Discussion of "Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal" by J. N. K. Rao

This comment emphasizes the importance of model checking and model fitting when making inferences about finite population quantities. It also suggests the value of using unit level models when making inferences for small subpopulations, that is, "small area" analyses [arXiv:1108.2356].Comment: Published in at http://dx.doi.org/10.1214/11-STS346B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Revenue Monotonicity in Combinatorial Auctions

Along with substantial progress made recently in designing near-optimal mechanisms for multi-item auctions, interesting structural questions have also been raised and studied. In particular, is it true that the seller can always extract more revenue from a market where the buyers value the items higher than another market? In this paper we obtain such a revenue monotonicity result in a general setting. Precisely, consider the revenue-maximizing combinatorial auction for $m$ items and $n$ buyers in the Bayesian setting, specified by a valuation function $v$ and a set $F$ of $nm$ independent item-type distributions. Let $REV(v, F)$ denote the maximum revenue achievable under $F$ by any incentive compatible mechanism. Intuitively, one would expect that $REV(v, G)\geq REV(v, F)$ if distribution $G$ stochastically dominates $F$. Surprisingly, Hart and Reny (2012) showed that this is not always true even for the simple case when $v$ is additive. A natural question arises: Are these deviations contained within bounds? To what extent may the monotonicity intuition still be valid? We present an {approximate monotonicity} theorem for the class of fractionally subadditive (XOS) valuation functions $v$, showing that $REV(v, G)\geq c\,REV(v, F)$ if $G$ stochastically dominates $F$ under $v$ where $c>0$ is a universal constant. Previously, approximate monotonicity was known only for the case $n=1$: Babaioff et al. (2014) for the class of additive valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation functions.Comment: 10 page

Optimal Auctions vs. Anonymous Pricing

For selling a single item to agents with independent but non-identically distributed values, the revenue optimal auction is complex. With respect to it, Hartline and Roughgarden (2009) showed that the approximation factor of the second-price auction with an anonymous reserve is between two and four. We consider the more demanding problem of approximating the revenue of the ex ante relaxation of the auction problem by posting an anonymous price (while supplies last) and prove that their worst-case ratio is e. As a corollary, the upper-bound of anonymous pricing or anonymous reserves versus the optimal auction improves from four to $e$. We conclude that, up to an $e$ factor, discrimination and simultaneity are unimportant for driving revenue in single-item auctions.Comment: 19 pages, 6 figures, To appear in 56th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2015

Do Market-Level Hospital and Physician Resources Affect Small Area Variation in Hospital Use?

This study evaluates the effect of market-level physician and hospital resources on hospital use. It is anticipated that higher hospital discharges are associated with (1) greater hospital and physician resources, (2) more differentiated hospital and physician resources, and (3) higher levels of teaching intensity in the community. Data on 14 modified diagnostically related groups (DRGs) and 58 hospital market communities in Michigan are analyzed during a 7-year period. Findings indicate that physician resources, hospital resources, differentiation of hospital and physician resources, and teaching intensity contribute only modestly to discharges, holding constant the socioeconomic attributes of the community and adjusting for the variation in hospital use over time. With the inclusion of hospital and physician resource variables, socioeconomic factors remain important determinants of the variation across market communities. Findings are discussed in terms of their implications for health care organizations, managed care programs, and cost control efforts in general.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68450/2/6.pd

Saturation of Spin-Polarized Current in Nanometer Scale Aluminum Grains

We describe measurements of spin-polarized tunnelling via discrete energy levels of single Aluminum grains. In high resistance samples ($\sim G\Omega$), the spin-polarized tunnelling current rapidly saturates as a function of the bias voltage. This indicates that spin-polarized current is carried only via the ground state and the few lowest in energy excited states of the grain. At the saturation voltage, the spin-relaxation rate $T_1^{-1}$ of the highest excited states is comparable to the electron tunnelling rate: $T_1^{-1}\approx 1.5\cdot 10^6 s^{-1}$ and $10^7s^{-1}$ in two samples. The ratio of $T_1^{-1}$ to the electron-phonon relaxation rate is in agreement with the Elliot-Yafet scaling, an evidence that spin-relaxation in Al grains is governed by the spin-orbit interaction.Comment: 5 pages, 4 figure

Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility

The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an e-approximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymous pricing for regular agents approximately extends to agents that satisfy this approximate regularity property. We apply this approximation framework to prove that anonymous pricing is a constant approximation to the revenue optimal single-item auction for agents with public-budget utility, private-budget utility, and (a special case of) risk-averse utility.Comment: Appeared at EC 201