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max = i;
mu = x;
}
}
return
max;
}
This technique is known as Thompson Sampling, and it can be extended
to any distribution. For example, using the average value rather than the
conversion rate might be modeled by using an exponential distribution
instead of the beta distribution. The sampling procedure is still the same; it
simplyusesthelargestpayoutsampledfromthedistribution ratherthanthe
largest conversion value. For the most part, these values are easily updated
and allow the optimization of the website design to be conducted in real
time.
After using a basic estimate, the next logical step is to use a model rather
than simply using the empirical value for each design. It might be the case
thatdifferentpopulationsofusersresponddifferentlytoeachdesign.Inthat
case, being able to predict an average value or a conversion rate using one of
the models discussed earlier in this chapter enables the optimizer to choose
the best design for each user to maximize the return for the site.
Conclusion
The techniques in this chapter are by no means the only approaches to
solving problems such as forecasting, anomaly detection, and optimization.
Entire topics could and have been written on both the general topics and
the specific techniques covered in this chapter. Additionally, the techniques
presentedhereremainactiveareasofacademicandindustrialresearch;new
refinements and approaches are being developed all the time. The goal for
this chapter was to provide a brief introduction into the approaches to give
practitioners some grounding in their use and a basis of comparison for
other techniques.
With that, it is also important to remember that even the simplest
techniques can yield good results. It is often better to use the simplest
method that could possibly work across a number of different problems
before returning to the original problem to further optimize the approach.
In many cases, going from 50 percent of optimal to 80 percent of optimal
