Timeline for Explaining to laypeople why bootstrapping works
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 11 at 23:35 | comment | added | Mario | @conjugateprior May I ask you kindly also comment/answer on a similar question? | |
| Sep 10, 2019 at 13:59 | comment | added | conjugateprior | @MasonBeau I meant all the data generation assumptions you'd need to derive a sampling distribution, and thereby the standard errors, t-statistics, and confidence intervals, analytically. (Certainly 'non trivial' from the layperson's perspective.) | |
| Sep 7, 2019 at 16:23 | comment | added | Hugo | What specifically are you referring to when you write "Indeed particularly convenient assumptions plus non-trivial math may allow you to bypass the sampling part altogether"? What kind of "non-trivial math" you're talking about? | |
| Aug 11, 2019 at 20:36 | comment | added | conjugateprior | This is 'for laypeople' so the deliberately unwritten but slightly more precise form of this sentence is "sampling with replacement is just a convenient way to get a sampling distribution by treating the ECDF as if it were the CDF" | |
| Aug 11, 2019 at 10:42 | comment | added | ayorgo | "Sampling 'with replacement' is just a convenient way to treat the sample like it's a population...", except that it isn't. How often does a statistician take a sample the size of an entire population? Bootstrap is just a clever computational trick that happens to work (most of the time). Cross-validation seems to be much closer to what's going on between populations and samples in real life. | |
| Jun 20, 2018 at 7:57 | comment | added | Eric Burel | Am I correct if I say that computing the variance of a value among the bootstrapped samples serves an equivalent goal as computing a confidence interval ? Since this way I estimate not only my value (say the mean) + also what my value could have been if I had made multiple draws. What would be the theoritical difference ? Bootstrapping since to exploit the sample data better and thus produce smaller intervals than usual methods for the same confidence level, am I right ? | |
| Dec 1, 2015 at 7:20 | review | Suggested edits | |||
| Dec 1, 2015 at 8:18 | |||||
| Apr 11, 2014 at 18:45 | comment | added | RobertF | Bootstrapping runs into problems if you're attempting to estimate the sampling distribution of an order statistic (such as the maximum), since bootstrap samples cannot draw a higher value than the maximum value in the original sample. See stats.stackexchange.com/questions/9664/… | |
| Apr 30, 2013 at 9:05 | comment | added | Lucas Morin | From what I understand it works because: it's the only thing we can do and it's likely to work... is that enough ? In what case bootstrapping doesn't work ? | |
| Apr 10, 2012 at 17:34 | vote | accept | Alan H. | ||
| Apr 10, 2012 at 7:34 | comment | added | MånsT | @cardinal: Nice comment. A lot of people think that the bootstrap and resampling are the same thing when in fact the latter is a tool used for the former. A similar misconception is that many users of statistics tend to get MCMC and Bayesian analysis confused. | |
| Apr 9, 2012 at 2:11 | comment | added | cardinal | @naught101: "Reasonably large" can be quantified pretty well by the D-K-W inequality (if you'd like, you can look at my answer in the link in the OP's question) and regarding lots, it depends on the sample statistic of interest, but if we have $B$ bootstrap samples, then with simple Monte Carlo we know that the standard error is of order roughly $O(B^{-1/2})$. | |
| Apr 9, 2012 at 2:05 | comment | added | naught101 | @cardinal: how large is "reasonably large" and how many is "lots"? (if there is a good answer to these questions elsewhere on the site, feel free to point me in that direction) | |
| Apr 9, 2012 at 0:32 | comment | added | cardinal | .../...calculate the quantities of interest directly for our pretend distribution, we'd prefer to do that. And, that would be the real bootstrap. But, usually we can't, so we're reduced to having to resampling, instead. | |
| Apr 9, 2012 at 0:29 | comment | added | cardinal | (+1) This is a good answer. I think there may be a way to further draw out a very important point, though. In the way the bootstrap is normally carried out, there are two effects that are happening. First, we are pretending that the sample we have obtained is a proxy for our population. This is nominally a reasonable thing to do, provided our sample size is reasonably large. However, we usually have a hard time calculating the actual quantities of interest from that pretend distribution. So, we have to estimate them, and this is why we draw lots of bootstrap samples. If we could.../... | |
| Apr 8, 2012 at 23:02 | comment | added | Peter Flom | Nice answer. I especially like the penultimate paragraph. | |
| Apr 8, 2012 at 22:39 | history | answered | conjugateprior | CC BY-SA 3.0 |