Statistics

This is likely beyond the power level of this board anon.

Where did you pull that stochastic process from, it's fluctuating as fuck (no closeness conditions on the increments from t to t+du)

What do you really compute when you integrate over the value of the function of u, not the probability density function of u? Or Is that really a cdf?

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238KB, 500x557px

>>8634179
Why not do your own homework?

>>8634224
t = {1,2,3,...}
Marginal density of u1 and u2 is

integral from 1 to 0 of 1*sin(pi*u1*t)du

>>8634227
B/c I don't the answer?

>>8634247
>Marginal density of u1
But the pdf of u is
f(u)=1
and other than that there is not pdf involved, why a the marginal density computed by evaluating some function of u (the sin expression).

Also, as far as I can see, the value at t=5 isn't correlated with the one at t=4 any more than it's correlated with the one at t=2, right? For each t, you sample anew.

>>8634266
I think I calculated the Cov function wrong, as I got a non-zero value.

I meant X1 and X2 not u1 u2 in >>8634247
apologizes. I think the mistake is in the Cov != 0 though as that makes sense. Thanks mate.

>>8634278
Although if g is some function (like the sin), then you can compute the pdf for g(X) form the one for X.
https://en.wikipedia.org/wiki/Probability_density_function#Dependent_variables_and_change_of_variables

Probably you don't need that for this example, though.

>>8634179
Is this a statistics general?

hi /sci/ I am a statistics/machine learning pleb and this is my first time so pls be nice.

I have ~300 patients and gene expression values for ~19000 genes and a groundtruth file that has the "time to progression (of cancer)", "time observed" for each patient, with about 20% of the "time to progression" missing.

I've gathered that the basic approach should be along the lines of: feature select, make a generalized linear model, make a cox regression

So I took all my data, did LASSO (from what I understand, some bastardized step-wise regression). then I split my data into a training set and test set (80% train, 20% test, with the labels being a boolean vector indicating if the cancer progressed or if it's censored) and I applied the weights I got from LASSO to "feature select" on my X_train and X_test data.

Then I did a Cox Regression on the transformed training set and the associated "progression times" , and generated lifetime estimates on my test set.

First thing I noticed: There seem to be two values that the lifetime estimates take, not a range of values. So I have a few questions:

1) How can I incorporate the time observed into the survival analysis? If a patient lasted 1200 days without progressing, (average is like 600 days), how do I make use of that information? Right now it treats a censored value for someone who was observed for 10 days the same as the 1200 one. I have some sloppy ideas like artificially coming up with a progression time, but I was hoping there was a more rigorous way

2) I know if I fit the Cox regression to all of my data, I feel like I would be introducing some bias because I used the data to feature select. I know about the concept of nested cross-validation and all — but what I want to do is fit it to all the data, (anticipating another binary split of the data), and explore both of those to try and see if I can find distinguishing features within the subsets to increase specificity

>>8634717
sorry for the long post, I can clarify some unclear things if need be

if anyone has suggestions as to approaches I ought to take, that would also be appreciated.

oh, and in addition to gene expression data, I have data of the same dimensions with the relative difference of the gene expression b/t tumor and normal tissue for each gene for each patient (some NaNs) and another one for mutations, filled with 1s and 0s indicating mutations or not. I chose to proceed with just the expression data because the literature seems to get far using just microarray data (a picture/heat-mappish version of my raw numbers), and I am still searching the literature to see how those numbers might be appropriately incorporated

any other advice or help would be appreciated too

thanks guys

>>8634717

/sci/ is a lot slower than what you might be expecting.

You probably should make your own thread if you want to get a response.

>>8634767
will do, thanks anon!