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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214 views

Profile likelihood

I am considering a normal distribution with mean $\beta_1 + \beta_2\exp(-\phi x)$ and variance $\sigma^2$, i.e. $y \sim N(\beta_1 + \beta_2\exp(-\phi x), \sigma^2) $. My aim is to calculate the ...
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F-distribution likelihood interval, does it have to be symetric?

F-distribution : https://en.wikipedia.org/wiki/F-distribution I was told that the confidence interval for the ratio of variances (the $F$-function) is a symmetric interval for instance : $$ [ F_{1 -...
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Is“ power” the same as “alpha” in context of statistical significance?

I have read some notes and comments on different websites . It seems that a refererence to power could mean that it equals the alpha term used frequently in basic statistics.
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Can I use chi square goodness of fit test to solve the following problem?

I got the following question for my statistics finals exam yesterday. As the average proportion of female in the three locations is 0.473 I made the following table. 1) How can I proceed from here? ...
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Variational Inference: Computation of ELBO and CAVI algorithm

I am reading/studying this paper 1 and got confused with some expressions. It might be basic for many of you, so my apologizes. In the paper the following prior model is assumed: $\mu_k \sim \...
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What is the basis for statistical inference?

I wrote in a document something similar to this: Based on the collected samples, we hope to infer ... I was asked to provide a citation for my claim. I guess I ...
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56 views

Does model $R^2$ affect the interpretation of its coefficients?

First question: is it possible for a multiple regression model to have "big" and significant coefficients but a low $R^2$ value? Let's say the value of $R^2$ is 0.0005 and my coefficient of interest ...
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17 views

Kernel density, why does my subset appear to have a larger spread than the original series?

I have a series that is 1500 observations long called alt_intercept. From it, I created a subset that contains values only if another series (called pvalue) is less ...
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What if errors (residuals) follow other distribution rather than linear regression? [duplicate]

Recently, I'm studying linear regression. I've heard that errors always follow normal distribution because they are supposed to do (in the point of they are noises). But suddenly I just wonders what ...
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29 views

why does y axis sometimes change from normal histogram to kernel density?

Consider the distributions I have plotted below. They are of the same variables, one in normal histogram form and another in kernel density (Epachanov). As far as I know, the auc of the kernel ...
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How to identify relationship between variables from scatterplots?

I want to understand the relationship between a region's health and wellness demographics (% obese, % smokers etc.) and their injury rates, for ex. how does change in a metric say '% obese people' ...
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174 views

Performing repeated measures ANOVA on unstacked data in R

I am trying to do a repeated measures ANOVA on unstacked data for my experiment. For background, my experimental design is as follows: I have 160 stimuli divided evenly into 8 counterbalanced list, ...
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What is the suitable distance function for zero-inflated matrix?

I have a feature matrix, where the columns correspond to the features and the rows are the data points. My matrix is zero-inflated, meaning there are many false-negative zero entries in my matrix. I ...
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References: CI interval for preimage of Poisson mean

Looking for references or where to look to be able to deal with the following. Suppose I have some count data $(X_i)_{i=1}^{z}$, such that each $X_i$ is independent and Poisson distributed with mean $...
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29 views

Best sampling method within the normal family

Suppose that we want to make the best Bayesian inference about some value $\mu$ we have some normal prior about it. I.e. $\mu\sim N(\mu_0, \sigma_0^2)$ with known parameters. To do so, we can choose ...
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Compute the parameters of a distribution from samples drawn from the tail of the distribution

I have a collection of N samples drawn from a population by the following process: Draw M samples from the population, where each sample is a non-negative real number Drop all but the N samples with ...
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Testing equality of coefficients from two different regressions

This seems to be a basic issue, but I just realized that I actually don't know how to test equality of coefficients from two different regressions. Can anyone shed some light on this? More formally, ...
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Sufficient Statistic of Uniform $(-\theta,0)$

Let $X_1, ... , X_n$ be i.i.d random variables Uniform $(-\theta,0)$ , with $\theta > 0$ parameter \begin{align}f_{\theta}(x_1,x_2,\cdots,x_n)&=\prod_{i=1}^nf(x_i;\theta) \\&=\frac{1}{(\...
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Complete Sufficient Statistic of Uniform $(\theta,2\theta)$

Let $X_1,....,X_n$ be iid Uniform $(\theta,2\theta)$ , $\theta >0 $ It is easy to show that $T=(X_{(1)}, X_{(n)} )$ is a sufficient statistic for $\theta $ and we want to show it is not a complete ...
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Does random sampling from a dataset produce the same distribution as the original space?

Let's say we have a dataset $D$ with $N$ rows and $M$ columns. Each column is a feature. And for each feature $X_1, X_2,..., X_N $~ iid $F_p$ where $F_p$ is the distribution for feature p. Now let's ...
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37 views

Observed deterministic variables in MCMC

I need to model a measurement of an "exponential decay" i.e. I have a histogram of counts $Y$ over an array of (time-) intervalls. I want to use MCMC to infer parameters ($A_1,\lambda_1,A_2,\lambda_2,\...
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How to infer a missing observation in a state space model?

I read here that "structural time series models handle missing values naturally, following the rules of conditional probability. Posterior inference can be used to impute missing values, with ...
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Is it a valid to use one sample to estimate the population parameter and to decide whether another observation is in the population?

I have two groups of samples. Sample A is obtained from population A and sample B is a mixture of unknown origin i.e. some observations of sample B may come from population A and some may not. How can ...
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38 views

Test vs control group - how to increase the accuracy of my estimate?

I would like to find out if there is a way to reduce the statistical noise from my estimate of incremental value added from a certain customer treatment. Assume we have a group of clients for which we ...
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Extracting useful metrics from price info

First, an admission: my stats knowledge is minimal - purely practical applications in a fairly narrow range. I'm mostly a mechanic with a good bit of experience building and wrenching on ML/DS systems ...
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How to bootstrap samples from data that has more than dependent variable?

I understand bootstrap sampling with replacement. But what i still not sure about is that how to apply this approach to sample from data that has more than one dependent variables. For example, ...
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Looking for resources (papers, books) that explain the impact that non-random sampling has in test statistics

The majority (if not all) of test statistics assume random sampling. Consequently, probability values obtained in t-tests, ANOVAs, regression, HLM, etc., are intrinsically linked to the assumption of ...
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Synthetic Control method: how to select V matrix?

I am learning Synthetic Control method and reading paper."Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program" We need to minimize ...
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308 views

Histogram interpretation

I am working with a dataset (90000 observations) and have the following histogram plot (100 bins): The distribution looks normal. I see collections of 3-bins forming some kinds of count peaks. How ...
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74 views

Weighted average distribution

Consider I have $2$ returns time series random variables $r_{i,t}=\ln{\left(\frac{p_{i,t+1}}{p_{i,t}} \right)}\stackrel{(i.d.)}{\sim}\mathcal{N}(\mu_i,\sigma_i)$. Let's now compute a weighted ...
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236 views

How to make Bayesian-style inference for a Poisson process?

I am working on a fleet management software recently. Normally, the arrival of merchant request is a Poisson process. That is to say, on average we have a new merchant request every 10 minutes, but ...
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What exactly is the 'population' in samples of one time occurrences?

for example, let's say there is a policy that randomly allocated immigrants to every municipality of a country, and I am interested in the effect of increased immigrant population on voting outcomes. ...
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Which statistical test to use for binned data?

I researched for hours but cannot find the direction for the right test to use. I have a frequency distribution which shows bins on the x-axis that contain amount spent: 0-5\$ 6\$-10\$ greater than ...
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Central Limit Theorem - Significance of Sample Count

According to a Khan Academy's lecture, the Central Limit Theorem is defined as follows: Central limit theorem states that as the sample size increases, the sampling distribution of the sample mean ...
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What exactly is a prior in MAP and how do we get it?

I've recently been studying MAP (Maximum a posteriori estimation). From what I've learned, the prior P(Θ) is an expected distribution of Θ, where Θ is a likelihood <...
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Generalizing Bayesian methods by assuming a “distribution of distributions” instead of a prior

Bayesian methods assume a prior distribution with several hyperparameters. Unfortunately, this is asymptotically incorrect, because distributions in the real world are never exact. For example, the ...
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Why Mann-Whitney stat value is different in R and Python?

I'm calculating Mann-Whitney for a two-sided hypothesis and I'm getting different values for the statistic value: in R ...
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A measure of confidence given data with known variation coefficient

I need to create a classification model to diagnose a certain illness, for that i have been given a dataset of 7 analytes (medical features) with known variation coefficients due to biological ...
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1answer
265 views

use and misuse of Winsorization

I am doing research on Winsorization (and trimming), which has been broadly applied in many fields, but I think many researchers didn't do it in a "rigorous" way. Or maybe even worse, they misuse it. ...
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How can I normalize Bayesian Network query result?

While taking a Bayesian network tutorial on YouTube, I was watching a video explaining the Bayesian Network probability inference. Somehow, at the end of the tutorial, the lecturer did not explain how ...
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29 views

error estimate or confidence interval on a probability

Imagine I have $N$ 6-sided die, all identical but not fair, so that the probability of getting 1 is $P(1)$, the probability of getting 2 is $P(2)$ etc. I would like to run an experiment (rather than ...
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Are bayesian methods inherently sequential?

Ie, to do sequential analysis (you don't know ahead of time exactly how much data you will collect) with frequentist methods requires special care; you can't just collect data until the p-value gets ...
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Why is degrees of freedom not considered while calculating standard deviations of samples in independent samples t-test?

In paired samples t-test, while calculating the standard deviation of differences, we take into consideration the degrees of freedom in the formula of calculating t by using n-1 instead of n for ...
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142 views

Combining the result of two uncertain measurements

What is the best way to combine the results of multiple uncertain measurements? For example, let us assume that I want to measure the relation y ~ b*x. I run my experiment and I estimate the the ...
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1answer
44 views

Inference using robust statistics

I'm simulating the overall usage of a cluster using historic deployment data. Due to the nature of the simulation, there are some heavy points (i.e. very low overall usage). As a result, the variance ...
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527 views

Does the posterior necessarily follow the same conditional dependence structure as the prior?

One of the assumptions in a model is the conditional dependence between random variables in the joint prior distribution. Consider the following model, $$p(a,b|X) \propto p(X|a,b)p(a,b)$$ Now suppose ...
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Debiased regularised regression (elastic net)

I have ~55,000 binary observations and 12 explanatory variables (EVs). I am looking to perform variable selection, followed by inference on the effect of the retained EVs on the binary outcome. Since ...
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68 views

If the VIF is 2 then what is the value of correlation coefficient $R^2$

If variance inflation factor is 2 what is the value of correlation coefficient $R^2$? $$VIF = \frac{1}{1-R^2}$$ Given $VIF =2$, then is this calculation correct? $$\begin{align} 2 &= \frac{1}{1-...
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Minimizing bias in explanatory modeling, why? (Galit Shmueli's “To Explain or to Predict”)

This question references Galit Shmueli's paper "To Explain or to Predict". Specifically, in section 1.5, "Explaining and Prediction are Different", Professor Shmueli writes: In explanatory ...
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What is the meaning of × in statistics?

What is the meaning of the symbol × in an ANOVA context? More specifically what is the meaning of × in the following table? ...