Questions tagged [variance]

The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

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11 views

How to measure the variance of error?

So I have a predictive model generating a list of $\hat{y_i}$, and the error of each forecast is $\hat{y_i}-y_i$. I would like to measure the variance of the errors. This can be calculated by $$\...
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Why are these statistics used to find out the sample variance's distribution

It's pretty much what the title says, I'm using Canavos' Applied Probability and Statistical Methods to refresh what i know about the sample distributions. I'm now looking at how the sample variance's ...
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Entropy evolution while learning?

It is fairly well known that $$H(X|Y)\le H(X),$$ the posterior entropy is smaller than the prior entropy. This is similar to $$\mathbb{E}_Y[\mathbb{V}ar_X[X|Y]]\le \mathbb{V}ar_X[X]$$ which follows ...
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Variance of X and Variance of Log(X). How to relate them?

I have the variance of a random variable X and I want to obtain the variance of log(X). Is it possible if I dont know its PDF? If I assume that X has a lognormal PDF, how variances should be related?
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Comparison of explaned variances in PCA

I computed a PCA and am interestet in the explained variance of the first unrotated component. The same procedure was used in a previous study. Question: How do I test whether the two explaned ...
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Can variational autoencoder be used to generate similar images?

I trained the variational autoencoder . Suppose if we take the mnist dataset and visualize it, the distribution of classes are clustered but are very close to each other. When i take a point/encoding ...
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Repeated Measure of 'robustness'

I have three small 20x5 matrices, with each one being collected on at a different time point. What I would like two is which columns show the smallest difference from each other across the 3 matrices,...
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45 views

Intuition About Principal Component Directions

I am trying to really get a deep understanding of PCA. From my understanding, a principal component is defined as $$\mathbf{z}_k = \phi_{1,k} \mathbf{x}_1 + \ldots + \phi_{p,k} \mathbf{x}_p = \mathbf{...
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Modeling approach to showing a parabolic effect is greater than that expected by scale boundaries

I have conducted an experiment where raters rate different nations on a DV. Each observation is a different nation. I calculated a mean and SD of the DV for each nation. The data we are working with ...
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41 views

How to normalize if variance is zero?

How do I normalize a dataset to z-scores is some features have variance zero? Is throwing them away beforehand the only solution?
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25 views

Why would you subtract the mean of your variance from your variance? [duplicate]

i recently stumbled over the following codeline: variancedm<-variance-mean(variance) Is this a common way to normalize/standardize variance ? Why would you ...
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Why do we normalize variance for regressions?

I'm currently analyzing trading strategies and was struggling with some paper results. For column 2, they analyze the relation from the monthly returns of their strategy (rwml,t) on the realized ...
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Why consider the variance rather than the entropy of estimators?

It is a rather common thing to be concerned with the variance of an estimator. For instance, confidence intervals for the mean can be constructed based on the standard error. Often, however, we look ...
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What statistic to use in testing the variance of maximum likelihood estimators

(A physicist self-studying statistics here) I was previously confused about the meaning of the standard error in a maximum likelihood estimate. Certain stack exchange posts (linked below) have gone ...
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Estimate parameters of inv-Wishart distribution using Bayesian

$\Sigma \sim Inv-Wishart_{v}(\Lambda^{-1})$ Suppose that I have a set of observations of $\Sigma$s, I wonder if there is a conjugate way to estimate the value of $v$ and $\Lambda$ (especially $\...
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Volatility Models: Does this model have a name?

I am looking at some volatility models and the following functional form pops up naturally $$ \xi_t ^2|x = \sigma^2 x^{2\beta} + u_t. $$ Here $\xi_t^2$ represents the square residual and the terms $\...
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60 views

Variance of $\chi^2$ statistic depends on $df$ but not on $n$?

I have an $r\times c$ contingency table. The chi-square statistic for the table is equal to $\chi^2 = \sum_{i=1}^{rc} (O_i - E_i)^2 / E_i$, where $O_{i}$ are the observed and expected counts for cell $...
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If $\operatorname{Var}(X+Y)=10$ and $\operatorname{Var}(Y+Z)=20$, what is the upper bound for $\operatorname{Var}(X+Y+Z)$?

The lower bound can be zero, by having covariance matrix $\Sigma= \begin{bmatrix} 20 & -20 & 0\\ -20 & 30 & -10 \\ 0 & -10 & 10\end{bmatrix}$ producing $$[1,1,0]^T \Sigma [1,...
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What is the formula for the conditional variance when taking the derivative of a Gaussian process?

The formulae for the conditional mean and variance of a Gaussian process is given by equations (2.23) and (2.24): Also, the formula for the covariance of the derivative of a Gaussian process is given ...
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Variance–covariance matrix in meta-analysis of variation metafor

I'm conducting a meta-analysis on estimating a gold standard measure from other simpler measures. To determine the error of estimation, I derived the standard deviations of the differences between the ...
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How to calculate variance of a data set with frequency spread over multiple years

If I have 4 books, with multiple copies of each book - [2,3,1,2 respectively], and I have 2 years data of these books. Taking the example of book A, total number of issues of the book A in 2 years ...
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$var(T(X_1$,…,$X_n)) = 1/n var(X_1)$ (for $n \to \infty$): When does that hold?

Let $X_1,...,X_n$ be an i.i.d. random sample, and $T(X_1,...,X_n)$ a statistic. In a book (The Jackknife and the Bootstrap by Shao and Tu) I read, that under certain regularity conditions, $$\lim_{n \...
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Determining the variance of a linear regression prediction from only mean and standard error

I'm not sure there's a mathematically valid way to do what I want to do. Let's assume a simple bivariate regression $$y = \alpha + \beta x + \varepsilon$$ I have the following results for this ...
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For the German Tank problem, why do we assume symmetrical samples?

I have read that for the German Tank problem, one assumption to make is the following: 'By symmetry, one would suppose that the number of unobserved labels above X(n) should be about equal to the ...
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26 views

Why is my regression intercept too low ? (General question)

Im currently trying to solve the following regression problem. Since my results for the first column are correct, im sure im on the right way but: For the second column i tried the realized variance ...
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Estimating population variance considering both population sample variance AND sampling method variance

I want to estimate the variance of a normally distributed population. I can take N samples and calculate the sample mean and sample variance, which would normally suffice; however, the sampling method ...
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Cokriging variances differ using cross validation

I'm investigating cokriging using various metals in the Meuse dataset but the variances output by R when I predict values at gridded points differ substantially from the variances produced by cross ...
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42 views

Variance of X-Y and X-Z when Z and Y are correlated

I have a hard time solving the following issue, so hopefully someone is willing to help. I believe I am almost there but just missing a single step. There are three random variables $X$, $Y$, and $Z$ ...
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Choosing an estimator function due to variance and bias

I am working on an assignment that requires me to compare two estimators $T1$ & $T2$ for an unknown parameter $\theta$ based on their MSE. They both have the same MSE of 3, T1 having a variance ...
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Sampling method to represent a larger demographic

I have a set of Google search queries for a particular user. Every query has its frequency, that is the number of times the person searched it for. Now I have to infer some information about this ...
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What is the difference between high variance in k-fold cross validation and high variance in machine learning model?

I have this question because of what is mentioned on a book: Does this high variance mean that the model you are evaluating has high variance (overfitting)?
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Unequal Sample Size, Similar Variance

I'm comparing an intervention using a pre and post knowledge survey. My pre sample size is n=37, my post is n=32. The variance for the pre is 7.08 and 6.94 for post. The histogram of the pre is skewed ...
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Bias and variance in the model o in the predictions?

This topic confuses me. In the literature or articles, when talking about bias and variance in automatic learning, specifically in cross-validation, do they refer to the high bias (underfitting) and ...
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Questions about calculate the first k-th principal components of VR-PCA?

Variance-reduced PCA VR-PCA, focus on the first component calculation, what about the k-th PCs? Any idea? Thank you!
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Are conditional mean in an AR(1)-GARCH(1,1) equal for different GARCH(1,1) processes of the same data?

I have created a Markov-Switching GARCH model, where the volatility is defined to be switching between two different GARCH(1,1) processes. The data is assumed to have zero mean, where the data is ...
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Binomial distribution - Variance (Experimental vs theoretical)

Just been experimenting with creating a simulation for the binomial distribution. I've made an applet in Geogebra that generates the histogram, mean of the experimental data, the variance of the ...
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Understanding variance stabilization and its uses

I recently came across the variance stabilization method that tries to remove the dependency of variance from the mean(for example consider poisson distribution). ...
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29 views

Comparing means, having a large variance

Currently I am working on a project in which i do have two different sample-sets with a limited size and a large variance. Furthermore, I do have a bigger data-set that gives information about the ...
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Variance of Mean Response at the Mean of the Data

My question concerns the variance of the mean response as outlined in this short article or in this Wikipedia entry. Basically, the variance of the mean response is given by $$\text{Var} \left(\hat{\...
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Predicting Sales With and Without Events?

I have data from a retailer that contains aggregate sales over weekly periods, grouped by postal codes. Within this data, there are several 'promotional events' that occur at various discrete time ...
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38 views

How can we write the sample variance's formal definition of a continuous random variable considering Bessel's correction? [closed]

I am trying to find the formal way of writing the sample variance of a continuous random variable considering Bessel's correction. I ask because the sample variance is usually written this way: $$ ...
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Where is my mistake in derivation of total variance?

I'm obviously doing something wrong here.. could someone please point it out? By definition of variance: $$ \mathrm{Var}[Y] = \mathrm{E}\left[(Y-\mathrm{E}Y)^2\right] $$ By definition of total ...
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Don't understand why glmm random effect variance is zero. Have reviewed similar questions still dont get it

I study a colonially-nesting bird species. I am trying to perform an AICc evaluation of GLMMs for a nest site selection study. I collected data at nest sites and paired random sites. I want to ...
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Variance of autocorrelation

At this link I have seen the following formula whereas $$ r_k = \frac {\sum_{t=k+1}^n a_t*a_{t-k}} {\sum_{t=1}^n a_t^2}$$ $$Var(r_k) = \frac {n-k}{n*(n+2)}$$ where $r_k$ is the autocorrelation at ...
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Estimation of variance of mean of Bernoulli distribution, if sample is degenerated [duplicate]

If $X_1,X_2,…,X_n∼Bernoulli(p)$ Variance of the average of $X$ is $Var[S_x/n]=\frac{p(1−p)}{n}$ But if we have sample, where all $X$ are equal, $\hat{p}=1$ (or zero), and estimation of var of ...
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Granger Causality: Sum of errors vs. determinant

I have been measuring Granger Causality between pairs of vectors processes (i.e. 2 vectors consisting of multiple time-series variables). Most of the equations I find in references utilize a ...
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variance of the square of the bias on linear regression

Basic setting let the linear model be: $$ \mathbf{y}=\mathbf{X\beta}+\epsilon $$ where $\epsilon \sim N(0,\sigma^2\mathbf{I}_n)$ $n$ is the number of samples $p$ is the number of attributes. $\...
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Low Bias in an overfitted model

I have a question about the bias-variance tradeoff in machine learning concerning the implications of overfitting: Assuming $y = f(x)$ + some noise, the error of our model for any input $(x,y)$ is ...
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53 views

Mean and variance of a variable (inside a function) without known its distribution, but known mean & variance of the function

Let $$Z_k = A\, e^{i(2\pi B+\phi_k)}, \qquad k =1,2,3\dots$$ be a complex function with dependent on $\phi_k$ and others are real constants. Assume that the mean $\mathbb{E}[Z_k] = \mu_{z_k}$ and ...
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Confused regarding how to attribute changes in variance to different potential causes

I am looking at baseball exit velocities (how fast the ball hits off the bat) in different stadiums over 2017, 2018, and 2019. 2017 Variance: .4 2018 Variance: .43 2019 Variance: .54 So I am ...