Linked Questions

59
votes
4answers
14k views

What problem do shrinkage methods solve?

The holiday season has given me the opportunity to curl up next to the fire with The Elements of Statistical Learning. Coming from a (frequentist) econometrics perspective, I'm having trouble grasping ...
10
votes
4answers
2k views

How does one explain what an unbiased estimator is to a layperson?

Suppose $\hat{\theta}$ is an unbiased estimator for $\theta$. Then of course, $\mathbb{E}[\hat{\theta} \mid \theta] = \theta$. How does one explain this to a layperson? In the past, what I have said ...
17
votes
2answers
3k views

Is there a graphical representation of bias-variance tradeoff in linear regression?

I am suffering from a blackout. I was presented the following picture to showcase the bias-variance tradeoff in the context of linear regression: I can see that none of the two models is a good fit - ...
7
votes
4answers
2k views

Why must one trade off between bias and variance?

Apparently, a learning algorithm must make a trade off between bias and variance when producing a hypothesis. Bias means systematic deviation from data. Variance refers to the error due to ...
11
votes
2answers
3k views

Biased bootstrap: is it okay to center the CI around the observed statistic?

This is similar to Bootstrap: estimate is outside of confidence interval I have some data that represents counts of genotypes in a population. I want to estimate genetic diversity using Shannon's ...
7
votes
2answers
1k views

Bias / variance tradeoff math

I understand the matter in the underfitting / overfitting terms but I still struggle to grasp the exact math behind it. I've checked several sources (here, here, here, here and here) but I still don't ...
6
votes
1answer
433 views

When will a less true model predict better than a truer model?

In "To Explain or to Predict?", Pr. Galit Shmueli said that sometimes a less true model can predict better than a truer model. Why is it so? When will it happen? How does it happen? Is explanation a ...
1
vote
1answer
2k views

Interpretation of low bias and variance for train/test errors

Based on the extensive discussion in this post, I understand that the goal is to achieve low bias and low variance. Now, in terms of train and test errors, does it imply that achieving low bias and ...
2
votes
1answer
721 views

Relation between MSE and Bias-Variance

If MSE is $$ \mathrm{MSE}(\hat Y) = \mathrm{Var}(\hat Y) + \mathrm{Bias}^2(\hat Y) $$ and the Bias-Variance decomposition is given by $$ \mathrm{Err}(\hat Y\,|\,X=x_0) = \mathrm{Var}(\hat Y) + \...
5
votes
0answers
742 views

Bias Variance tradeoff from a Bayesian perspective

I know the general question about bias variance has been asked before. I understand the frequentist approach and the concept of model selection and the impact of bias and variance on "accuracy" of a ...
3
votes
1answer
184 views

What is parameter instability? How can I measure it? [closed]

What is parameter instability and how can I measure it? If my model is having a hard time to forecast out-of-time samples, could parameter instability or populational instability be the cause of it?
2
votes
2answers
80 views

Total Cost Shrinkage

I have a question regarding Shrinkage Methods. I am currently writing a term paper about ridge regression and lasso and before explaining the two methods, I want to give some theory on why shrinking ...
0
votes
1answer
74 views

Improving a boosted regression model or change?

I am looking at a data set that contains multiple predictors and a continuous response. Using dismo along with gbm I built (a terrible one?) model. Using the package sROC, I got an AUC or 0.48 - so my ...