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It looks from the comments the problem is that the variance at each site is large

In general, and you don't have enough samples to reduce the variance. So you're looking for ways to use approach of using additional measurements of other values (related) observations. This is a not the one you are interested in directly) was useful approachin many problems in the past, here so it sounds like a good idea in your case as well. Here are a few things to look at:

Binary classification

  • Another idea is

    This can be simple to try collaborative filteringsince there are packages readily available and there are not many parameters to tune. ThisI'd try using a classifier called SVM, basicallyit works well in many cases, can deal with limited training data (looks like that's an issue for you). Again, there are SVM packages available that you can download and just run (libsvm is one example, but there are many others).

    The disadvantage of this is that it may become resource-consuming if you want a classifier for each probe. Your input dimensionality is 250,000. A simple linear classifier needs roughly one number per dimension, so 250,000 numbers. If you need such a classifier for every probe, this will require 250,000^2 numbers total, which is a lot. There are ways to go around this, but that's one concern.

    Collaborative filtering

    Collaborative filtering basically allows you to predict the value of one item from the values of related items. Say you know that I liked two movies M1, M2, and disliked two others, M3 and M4. Using collaborative filtering, you can predict whether or not I will like a new movie M5. In your case, you are not doing a completely blind prediction for M5; you do have some (although very noisy) observation. So you would combine that observation with the prediction from other features. This might be simpler

    The advantage of this is that there is only one model (as opposed to implement if you are interested in multiple one classifier per probe). So this is easier to scale.

    One model would work something like this. It would group probes that are either all "same" or all "different" most of the time. In (These groups would be learned by the classifier approachmodel from training data.) Then, you'd need one classifier for given a new array, it would use these groups and data from other probes in each probe you want group to determine whether a group issame or different. If there are many such probes, you'll need again, "same" or "different". This question had a lot of classifiers. With link to what looked like an easy intro to collaborative filtering.

    The main disadvantage is, I'm not sure you may do with a single can find an implementation of the model you need for all probes togethermicroarrays online (or anywhere). You'd probably need to derive something suitable for your data, which is not difficult, but requires knowing what to do.

    Another disadvantage is, you'll probably need more training data for collaborative filtering to work.

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    It looks from the comments the problem is that the variance at each site is large, and you don't have enough samples to reduce the variance. So you're looking for ways to use additional (related) observations. This is a useful approach, here are few things to look at:

    • If the task is to determine whether a given probe is a 'match', you can just pose is at it as a binary classification problem. The input features to a classifier will be ALL the probes in the array. The classifier will determine automatically which of these are useful. If the variance at the target probe is actually small, it may decide to just look at that probe only. If other sites (probes) are helpful too, it may decide to look at them as well. Classifiers can automatically construct complex rules that take into account one or many probes, as needed.

    • Another idea is to try collaborative filtering. This, basically, allows you to predict the value of one item from the values of related items. Say you know that I liked two movies M1, M2, and disliked two others, M3 and M4. Using collaborative filtering, you can predict whether or not I will like a new movie M5. In your case, you are not doing a completely blind prediction for M5; you do have some (although very noisy) observation. So you would combine that observation with the prediction from other features. This might be simpler to implement if you are interested in multiple probes. In the classifier approach, you'd need one classifier for each probe you want to determine is same or different. If there are many such probes, you'll need a lot of classifiers. With collaborative filtering, you may do with a single model for all probes together.

    Note: neither of this will give a "significance score" (as in t-test, for example). You'll get a confidence value, but you won't be able to say that the findings are statistically significant with a certain confidence.
    show/hide this revision's text 2 added 960 characters in body

    It looks from the comments the problem is that the variance at each site is large, and you don't have enough samples to reduce the variance. So you're looking for ways to use additional (related) observations. This is a useful approach, here are few things to look at:*

    • If the task is to determine whether a given probe is a 'match', you can just pose is at a binary classification problem. The input features to a classifier will be ALL the probes in the array. The classifier will determine automatically which of these are useful. If the variance at the target probe is actually small, it may decide to just look at that probe only. If other sites (probes) are helpful too, it may decide to look at them as well. Classifiers can automatically construct complex rules that take into account one or many probes, as needed.

    • Another idea is to try collaborative filtering. This, basically, allows you to predict the value of one item from the values of related items. Say you know that I liked two movies M1, M2, and disliked two others, M3 and M4. Using collaborative filtering, you can predict whether or not I will like a new movie M5. In your case, you are not doing a completely blind prediction for M5; you do have some (although very noisy) observation. So you would combine that observation with the prediction from other features. This might be simpler to implement if you are interested in multiple probes. In the classifier approach, you'd need one classifier for each probe you want to determine is same or different. If there are many such probes, you'll need a lot of classifiers. With collaborative filtering, you may do with a single model for all probes together.
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