total Number of borrowers (by rating) | Number of defaulters (by rating and a subset of total borrowers) Rating ...
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Significance testing for correlations

Say I have a set of predictions $X$ which predict some variable $Y$. The correlation between $X$ and $Y$ is $r$. How can I determine if $r$ is significant? My intuition would be to do a monte carlo ...
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Sampling: On the Relative Efficiency between SRSWOR and Stratified Random Sampling

In this situation simple random sampling is conducted without replacement. I have a stratified sample. My task is to compare the relative efficiency between stratified random sampling and simple ...
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What statistical test is suitable to summarise patient time in hospital with health condition

I am working on a dataset in which I am trying to summarise patient time in hospital by age and any health condition(e.g Cancer, Deprivatin, Depression or any). In my case it's Deprivatin. Patient ...
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Is having 2 time related variables in a logistic model appropriate?

I'm doing a study looking at the impact of the coronavirus pandemic on risk adjusted patient outcomes. I am building a model that looks like this: mortality ~ pandemicperiod + riskofdeath + ...
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Assessing the accuracy of a particular A/B testing design methodology

I commented to a colleague that we could improve our measurement of treatment effects by ensuring proper randomisation into treatment and control groups by balancing the treatment and control groups ...
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Methods for drawing population inferences from multiple sub-population datasets

What would be an appropriate model or method for making inferences about a broader population quantity from multiple quantities representing subsets of the population? Imagine, as an example, that I ...
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good intermediate-level textbook for undergraduate applied statistics in data science?

I will be teaching an applied statistics course for the first time and the main audience will be 2nd and 3rd year undergraduates, mostly data science majors. They will have an intro statistics course ...
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Estimating priors and marginal likelihood of Gaussian distribution

I am new to Bayesian Inference and MCMC, and I am currently reading the "A Conceptual Introduction to Markov Chain Monte Carlo Methods" by Joshua S. Speagle. The paper can be found here: ...
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For a block randomized experiment how many possible unique assignments are there?

In a block randomized experiment say of 4 individuals split into 2 even blocks with 1 individual in each block getting assigned to treatment and the other control, how many possible unique assignments ...
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Statistical inference question evaluating a joint probability mesure w.r.t. a distribution

Note: I have edited this question and delted my old question after following the guidlines to be more clear. I hope this new question is clear and well posed. I attempted this question but I got stuck ...
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Bootstrap Standard Error vs Standard Error from sample

For doing inference of a population parameter from a sample, under which examples is better to calculate the standard error using bootstrap distribution of the mean than directly using the standard ...
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Maximum Likelihood Estimator for Bernoulli distribution

Given a random sample $X_1, X_2,..., X_n$ from Bernoulli distribution. The log-likelihood function is: $\mathcal{L}(\theta) = \sum_1^n x_i^*\log{\theta} + (n - \sum_1^n x_i^*)\log{(1-\theta)}$ Score ...
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Distribution of rainfall over locations per year [duplicate]

$5.2$ Suppose $X_{1}, X_{2}, \ldots$ are jointly continuous and independent, each distributed with marginal pdf $f(x)$, where each $X_{i}$ represents annual rainfall at a given location. (a) Find the ...
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Asymptotic normality of OLS estimators in practice

Apologies in advance because I notice quite a few questions that have similar titles but I didn't see one that answered my specific curiosity: Supposedly OLS coefficient estimators are asymptotically ...
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Proving a result in maximum likelihood theory: accuracy of the quadratic approx. to loglikelihood

I need help proving a result shown in a paper. I am reading Assessing the Quadratic Approximation to the Log Likelihood Function in Nonnormal Linear Models by Salomon Minkin. The paper defines several ...
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Bayesian book not outdated [duplicate]

I did an introductory course to Bayesian in my master's degree in Statistics. I did not understand much since it was too much in short time, very concentrated. We have covered from the most basic (...
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Using the Median to Estimate a Parameter

I am trying to use the Median to estimate the value for the parameter $a$ in the following PMF. \begin{equation} \label{eq1:givenpdf} \mathbb{P}\left[X=\frac{a}{n}\right] = \frac{36}{5}\frac{n^2}{\...
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Comparing the probabilities of 2 different completely separate models that predict different outcomes

You have 2 separate models, one is a binary classifier that predicts whether a customer will pay off their credit card balance on time and another binary classifier (separate model) whether a customer ...
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What sources of uncertainty are included in a (95%) confidence interval?

Today, I came across an interpretation of 95% confidence interval (thereafter "CI"). The text has been written from education science perpective saying that, beside a (1.) random sampling ...
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Convergence Rate of $t$ Test Statistic (Regression)

Consider a simple regression model, $y=\beta^Tx+\epsilon$, say using the cars dataset. We get the following summary: ...
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Is synthetic minority oversampling technique a good approach for small samples?

This question refers to the statistical performance (usefulness) of synthetic minority oversampling technique in small samples. Suppose one has a data set with 300 observations, and two classes: 0 = ...
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How to test interaction effect with small sample size?

Into my model x is categorical variable with 3 categories: 0,1 & 2, where 0 is reference category. However number of "0" categories are much larger than others (1,2) which increases the ...
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1 vote
1 answer
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What is the justification of using the first-order Taylor expansion in the proof of asymptotic normality of MLEs?

Proofs of asymptotic normality that I have seen involve taking the first-order taylor expansion of the score function (derivative of the log-likelihood) about the MLE estimate evaluated at the true ...
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1 vote
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Inference Modeling for COVID Data

I am trying to build a model to analyze the relationship between COVID-19 mortality rate in each U.S. state or county (y) and independent variables (x) including: Vaccination rate: 1st, 2nd, booster ...
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2 votes
1 answer
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Hypothesis Testing when the aim is to claim that the two population mean (or any other statistic) are same

In general, when doing hypothesis testing, we want to claim that the concerned statistic is different between the two population. Hence we assume as our null hypothesis that there is no difference in ...
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3 votes
2 answers
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What to do if you Double count in experimental design?

I have to run A/B/n tests for a subscription service. Generally computing metrics for this situtation is ok: For example, coversion rate experiments. We have 1000 prospects in a group, and (say) 89 ...
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Bayesian Prior definition [closed]

The prior of an inference problem where we try to infer $x$ from observations $y$ is defined as $P(X)$. Often (e.g.) I see another definition where the prior is defined as $P(X|Q)$, what exactly is $Q$...
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UMVUE of $ \theta^2 (1- \theta ) $ X is random sample from bernoulli distribution

Let $ X_1, X_2 ..... X_n $ be a random sample from bernoulli distribution with parameter $ \theta $ , Obtain UMVUE of $ \theta^2 (1- \theta ) $ MY APPROACH I calculated that T = $ \sum X_i $ is ...
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How to infer noise map from noisy data?

I am given noisy measurements of the solution of a PDE at different times, each measurement is drawn from a Gaussian distribution having as mean the solution of the PDE at that time and a standard ...
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Comparing two cross-correlation functions with one another

Say for example I calculated two sets of cross-correlation matrices, one that compared time series A1 and A2 for 10 test subjects and another that compared time series B1 and B2 for the same 10 test ...
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Compute the Maximum A Posteriori (MAP) estimate of θ

How can I compute the Maximum A Posteriori (MAP) estimate of $\theta$ with those informations: a discrete random variable y with values in {1, 2, . . . , N} has a Binomial distribution depending on ...
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6 votes
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MLE for a modified German tank problem

Suppose I have a distribution $U(0,a)$ where $a$ is unknown and we are interested to estimate it. Someone who has access to $n$ samples $\mu_i$ of this distribution instead decides to create a ...
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Can you build a predictive model on the basis of case studies?

Can you build a predictive model on the basis of case studies? Suppose you are given a list of 1000 patients and a detailed itemisation of their injuries (but you are given no information on patients ...
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Getting multiple states in coxph output R

I'm trying to do a cox-regression with a time-dependant covariate. The time is measured in hospital days (0, 1, 2, 3, 4). And each day has a unique entry for the continious variable VAR1. I've created ...
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3 votes
1 answer
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Sampling Distribution of Reciprocal of Sample Mean

Given $X_1, X_2,..., X_n $ i.i.d. random variables. $E[X_i] = \mu_1 \in \mathbb{R} $ $\&$ $ V[X_i] = \sigma_1^2 \in \mathbb{R}^+$ $\forall i \in \{1,2,3,...,n\}$. The statistics $\bar{X} = \frac{...
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2 votes
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Sample size to assess grade deflation

My friend is a teacher at a University. In her course there is only 26 students, 13 of them fails, so she got deflation grade for this class. She believes that 26 students are not a good sample size ...
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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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