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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Motivating use of Bayesian splines in excess mortality estimation

I'm reading this paper estimating excess deaths induced by the pandemic. That is, roughly, it constructs a model to estimate how many deaths (from all causes) would have occurred if the pandemic had ...
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Statistical Inference: Definition of contrast function

Reading a paper recently regarding results on parameter estimation and I came across the terminology "contrast function" which was a function constructed out of a sample. If I compare it to ...
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Interpreting coefficient in a Diff-in-Diff (fixed effects model)

I am running a DiD model with fixed effects to find the causal effect of traffic cameras on my outcome variable: share of car accidents of total accidents per neighborhood. The treatment, road cameras,...
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Estimating Standard Deviation from sample mean, median and quartiles

I've been trying to estimate the standard deviation from a sample with N = 8149. I've seen a few alternatives to perform this and they all use the IQR. Here's the sample data I have: ...
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6 votes
3 answers
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Should stepwise regressions also be avoided for exploratory (hypothesis generating) modelling?

In a recent paper, Andrew Tredennick and colleagues (2021) suggested to use the drop1() function in R for exploratory modelling (that is to generate new hypotheses ...
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"De-meaning" or "Differencing the mean of..." in mathematical term

In a standard regression literature, the following terms are used almost interchangeably and are used also loosely: "De-meaning the equation gives..." "Differencing the mean of the ...
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Estimating total number of consumers based on observed transactions

I read through most other questions of this type and didn't find a relevant situation. I want to predict the total number of consumers and repeat consumers that shopped in the past month, however, ...
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2 votes
1 answer
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Bootstrapping confidence intervals in randomization model and population model

Ernst 2004 shows that the permutation tests in the random assignment scheme (e.g., controlled experiment) and in the random sampling scheme (e.g., observational study) share the same constructing ...
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Frequentist inference with Dirac delta as prior

Would likelihood-based frequentist inference amount to the same as Bayesian inference, but where the "frequentist prior" $\pi^F(\theta) = \delta_{\theta^*}(\theta)$ with $\delta_{\theta^*}$ ...
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Numerically solving the Forward equation to estimate SDEs

In books [1] dealing with inference for SDEs, why is the approach of numerically solving the forward PDE to obtain numerical estimate of the PTD not studied? One could then use this PTD to perform a ...
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Regression discontinuity vs propensity score matching

I have recently read some pieces suggesting that regression discontinuity designs could be the best statistical approach for causal inference stemming from non-randomized studies (eg 1 and 2). However,...
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258 views

Frequentist inference with a null hypothesis that reflects theory a good-enough belt around it

TL;DR: With frequentist statistics, does it make sense to 1) no longer use significance testing, 2) set the point null hypothesis to reflect theory and decide a priori when to refute it, and 3) use a ...
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Categorical linear-model coefficients from a pairwise competition experiment

I am presenting a question for which there may be a simple statistical answer, but I have prefaced it with perhaps a longer explanation, to err on the side of caution, in hopes that the data make more ...
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2 answers
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What should I check/test when I want to generalize from a sample to the population?

How do I ensure that I'm allowed to generalize findings from a sample to the population? So far, I'm only aware of the standard error. Is this (alone/itself) sufficient or even valid? As the CI is ...
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Can the Bayes factor be negative?

This is what I saw in a source I am referring to: Since both the numerator and the denominator are probabilities (so they can only take any value between 0 and 1), how can the result of division be ...
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How to implement logistic regression deviance from scratch

As a learning exercise, I'm trying to implement the deviance for logistic regression from scratch. I understand the deviance to be: $\mathcal{L}_S - \mathcal{L}_M$, where $\mathcal{L}_s$ is equal to ...
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1 vote
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How can we use shannon entropy to discriminate between two similar probability distribution function?

I studied two papers related to discriminating between two similar distributions using Shannon entropy. But both of them had different views. Can anyone explain what would be the basic flow of idea to ...
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Covariance of a sample statistic for two independent bivariate random variables

I have a somewhat convoluted question here. Suppose I have paired random variables $X$ and $Y$. That is, when I draw samples, I get one instance of $X$ and an associated instance of $Y$. Then I can ...
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1 vote
1 answer
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Logistic regression- is it okay to build a model that maximizes recall and use the coefficients for inference

I'm a novice in the field of ML and stats. So I have a dataset where the target feature (dependent variable) is binary (True, False), I'm trying to make some inferences and find features in the ...
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How would we define a "model" in terms of its relation estimators and statistics?

I found this to be an interesting post but I want to hone in on the definition of a model. It defines a model as: the function (or pooled set of functions) that you may accept or reject as being ...
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PCA graph: Formal analysis of how each loading effects individual players?

Here is a PCA example, with environment variables loaded in blue, species in red, and sites in black. I am trying to make two specific interpretations. I want to know if they are right and if there is ...
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How to calculate sampling error for proportionate sampling?

I have done sampling using Proportionate Stratified Random Sampling. The table below shows the proportion of each groups in the sample and population. This is the formula for Standard Error (...
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Resources to help a recent statistics graduate deal with real world statistical problems

I recently got my master's in biostatistics, so I know the basics. However in my work there are many situations where people ask me "would it be statistically valid to do xyz" and I really ...
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Finding uniformly most powerful test for $H_o: \theta = 0$ vs $H_a: \theta = 1$, from pdf $\frac{e^{x-\theta}}{(1+e^{x-\theta})^2}$

Finding uniformly most powerful test for $H_o: \theta = 0$ vs $H_a: \theta = 1$, from pdf $\frac{e^{x-\theta}}{(1+e^{x-\theta})^2}$ So I believe I want to use Neyman Pearson lemma. Which from my text ...
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2 votes
1 answer
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Covid data analysis question

This might be a dumb question but I'm doing a basic data analysis for a medical group. Previously, I did a project for them where we looked at patient outcomes in a major hospital (let's call it "...
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Why is R-squared Not Valid for Nonlinear Regression? [duplicate]

Why is R-squared Not Valid for Nonlinear Regression? Why we generally do not use it in nonlinear regression?
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what does the alpha symbol represent in the standard equation used for inference by enumeration

can anyone tell me what the alpha means in the following equation (used for inference by enumeration)?
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How to sort individual tasks by duration when the only available data is the duration of two tasks together?

I have 2 sets of tasks, $S1$ and $S2$. A task can only belongs to one of the set (the intersection is empty). There is 21 differents tasks in $S1$, 57 in $S2$. A task from $S1$ is always followed by a ...
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Comparison between true simulated value and parameter estimation

I would appreciate any help regarding the following problem: Assume I am simulating time series data, for example of a sinusoidal wave with the equation: y(t)=A*sin(2*pi*f*t) Now, I use this model for ...
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3 votes
2 answers
102 views

Assumptions in causal machine learning

I am currently reading about causal machine learning, e.g. causal bayesian networks. I am wondering about the assumptions on that the causal machine learning models are based. For example, for linear ...
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9 votes
1 answer
588 views

Is there a standard measure of the sufficiency of a statistic?

Given a parametrical model $f_\theta$ and a random sample $X = (X_1, \cdots, X_n)$ from this model, a statistic $T(X)$ is sufficient if the distribution of $X$ given $T(X)$ doesn't depend on $\theta$. ...
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Using Pairwise Differences Between Two Conditions as Data (Bayesian)?

Suppose I have measurements for the expression-level of a "gene" from two groups of arbitrary (possibly different) sizes. Maybe one group is a control and the other treated. $x$ = <4.5, 5....
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1 answer
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Why is "proving" alternative hypothesis true, harder than "proving" Null hypothesis false

I understand the concept of the NULL hypothesis and how to reject it, however I would like to be able to explain why this is a better approach than trying to prove the alternative hypothesis true. ...
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Why 1 dof test does not follow $\chi^2$ with 1 dof distribution?

This is related to a comment made in F. Harrell's Regression Modelling Strategies page 32 of Sec 2.6 on Multiple Degree of Freedom Tests of Association. Consider $E(Y|X)=\beta_0+\beta_1 X+\beta_2 X'+\...
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Neyman-Pearson’s Lemma a to define the rejection region of the type nx > κ Bernoulli [duplicate]

I'm working through the following question: I understand that the formula is: Likelihood(Theta_0) / Likelihood(Theta_A) As its bernoulli, I think it shoudl work out as below but I am at a loss on how ...
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2 votes
2 answers
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How to interprete and describe the results of a Wilcoxon Signed Rank test?

I'm trying to learn about rank tests, and having doubts abouut how I should a result from a Wilcoxon Signed Rank test. Suppose, we are given: Z = -2.201, r = - 0.845, P < 0.05, then how should I ...
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Intuition for the perfect correlation between sufficient statistic and score function

I have recently learned that: Cramer Raw Lower Bound is achieved when there is perfect correlation between T(X) statistic and U(theta, X). Is there any intuition behind this? I cant quite understand ...
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1 vote
1 answer
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Hypothesis testing of my usage data

I have usage data for the first month of operation of my music business. In this user can listen to traditional songs in diff vernacular languages. I see that 30% of user accessing my business from ...
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Hypothesis Testing of t-distribution

An auto manufacturing company wants to estimate the variance of kilometers per litre for its one of the auto model. A random sample of 25 cars of this model showed that the variance of kilometres per ...
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Best estimate of a variable from two observations with different efficiencies

Problem Suppose to measure the frequency of a certain rare event (e.g. particle count) with two instruments $I_1$ and $I_2$ for a time $\bar{t}$, the same for both instruments. We expect the same ...
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Disease Control Rate for a Clinical Trial problem

Recently, I have come across a 2-armed clinical trial problem which attempts to find a "Disease Control Rate" (DCR) for patients in the treatement and placebo arms. On the Internet I found ...
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Component reliability with an uncertain starting time

I have a lab data analysis challenge which I think can be viewed as a kind of reliability analysis problem. Imagine a warehouse is filled with light bulbs that were installed at some unknown times in ...
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3 votes
1 answer
70 views

Infer $p(x|y)$ given $p(y|x)$ and $p(y)$

Given $p(y)$ and $p(y|x)$, how can we infer $p(x|y)$? Or to what extent can we know about $p(x, y)$?
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7 votes
1 answer
361 views

Minimizing Kullback–Leiber divergence using the Hessian

Considering two continuous probability distributions $q(x)$ and $p(x)$, The Kullback–Leiber divergence is defined as the measure of the information lost when $q(x)$ is used to approximate $p(x)$. \...
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1 vote
1 answer
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How to perform a linear regression to data which has transient behavior and saturation?

I am trying to linear-fit data in intermediate time scale (theoretically assumed to be linear) in the absence of the transient behavior in initial time and saturation after some time. For instance, ...
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Rao Cramèr Lower Bound problem

Let $X_1, · · · , X_n$ be a random sample from the uniform distribution on $[0, θ]$. I want to get the variance of the maximum likelihood estimator of $θ$ and check whether the variance decrease at ...
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minimizing kullback-Leiber divergence

This paper is showing how KL divergence can be minimized by matching the expected values of the sufficient statistics. More precisely, For any distribution p of the exponential family with pdf: $$ p_{\...
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How can I disaggregate the impact of a group of variables using machine learning?

I have a problem where the target variable Y (continuous, values: 0-1) is controlled by large number of variables. These variables can be grouped by the nature of the data: ...
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2 votes
1 answer
28 views

Infer (supposed) Poissonian probability from data

Suppose to count the drops of rain in a square meter in 15 seconds, producing 16 observations: 40, 20, 24, 15, 23, 12, 39, 26, 29, 33, 16, 36, 17, 32, 40, 15. What is the probability of counting 28 ...
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1 vote
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Modeling "Pay as Much as You Want" with a Bayesian Model

I have data of sales of a certain product which is sold "Pay as Much as You Want". The daily data is in the form of number of sales per day and the total revenue per day: Day Sales Revenue ...
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