muthu untro

1 files changed, 3 insertions, 3 deletions

diff --git a/intro.tex b/intro.tex
index 33ce910..e2835a8 100644
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@@ -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 $i$