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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Generating random data points following a Poisson point process from observed data points [duplicate]

I am a bit new to the domain of Spatial Statistics. So I am trying to generate complete spatial randomness(CSR) data with summary statistics similar to that of the observed data(data points in 2D). ...
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Statistical power of tests on unequal and known variances vs equal but unknown variances

Suppose you are testing for differences in two normally distributed variables. In the following situations: -Variables have known but unequal variances -Variables have variances that are unknown but ...
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Empirical variance of simulation estimate

Consider the following quantity of interest: $$I[a,b]=\int_{a}^{b}g(\theta)h(\theta), \ldots (1)$$ that is, the expected value of some function $h(\theta)$, of $\theta$ distributed $g(\theta)$. ...
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How to deal with skewed data?

I want to examine 2 variables of experience: A. Regular practice - hours. B. Formal practice - days. Both variables are right-skewed, with extreme outliers (Experts) and many subjects with zero ...
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Estimate negative binomial dispersion parameter $k$ using mean and proportion of zeros

I came across supplemental methods of a paper estimating the mean ($R$) and dispersion ($k$) of a negative binomial distribution that stated: Page 8: "Given estimates of the mean ($\hat{R}$) and ...
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How to show Neyman orthogonality of the score

In section 4.1 of this paper, the authors talk about the PLR model: \begin{aligned} &Y=D \theta_{0}+g_{0}(X)+U, \quad E_{P}[U \mid X, D]=0 \\ &D=m_{0}(X)+V, \quad E_{P}[V \mid X]=0 \end{...
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Probability of finding an object on the beach: Bayes theorem [closed]

Introduction Beach litter surveys are collections of observations that detail the object and quantity found of that object within a defined length of shoreline. The sampling protocol was initially ...
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Bootstrap Basics

When using random sampling (bootstrap), I get 3500 estimates of R squared. Curious as to what causes the variation between these individual estimates as they've all been pulled from the same dataset. ...
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Is there any reference justificating a P<0.10 as a cutoff for likelihood-ratio tests?

I am conducting log-likelihood-ratio tests to examine the goodness of fit of two competing logistic regression models. The test is the traditional log-likelihood-ratio test, in which I compare the ...
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Is the MLE of a statistic always defined?

My current understanding is that the MLE of a statistic is the mode of its posterior pdf under a uniform prior. The problem with this is that I don't think the posterior pdf needs to exist. The ...
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is this pseudoreplication?

I'm sampling 5 different fields using transects. I'd like to gauge soil moisture and how it varies based on each field. If I choose five pre-determined points within each field and then take their ...
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Cross validation within a bootstrap sample: is leakage a problem here?

I would like to calculate the sampling distribution for logistic LASSO coefficients. One approach to calculating this sampling distribution is described on page 143 of "Statistical Learning with ...
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How many type I errors have I made in my career? (I saw this posted by a LinkedIn connection.)

I saw the following post on LinkedIn and was curious to have it dissected on Cross Validated. How many type I errors have I made over the years? I've run a lot of A/B tests in my career. I was just ...
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Why should we care about DAGs for causal inference? [duplicate]

I am not acquainted with Pearl's approach for causal inference. From what I have seen so far, the causality is inferred from directed acyclic graphs(DAGs). Rubin's Causal Inference Sec 7.5 proved a ...
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How do we select model for causal inference?

I am reading Rubin's Causal Inference Sec 7.5 in context of completely randomized experiment. It says performing linear regression will produce asymptotically unbiased estimate of causal effect, ...
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Generative model that satisfies certain algebraic constraints

Disclaimer: I need guidance and help with where to start looking for solution of the problem I have described below. My background is in optimization and I am new to statistical methods, so there is a ...
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Weak convergence of sample quantile and quantile

If $X_1,\dots, X_n$ iid samples from CDF $F(x)$ and assume that $F$ is first order differentiable at $\xi_p$ with $f(\xi_p)>0$. Let $F_n$ be the empirical CDF of $F(x)$. Then $\hat{\xi}_p=F^{-1}_n(...
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How to find the expected mean of a very smalll subgroup, while still considering the larger group?

Context: For a Machine Learning challenge, I have a national exam dataset, containing over 3 million scores, from over 5k cities (unbalanced distribution). For example: ID City Other Score 01 NY ... ...
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Difference between Predictive Inference and Causal Inference

I am looking for functional mathematical notation to explain the difference between Predictive Inference and Causal Inference? I list an example model. I also list links further down that give ...
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Two possible definitions of confidence regions: which one to choose?

Let's say you have a parameter vector $(p,q)$ consisting of two proportions, and you want to find a confidence region for the estimator $(\hat{p},\hat{q})$. Define \begin{equation} H(x,y,p,q)=\frac{n}{...
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Running regression on the entire dataset vs running on smaller dataset then take average of coefficient?

Suppose we have a big data set where even if I break it into 10 smaller pieces the number of data points in each piece still far outnumbers the number of variables. Now if I run regression using two ...
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Why not just testing alternative hypothesis? Why do we need null hypothesis?

Why not just testing alternative hypothesis? Why do we need null hypothesis? For example, I am testing the effectiveness of a new drug. I can choose two groups: control and experimental. Based on the ...
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Is there a statistical test for one participant measured many times?

Pretty much throughout my undergrad and postgrad, I have always learned statistical models predicated upon things like large subject size. I also know that a lot of repeated measures designs typically ...
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How to find the likelihood probability of an exponential data model

I have a very basic knowledge in statistics, so I am struggling a bit with the ideas of Bayesian inference. My data model looks like this, $$ z(t) = \sum_{n = 1}^{N} e^{j 4\pi/\lambda \sqrt{(x_{n, t -...
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A and B are 99% correlated. C is highly correlated with A. Should C be also equally correlated with B? [duplicate]

I have a simple correlation question: there are three variables, A, B, C. A and B are 99% correlated. C is 95% correlated with A. But it is only 88% correlated with B. Is this unusual? Should C be ...
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How large of a dataset should I use for building a statistical model?

I'm in the process of building a statistical model for housing sale prices. I am drawing inferences and trying to predict the price of a home as if it was sold in the year 2021. I am using a 600k+ row ...
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Testing if year-to-year change is significant?

I have Two related questions: 1) I have raw counts for voting vs. non-voting for the years 2018 and 2020. 2018 -> 11,000 voters and 3,000 non-voters 2020 -> 10,000 voters and 3,500 non-voters ...
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Transformation of uncertainty intervals - how to log transform SE and 95% conf interval?

A question from Gelman; 'On page 15 there is a discussion of an experimental study of an education-related intervention in Jamaica. The point estimate of the multiplicative effect is 1.42 with a 95% ...
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How to interpret this formula with probability of an individual becoming infected over x days?

I am trying to understand a formula in this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5444538/#:~:text=Low%20Risk%20of%20International%20Zika,the%202016%20Olympics%20in%20Brazil). In the ...
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Understanding "In Bayesian inference, the difference between data and a parameter is that one is observed (data) and one isn't (parameter)" [duplicate]

In his statistical rethinking course, Richard Mclreath states "In Bayesian inference, the difference between data and a parameter is that one is observed (data) and one isn't (parameter)" I ...
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Conventional autoencoder training instability [duplicate]

I am currently writing an autoencoder in python (torch); its encoder is intended to serve as a compression tool. The input dataset contains a mix of numerical data (including large integers), ...
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How to use causal inference models when we don't know the structure of the graph?

I have recently started reading some materials in Causal Inference. Based on readings, we assume a graph that explains the relationship between treatment, outcome, and confounders. Then, they propose ...
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Negative F-test value comparing two nested models

I am comparing two non-linear nested models - let me call them model A and model B. Model B has one parameter more than model A, i.e. model A can be obtained as a special case of model B. These two ...
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What is the covariance between two log relative risks?

In a randomized experiment with two groups (treatment and control), suppose the response variable, $Y$, has 3 categories (0,1,2): $y_{0_{i}}$,$y_{1i}$ and $y_{2i}$, in which $i$ denotes the $i^{th}$ ...
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Use inferential statistics in a descriptive manner

I am currently evaluating usage data from an online trainer. To answer my central question, I have determined a subsample from this data that meets certain criteria. These data can be categorized in ...
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Identifying set of variables with high values across subjects and conditions

I have a series of 2D matrices (one for each subject in my dataset). Each matrix holds information about the activity of a set of brain regions (reg1, reg2, …) across multiple conditions (y1,y2,…). ...
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Estimating $\theta$ based on censored data when $X_i\sim \text{Uniform}(0,\theta)$ with $\theta\ge 1$

Suppose $(X_i)_{1\le i\le n}$ are i.i.d $\text{Uniform}(0,\theta)$ random variables where $\theta \ge 1$. We observe $Y_i=\min(X_i,1)$ instead of $X_i$. I wish to estimate $\theta$ based on the data $(...
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Correlating two matrices $A,B$ with stochastic dependency structure imposed by cross-validation

Consider a labelled data set $$D = \{(x_1, y_1),...,(x_n, y_n)\} $$ on which we want to evaluate a machine learning algorithm using $k$-fold cross validation with $m$ different random seeds. This ...
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Is post-variable-selection multimodel inference a bad idea?

If I understood correctly, in this answer, Ben Bolker says that using inferential methods after having performed AIC-based model selection is wrong because "standard inferential methods assume ...
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Inconsistent result in proportion test in R

I have some problems understanding the results of this online experiment. I sent my website users 2 types of messages that can result in a subscription or not. The users can belong to two different ...
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2 answers
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Can one perform Bernoulli trial by restarting trial if everyone is assigned control or treatment?

Suppose I have $n$ patient. I want to give an assignment of treatment such that probability of patients receiving treatment is $0.5$. Say I have $n$ unbiased coins to determine treatment or control ...
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Does directionality matter in regression for cross-sectional studies?

I am trying to see if slow walking is associated with certain brain regions. I think it makes most sense that brain atrophy leads to slow walking, so my model would be ...
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What can you infer from being always above the median and the mean?

In the context of a national competition, what can you infer from being always above the median and the mean in all modules? Say, that all marks are normally distributed, does it always mean that for ...
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Is there any general consideration on the lack of balance in sample size for (any) inference?

I'm wondering if there are any suggestions, good practices, thoughts about the imbalance between data size in each compared group? I ask apart from any concrete statistical test (Welch, Kruska-Wallis, ...
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Best way to create a supersaturated sesign

I have full data for $2^{12}$(All the 4096 runs) full factorial design. I know the exact model, I created all the data. I am trying to create a D-Optimal Supersaturated design for an application. I ...
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Detecting and dealing with outliers in a sales prediction dataset of "Rossmann"

I have been working on a dataset for which the task is to forecast the sales of the drug sold by 1115 drug stores of the Rossmann chain. The dataset is fairly large with over 1m records and as many as ...
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Constructing a population random sample from subpopulations random samples of equal size

I have a very basic question about random sampling. Consider the following: Population Population size Sample size Male 1200 200 Female 800 200 Where each sample for the population partitions have ...
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Methods to calculate confidence interval for proportion with potential bounds?

I am trying to calculate the confidence interval on a time series proportion. For example, I have 1000 years of data, and I use 20 days to calculate some proportion. The thing is, I know the ...
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Confidence interval over mean or over all values?

Say I have a dataset generated by running my AI on a boardgame. The data set consists of two "main" values: Actual gained reward from running the AIs optimal policy and the reward my AI ...
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What is the best approach to evaluate the effect of an intervention on different segments?

I have a dataset post A/B test which looks like this: ...
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