I have the capacity to take samples on "n" days per year. I could take all the samples in the first "n" days, or I could spread them out in different ways over the interval. I am trying to think about how to describe that distribution so that I can focus on the best choices and describe that to others. I suspect that this is a common problem somewhere but I do not know the key words that might unlock the literature.
As you say, I would think "distribution" is the correct/key term, as in "samples were uniformly distributed throughout the sampling period", or "sample days followed a binomial distribution", or "the distribution of samples was arbitrary, and is shown graphically in Figure X", etc. etc.
if you are considering dispersion, also terms such as outliers or errors maybe useful
Dear Timothy,
your question is quite common, and it was widely discussed in 1970s-90s in experimental design planning. You can get some basic foundations from classical book Fedorov V. Theory of optimal experiments, New York, 1972. A bit more recent is Montgomery D. Design and analysis of experiments, 2013.
Hope it helps.
I would be surprised if this was a part of any standard book on experimental design. In most experimental designs we think of nice things like Gaussian distributions or Poisson. The distribution in this case can be unimodal, bimodal, or multimodal. I could have 3 observations early (Feb 3, 4, 5), three observations middle (Jul 6, 7, 8) and three observations late (Dec 22, 23, 24) for n=9. Describing this distribution as a mean (June 31) and a standard deviation of 139 days might (or might not) be the best description. Maybe mean + variance + skew + kurtosis and some measure of clumpedness or number of modes. Thank you Vladislav, I will look at the books. Awesome that they are both online. I liked the inclusion of mixture designs in the second book (though not relevant to my current issue).
I just found this, which seems like it is going in the right direction: https://repository.upenn.edu/cgi/viewcontent.cgi?article=1081&context=statistics_papers#:~:text=For%20a%20reasonable%20measure%20of,description%20of%20the%20measure%20dynamics.
Hi, Timothy,
if you want to get "best", or most informative, observations, I think you need to choose Fisher information matrix approach. And to optimize it with one of the various types of criteria: from statistical (like D-, A-, L-optimality, and others) to some special ones based, for instance, on cost of experiments, time expenses, and so on.
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