Questions tagged [variance-stabilizing]

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Optimal three parameter variable stabilizing transformation of a Poisson

In the paper: "On the classical choice of variance stabilizing transformations and an application for a Poisson variate", Shaul K. Bar-Lev and Peter Enis give an optimal two parameter ...
• 535
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Statistics based scheme for assigning weight to exam questions

I have a memory of taking some undergraduate statistics course, and the lecturer doing an example where he had a scheme for assigning weights to the problems of an exam based on the students ...
1 vote
35 views

Variance stabilization of Scaled Noncentral Chi-squared

For an integer $k > 0$, $\mu_i \in \mathbb{R}$, and let $\zeta_i \sim \mathcal{N}(0, 1)$, $1 \leq i \leq k$. In the background we are taking $k \to \infty$. Then the random variable $T$ has a ...
• 2,111
176 views

Variance stabilizing transformation for logistic regression

Question: Are there (known) variance stabilizing transformations for logistic regression? Backgound: As an M-estimator, logistic regression is asymptotically normal, under suitable regularity ...
• 301
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How does using log transformation for a confidence interval of the survival stabilizes variance?

I only found that it eliminates the estimator of survival from the variance formula, but could anyone show some references or write a few formulas to show how exactly the Greenwood becomes more stable ...
410 views

Variance-stabilizing transformation on a simple linear regression

I am currently working with variance-stabilizer method and readed something about it from my textbook. I want to understand it better so I would like to consider a case where I for instance have a ...
• 181
1 vote
52 views

Does it make sense to perform variance stablizing transform when a distribution is bimodal?

https://en.wikipedia.org/wiki/Variance-stabilizing_transformation The purpose of VST is "...such that the variability of the values y is not related to their mean value" according to ...
• 542
1 vote
258 views

VST for negative binomial random variable

https://en.wikipedia.org/wiki/Variance-stabilizing_transformation The variance stabilizing transform of a Poisson random variable is the Anscombe transform. What is the VST for a negative binomial ...
• 542
579 views

Underperforming SELUs - How to correctly constrain layer weights in TF/Keras?

The promise of SELUs and SNNs I first read up about the 'power' of SELUs on a machine learning blog post. The promise of a Self-normalizing Neural Network (SNN) ...
• 1,138
1 vote
691 views

Stabilizing the variation in a time series

Is it necessary to transform the data here in order to stabilize the variation in this series? I do not think it is. How "bad" do the fluctuations have to be before stabilization becomes ...
• 423
1 vote
255 views

Equivalent Variance-Stabilizing Function

I've been reading the book "Generalized Linear Models with Examples in R" by Dunn and Smyth. In chapter 5, they claim: Variance-stabilizing transformations h(y) used with linear regression ...
737 views

How do I prove the square root is a variance stabilizing link for Poisson?

I have searched google, and wikipedia, and have come up with nothing. If there are links that you could provide to help me figure out how to prove this, that would be very beneficial. Is it possible ...
• 257
6k views

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). ...
• 191
1 vote
2k views

BOX-COX TRANSFORMATION always stabilize variance

I am aware that box-cox transformation may make data set significantly normal distributed with constant mean and variance. But sometimes fails to convert data into normal. My question is even though ...
• 105
1 vote
171 views

ARIMA stabilization process

Initially, before apply arma model stationarity conditions must hold. According to that,time series data must have same variance and mean with normal distribution. If raw data is not normal then box ...
• 105
1 vote
266 views

Measure of stability

I am working on a machine learning project when I realized I add a question. This is not programming, nor statistic, nor a probability question, but a real pure mathematical question. So I think my ...
103 views

How to remove effect of different batch variances in linear modelling

I have a dataset with 300 rows/genes and 900 columns/samples. The data were collected in 10 different batches, and study design was balanced in all of the batches. However, there is a huge difference ...
2k views

Model stability and variability

I am using polynomial regression to predict mean occupancy in a hospital unit using average length of stay (LOS) and arrival rate to the unit. I am using different percentages of training sets to ...
870 views

What are some unstable classifiers?

In my understanding, classifiers that tend to overfit (high variance) are unstable. Two examples would be unpruned decision trees and k-Nearest Neighbors with small k. Can you suggest some more ...
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1k views

How to do a bias-variance analysis on a machine learning modelling process

I searched on topics of the bias and variance trade-off and got back lots of questions with different levels of response. The information is scattering too much and unsystematic to answer my own ...
• 463
5k views

How do I find a variance-stabilizing transformation?

I wonder how to solve this classical problem: Recall that for a binomial proportion $\hat p$ based on a sample of size $n$ we have $$E(\hat p)=p$$ and $$\operatorname{Var}(\hat p) = p(1-p)/n.$$ ...
15k views

interpretation of boxcox with lambda equal 0

I am working on this non linear data set, and running my Box-Cox I find that the best value to use is $\lambda = 0$. If I understand correctly, $\lambda =2$ implies $Y^2$. Similarly, $\lambda = -0.5$ ...
291 views

SARIMA model on original (unstable variability) or transformed (stabilized) series?

If my series requires a log-transformation to stabilize variability, do I apply the sarima function to the log-transformed series or the original series? Does the ...
341 views

Transformation versus projection to Normality

Can anyone explain the theoretical consequences of a traditional variance stabilizing transformation such as sqrt(lambda) for the Poisson versus projection to a normal distribution and the pros and ...
1 vote
3k views

How does Anscombe transformation stabilize the variance of a Poisson R.V.?

I was taught that a transformation f(X) is said to be a variance-stabilizing transformation if $[f'(E(X))]^2*Var(X)$ is independent of E(X). For a Poisson-distributed random variable X, E(X) = Var(X) ...
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1 vote
369 views

How to show that stability is improved when using bagging in an unsupervised context?

I have a data set of 200 observations and around 10 continuous variables. I would like to build a graphical model to study dependencies between variables. Unfortunately, my data is not very stable. ...
• 11
7k views

How large does a Poisson distribution's mean need to be to use normal distribution statistics?

As the mean of a Poisson distribution increases, the Poisson distribution approximates a normal distribution. I assume that once the Poisson mean becomes large enough, we can use normal distribution ...
• 14.3k
473 views

Relation between variance stabilizing transformations and effect sizes?

When researching effect size for proportions, in particular the paper Effect-Size Indices for Dichotomized Outcomes in Meta-Analysis, that at least two of the usual effect sizes are realy variance ...
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3k views

GLM vs square root data transformation

I am currently analysing some pretty awful/awkward data on the abundance of fish under three different "Hydro-Regimes" (5 abundance measurements for each regime - Short/Medium/Long). The current ...
31k views

Why is the square root transformation recommended for count data?

It is often recommended to take the square root when you have count data. (For some examples on CV, see @HarveyMotulsky's answer here, or @whuber's answer here.) On the other hand, when fitting a ...
61k views

What could be the reason for using square root transformation on data?

What is the primary reason that someone would apply the square root transformation to their data? I always observe that doing this always increases the $R^2$. However, this is probably just due to ...
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