**2.365 variance questions.**

I'm following the discussion in Field Experiments by Gerber and Green, Chapter 3 as well as these resources:
http://ocw.jhsph.edu/courses/StatMethodsForSampleSurveys/PDFs/Lecture4.pdf
http://home....

I know there are several questions (here and on other websites) regarding the comparison of values, but I am still lost with the data I have and the analyses I should conduct.
I have just 18 values (...

I want to make a model in which the dependent variable is nutritional levels of children, for this, I calculated $z$ scores like weight for ...

I'm analyzing codon usage using the model described in the following paper
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4494061/
In brief, this model uses a MCMC to estimate the pausing time for the ...

I am doing image processing and I want to calculate the variance of a histogram of pixel intensities.
The first method I have tried:
The images store the pixels values using double precision numbers,...

I often read about a rule of thumb, one can apply if the test of equal variances returns a significant result. Depending on the source, the proposed maximal $F$ ratio varies between 1.5 and 4, which ...

I am building a predictor for $y = f(x)$ using training samples ${(x_i, y_i)}$ (assume) drawn i.i.d from some distribution $p(x,y)$, by optimising the empirical L2-loss:
$f(x) = argmin_f \; \sum_i ||...

I'm simplifying a bit here, but my dataset contains 10 stations, each with measurements of growth at time increments. For each measurement, there are between 1-4 duplicates measured at the same day+...

I have a question regarding the following r code. Lets say I have a regression in r:regression <- lm(Salary ~ Education + Gender + age)If I were interested ...

If I was building a linear mixed-effects model and I changed the variance structure (let's say to a power function) to represent an increasing variance over time points, would the assumption of ...

In a multi-class classification problem, say 3 classes, the model outputs 3 probabilities, each representing the likelihood of belonging to one class, for example (0.7, 0.5, 0.4).
Is there a formal ...

A predictive model that I currently use relies on PCA with varimax rotation to reduce the dimensionality of the data (whether this is appropriate is a separate question).
The dataset consists of ...

I know from previous studies that
$Var(A+B) = Var(A) + Var(B) + 2 Cov (A,B)$
However, I don't understand why that is. I can see that the effect will be to 'push up' the variance when A and B covary ...

Empirical models, like regressions, generally assume the existence of errors in the data, and effectively ignore them during prediction. This results in an optimised mean projection, but it means that ...

I am working in R, and am trying to generate values of
$$
logit^{-1}(\alpha X_1+\beta X_2)
$$
with $\alpha,\beta$ such that $logit^{-1}(\alpha X_1+\beta X_2)$ ...

Let's say I have a bunch of events associated with individuals in my study:
...

I searched regarding change in variance over time, but everything I saw was about relatively long time series. I have a series of 5 time points, equally spaced, but with different people missing at ...

As the title says, i'm not sure how a variance test determines that a data set is Poisson.
I've attempted the question and have come up with the following:
...

I have data set that contains values between 10-25.c(21, 19, 12, 20, 25, 22,14, 14, 22, 11, 15, 14,
12, 13, 16, 23, 20, 16, 17, 16)We have been asked to give ...

What is the aggregate variance method for estimating the value of Hurst exponent?
How does it measure long range dependence?

I was studying Campbell, Chen, Viceira (2003)
https://dash.harvard.edu/bitstream/handle/1/3163263/campbellnber_assetallocation.pdf?sequence=2
I cannot really understand how they decompose the ...

How much greater is the shared variance between two variables if the Pearson correlation coefficient between them is -.4 than if it is .2?
Can someone help me understand how to calculate this?

Could someone maybe give an explanation and formulas in terms of sums or matrix operations for the calculation of variance based effects, and total effect indices?
The information given on Wikipedia: ...

I cannot share the data, due to confidentiality, therefore I will work random numbers. I have a parameter, lets say:
...

I plotted the accuracy of a Decision Tree model with varying depths.
I see that as the depth increases, the delta between the training and test set starts to increase to a point where they never ...

I have a task where I need to derive the variance of $10^{x-y+5-z}$
the variables are unrelated and the formula is all that's provided in the task.
I was thinking that the variance of $10^{x-y+5-z}$...

I am having trouble figuring this out. Any help would be appreciated.

The random variable Y has $E[Y]= \theta$ and $\text{var}(Y)= \theta^{1.5}$. Find the transformation $W$ that makes the variance of $W$ approximately constant.
I am unsure how to approach this problem....

I have 6 locations, 3 replications, 7 blocks, and 49 entries in a full diallel experiment. I am trying to find out the heritability for each trait in each location separately. So, here I have used the ...

The context that we are presented with a linear model
$$Y_i = \beta_0 + \beta_1X_i + \epsilon_i,$$
where $\epsilon_i \texttt{~} \mathcal{N}(0,\sigma^2)$.
We obtain predictions for $X_i$ by plugging ...

I have a few questions regarding on how diversity is defined since I've seen differing definitions in different papers.
In the paper "Measures of Diversity in Classifier Ensembles and their ...

I am comparing two temperature control devices both designed to maintain body temperature at exactly 37 degrees in anaesthetised patients. The devices were fitted to 500 patients forming two groups. ...

Suppose that $\{X_t\}$ is a weakly stationary time series with mean
$\mu = 0$ and a covariance function $\gamma(h)$, $h \geq 0$, $\mathrm{E}[X_t] = \mu = 0$ and $\gamma(h)= \operatorname{Cov}\left(...

Does explained variance hold for binary data?
That is can one use the explained variance truthfully as a parameter with e.g. sklearn's PCA?

Suppose we want to estimate posterior variance of $\alpha$ given x, i.e. var($\alpha|x$).
We have MCMC posterior samples $a_1,\dots, a_B$, which are not independent. Does $\hat{\text{var}}(\alpha|x) =...

I have a random variable, distributed as a sum of independent chi-squared random variables each with one degree of freedom.
$$ X = \sum_{i=1}^n \lambda_i \chi^2_{i(1)}$$
where $ \lambda_i$ are ...

I have a question regarding a certain derivation of the bias variance dilemma. Generally, I guess I have understood the derivation in e.g. Geman's Paper, or in books like Bishops Pattern Recognition. ...

I have just learned about the concept of bootstrapping, and a naive question came to mind: If we can always generate numerous bootstrap samples of our data, why bother to obtain more "real" data at ...

Say I have a study measuring a continuous endpoint for 3 sample assays on two days, i.e. before and after intervention. The measurements are performed several times by different people (repeated ...

I am working on calculating the expectation and then variance of the range from a Uniform(-theta, theta) distribution, but have gotten stuck.
Basically the first page I show how I get the pdf and ...

In a test of Variance, if the variance is less than a certain threshold, isnt it a good thing? Lesser variance is always good. Can somebody give me an example where it would make sense for us to have ...

There is an example given on the Scikit-Learn site that compares the bias-variance decomposition of the rmse of a single SVR model against a bagging ensemble. Unfortunately, the data is being ...

For real-valued samples (possibly known to lie in some interval, but without further constraints on them), I am interested in the tightest possible bound on the sample variance $\sigma^2$, given the ...

In An Introduction to Generalized Linear Models by Dobson and Barnett, exercise 1.4b&c is as follows:
Let $Y_1,...,Y_n$ be independent random variables each with the distribution $N(\mu,\sigma^...

I am simulating a hierarchical model with MCMC Bayesian methods. The model has three groups of individual effects modelled as random effects drawn from normal priors with mean zero and variances ...

I am running a negative binomial model without creating a glm object in R. I found an answer at StackExchange on how to get standard errors "by-hand" here, but it shows only how to get values on a ...

The bias and variance of a classifier determines the degree to which it can underfit and overfit the data respectively. How could one determine a classifier to be characterized as high bias or high ...

Given a seasonal rainfall time series X, suppose that I need to divide it into a linear trend (mY+q) and seasonal component. If from the auto-correlation and partial auto-correlation only lags ...

I am looking to analyse Likert scales, and want to assess whether there is 'sufficient variation' along the scale [i.e. that the majority of respondents are not 'clumped together' or a particular ...

- regression
- self-study
- mean
- mathematical-statistics
- r
- standard-deviation
- covariance
- bias
- normal-distribution
- time-series
- anova
- expected-value
- distributions
- estimation
- probability
- random-variable
- machine-learning
- hypothesis-testing
- correlation
- heteroscedasticity
- sampling
- sample
- pca
- confidence-interval
- unbiased-estimator

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