**Adaptive sampling** (also called response-adaptive designs) is where you adapt your selection criteria as the experiment progresses, based on preliminary results as they come in.

Adaptive sampling is especially important in medical research, where traditional sampling and research techniques may lead to ethical dilemmas and clinical trials that are not in the best interest of the patients involved. For example, traditional simple random sampling with a control group and an experimental group would lead to 50% of patients receiving a placebo, “treatment-as-usual“, or possibly no treatment at all. If a new drug looks like it could save lives, the better choice may be to place more patients into the experimental group. The usefulness of adaptive sampling isn’t limited to the medical fields: it is also useful in computer science, industrial research or applications, and many other fields.

As well as being ethically sound, response-adaptive designs also tend to be cheaper (Hardwick & Stout, 2017).

## Examples of Adaptive Sampling

One example is of a research project searching for gold in riverbeds in California. With no starting information on where gold is likely to be found, the researchers might begin by sampling river dust in a series of randomly chosen river locations spread out evenly throughout California. However, if a minuscule amount of gold was found in a river running through a certain valley from a certain mountain range, it would make sense to **change the sampling distribution** and run a larger proportion of samples in that area. This is adaptive sampling at its simplest.

Another example might be a study testing a new AIDS drug. In this blind study, volunteers might be placed randomly in either of two groups: the control group (taking a placebo), or the treatment group. Once the medicine begins to look promising, new participants could be added to the treatment group. You could also choose to divide this group into two sets, taking two different doses of the medicine. If the medicine seemed unpromising, the majority of new participants could be added to the placebo group.

## Adaptive Sampling Methodology

In standard sampling methods, you choose your whole sample before you even look at the data. In adaptive sampling, on the other hand, you stop part way through sampling and analyze/observe what you’ve recorded so far. Call your initial sample s_{1}, the initial values y_{s1}.

Now, choose the rest of the sample based on the data you’ve gathered. To do this, we want to choose data points that will minimize the mean squared error of the estimate given what you’ve observed so far. We can write this mathematically as

min *E* [ (Ẑ -Z )^{2} | s_{1}, y_{s1} ].

Here Z is the population quantity you’re measuring, and Ẑ is the estimate of that given your data. So E((Ẑ -Z )^{2} ) is the estimate’s error term.

Essentially, what you are doing is pinpointing the data points which gave you the most information. Then your future data selection is based on that information. Getting the min *E* [ (Ẑ -Z )^{2} | s_{1}, y_{s1} ] should give you optimal adaptive sampling. In real life research problems, we don’t generally achieve the optimal solution. However, we work to achieve practical, efficient adaptive sampling that gives us close to optimal results.

## References

Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.

Hardwick & Stout (2017). Adaptive Sampling Designs. Retrieved November 4, 2017 from: http://web.eecs.umich.edu/~qstout/AdaptSample.html

Thompson S. (1996). Adaptive Sampling. Wiley-Interscience.

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