From 4c6565a07b271974056dd2babd08ee26d82be1ef Mon Sep 17 00:00:00 2001 From: Stratis Ioannidis Date: Sun, 4 Nov 2012 23:38:51 -0800 Subject: muthu untro --- intro.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'intro.tex') diff --git a/intro.tex b/intro.tex index 33ce910..e2835a8 100644 --- a/intro.tex +++ b/intro.tex @@ -5,13 +5,13 @@ known to the experimenter. \E\ wishes to perform an experiment that measures a certain inherent property of the subjects: the outcome for a subject $i$ is denoted $y_i$, which is unknown to \E\ before the experiment is performed. Typically, \E\ has a hypothesis of the relationship between $x_i$'s and $y_i$'s, such as, say linear, \emph{i.e.}, $y_i \approx \T{\beta} x_i$; conducting the experiments and obtaining the measurements $y_i$ lets \E\ derive an estimate $\beta$. %The goal of experimental design amounts to determining which subjects to experiment upon to produce the best possible such estimate. -The above experimental design scenario above has many applications, from medical testing to marketing research and others. -There is a rich literature about various estimation, as well as for means for quantifying the quality of the produced estimate \cite{pukelsheim2006optimal}. There is also an extensive theory on how to select subjects +The above experimental design scenario has many applications, from medical testing to marketing research and others. +There is a rich literature about estimation procedures, as well as for means for quantifying the quality of the produced estimate \cite{pukelsheim2006optimal}. There is also an extensive theory on how to select subjects if \E\ can conduct only a limited number of experiments, so the estimation process returns $\beta$ that approximates the true parameter of the underlying population \cite{ginebra2007measure,le1996comparison,chaloner1995bayesian,boyd2004convex}. We depart from this classical set up by viewing experimental design in a strategic setting, and by studying mechanism design issues. -In our setup, experiments cannot be manipulated and hence measurements are considered precise.\footnote{Thus, the experiments of our interest are statistically significant, ones where each experiment provides a reliable outcome.} However, there +In our setup, experiments cannot be manipulated and hence measurements are considered precise.\footnote{Thus, the experiments of our interest are statistically significant ones where each experiment provides a reliable outcome.} However, there is a cost $c_i$ associated with experimenting on subject $i$ which varies from subject to subject. This may be viewed as the cost subject $i$ incurs when tested, and hence $i$ needs to be reimbursed; or, it might be viewed as the incentive for $i$ -- cgit v1.2.3-70-g09d2