= Cyrus Samii
{c}
{tag=Mathematics author}
\b[Cyrus Samii] is a <political scientist> at New York University whose methodological work concerns quantitative field research and <causal inference>. His academic biography connects the design of <randomized controlled trials> to empirical social research.<Affiliations and Bio by Cyrus Samii>[Affiliations and Bio, methodology and field-research description]{ref}
\Image[https://cyrussamii.com/wp-content/uploads/2025/09/Samii-Cyrus-profile.jpg]
{title=Cyrus Samii}
{description=Portrait linked as cds_self from Samii's personal academic biography; served directly by the original website.}
{height=280}
With <Peter M. Aronow>, Samii studied <sampling designs> in which every unit can be observed but some pairs can never be observed together. The distinction matters: positive individual <inclusion probabilities> suffice for an <unbiased estimator> of a <finite population total>, whereas the usual <Horvitz-Thompson variance estimator> also needs <pairwise inclusion positivity>.<Conservative variance estimation for sampling designs with zero pairwise inclusion probabilities by Peter M. Aronow and Cyrus Samii>[Section2, conditions1–2 and Sections2.1–2.2, observable and unobservable cross-products]{ref}
An original two-unit example makes the <single-draw variance identifiability obstruction> explicit. Fix two unknown population values $y_1,y_2$ and choose one index $J$ with <probabilities> $1/2,1/2$. The <Horvitz-Thompson estimator> is $\widehat T=2y_J$, so
$$
\mathbb E_p\widehat T=y_1+y_2,
\qquad
\operatorname{Var}_p(\widehat T)=(y_1-y_2)^2.
$$
An <estimator> based only on the selected index and its observed value has <expected value> of the form $[a(y_1)+b(y_2)]/2$. Such an additive expression cannot equal $(y_1-y_2)^2$ for every pair of real values. Taking the mixed <finite difference> at $(0,0),(1,0),(0,1),(1,1)$ gives zero for the additive expression but
$$
0-1-1+0=-2
$$
for the desired <variance>. Thus a single draw permits an <unbiased estimator> of the total but no universally <unbiased estimator> of its <sampling variance>. Independent auxiliary randomization cannot repair this: averaging that randomness still gives functions $a$ and $b$ of the same observed data.
This is a restriction imposed by the observation mechanism, rather than a shortage of algebraic ingenuity. It motivates separating <design-based inference> about a total from the additional information needed to quantify its uncertainty.
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