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We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…

This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…

In this paper, we first describe the generalized notion of Cramer-Rao lower bound obtained by Naudts (2004) using two families of probability density functions, the original model and an escort model. We reinterpret the results in Naudts…

This representative study of German search engine users (N=1,000) focuses on the ability of users to distinguish between organic results and advertisements on Google results pages. We combine questions about Google's business with…

Evaluating the incremental return on ad spend (iROAS) of a prospective online marketing strategy (i.e., the ratio of the strategy's causal effect on some response metric of interest relative to its causal effect on the ad spend) has become…

We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe. We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a…

We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…

We introduce a chance constrained optimization model for the fulfillment of guaranteed display Internet advertising campaigns. The proposed formulation for the allocation of display inventory takes into account the uncertainty of the supply…

Google's Ad Settings shows the gender and age that Google has inferred about a web user. We compare the inferred values to the self-reported values of 501 survey participants. We find that Google often does not show an inference, but when…

This paper studies the measurement of advertising effects on online platforms when parallel experimentation occurs, that is, when multiple advertisers experiment concurrently. It provides a framework that makes precise how parallel…

The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously…

Several current ultra-wide band applications, such as millimeter wave radar and communication systems, require high sampling rates and therefore expensive and energy-hungry analogto-digital converters (ADCs). In applications where cost and…

In this lecture note, we show a general property of the Cramer-Rao bound (CRB) that quantifies the interdependencies between the parameters in a vector. The presented result is valid for more general models than the additive noise model and…

We consider a causal inference problem frequently encountered in online advertising systems, where a publisher (e.g., Instagram, TikTok) interacts repeatedly with human users and advertisers by sporadically displaying to each user an…

In classical causal inference, inferring cause-effect relations from data relies on the assumption that units are independent and identically distributed. This assumption is violated in settings where units are related through a network of…

In computational advertising, a challenging problem is how to recommend the bid for advertisers to achieve the best return on investment (ROI) given budget constraint. This paper presents a bid recommendation scenario that discovers the…

Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…

Before A/B testing online a new version of a recommender system, it is usual to perform some offline evaluations on historical data. We focus on evaluation methods that compute an estimator of the potential uplift in revenue that could…

Precision and accuracy, as two crucial criteria for quantum metrology, have previously lacked rigorous definitions and distinctions. In this paper, we provide a unified definition of precision and accuracy from the perspective of…

Many results in the quantum metrology literature use the Cram\'er-Rao bound and the Fisher information to compare different quantum estimation strategies. However, there are several assumptions that go into the construction of these tools,…