arXiv subjects

Yosef Rinott

Publications and source records attributed to Yosef Rinott.

At least 19 recordsLinked to original sources

arXiv2025

Anchoring-Based Causal Design (ABCD): Estimating the Effects of Beliefs

A central challenge in any study of the effects of beliefs on outcomes, such as decisions and behavior, is the risk of omitted variables bias. Omitted variables, frequently unmeasured or even unknown, can induce correlations between beliefs and decisions that are not genuinely causal, in which case the omitted variables are referred to as confounders. To address the challenge of causal inference, researchers frequently rely on information provision experiments to randomly manipulate beliefs. The information supplied in these experiments can serve as an instrumental variable (IV), enabling causal inference, so long as it influences decisions exclusively through its impact on beliefs. However, providing varying information to participants to shape their beliefs can raise both methodological and ethical concerns. Methodological concerns arise from potential violations of the exclusion restriction assumption. Such violations may stem from information source effects, when attitudes toward the source affect the outcome decision directly, thereby introducing a confounder. An ethical concern arises from manipulating the provided information, as it may involve deceiving participants. This paper proposes and empirically demonstrates a new method for treating beliefs and estimating their effects, the Anchoring-Based Causal Design (ABCD), which avoids deception and source influences. ABCD combines the cognitive mechanism known as anchoring with instrumental variable (IV) estimation. Instead of providing substantive information, the method employs a deliberately non-informative procedure in which participants compare their self-assessment of a concept to a randomly assigned anchor value. We present the method and the results of eight experiments demonstrating its application, strengths, and limitations. We conclude by discussing the potential of this design for advancing experimental social science.

econ.GN↗

arXiv2024

Random Circuit Sampling: Fourier Expansion and Statistics

Considerable effort in experimental quantum computing is devoted to noisy intermediate scale quantum computers (NISQ computers). Understanding the effect of noise is important for various aspects of this endeavor including notable claims for achieving quantum supremacy and attempts to demonstrate quantum error correcting codes. In this paper we use Fourier methods combined with statistical analysis to study the effect of noise. In particular, we use Fourier analysis to refine the linear cross-entropy fidelity estimator. We use both analytical methods and simulations to study the effect of readout and gate errors, and we use our analysis to study the samples of Google's 2019 quantum supremacy experiment.

quant-ph↗

arXiv2024

Surgery duration prediction using multi-task feature selection

Efficient optimization of operating room (OR) activity poses a significant challenge for hospital managers due to the complex and risky nature of the environment. The traditional "one size fits all" approach to OR scheduling is no longer practical, and personalized medicine is required to meet the diverse needs of patients, care providers, medical procedures, and system constraints within limited resources. This paper aims to introduce a scientific and practical tool for predicting surgery durations and improving OR performance for maximum benefit to patients and the hospital. Previous works used machine-learning models for surgery duration prediction based on preoperative data. The models consider covariates known to the medical staff at the time of scheduling the surgery. Given a large number of covariates, model selection becomes crucial, and the number of covariates used for prediction depends on the available sample size. Our proposed approach utilizes multi-task regression to select a common subset of predicting covariates for all tasks with the same sample size while allowing the model's coefficients to vary between them. A regression task can refer to a single surgeon or operation type or the interaction between them. By considering these diverse factors, our method provides an overall more accurate estimation of the surgery durations, and the selected covariates that enter the model may help to identify the resources required for a specific surgery. We found that when the regression tasks were surgeon-based or based on the pair of operation type and surgeon, our suggested approach outperformed the compared baseline suggested in a previous study. However, our approach failed to reach the baseline for an operation-type-based task.

stat.AP↗

arXiv2023

Questions and Concerns About Google's Quantum Supremacy Claim

In October 2019, Nature published a paper [6] describing an experimental work that was performed at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer. Since then we have been involved in a long-term project to study various statistical aspects of the Google experiment. In [30] we studied Google's statistical framework that we found to be very sound and offered some technical improvements. This document describes three main concerns (based on statistical analysis) about the Google 2019 experiment. The first concern is that the data do not agree with Google's noise model (or any other specific model). The second concern is that a crucial simple formula for a priori estimation of the fidelity seems to involve an unexpected independence assumption, and yet it gives very accurate predictions. The third concern is about statistical properties of the calibration process.

quant-ph↗

arXiv2023

Google's Quantum Supremacy Claim: Data, Documentation, and Discussion

In October 2019, Nature published a paper describing an experiment that took place at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer. Since September 2019 we have been involved in a long-term project to study various statistical aspects of the Google experiment. We have been trying to gather the relevant data and information in order to reconstruct and verify those parts of the Google experiment that are based on classical computations (except when the required computation is too heavy), and to perform a statistical analysis on the data. This document describes the available data and information for the Google experiment, some main questions in the evaluation of the experiment, and some of our results and plans.

quant-ph↗

arXiv2022

Posterior Probabilities: Dominance and Optimism

The Bayesian posterior probability of the true state is stochastically dominated by that same posterior under the probability law of the true state. This generalizes to notions of "optimism" about posterior probabilities.

econ.TH↗

arXiv2022

Posterior Probabilities: Nonmonotonicity, Asymptotic Rates, Log-Concavity, and Turán's Inequality

In the standard Bayesian framework data are assumed to be generated by a distribution parametrized by $θ$ in a parameter space $Θ$, over which a prior distribution $π$ is given. A Bayesian statistician quantifies the belief that the true parameter is $θ_{0}$ in $Θ$ by its posterior probability given the observed data. We investigate the behavior of the posterior belief in $θ_{0}$ when the data are generated under some parameter $θ_{1},$ which may or may not be the same as $θ_{0}.$ Starting from stochastic orders, specifically, likelihood ratio dominance, that obtain for resulting distributions of posteriors, we consider monotonicity properties of the posterior probabilities as a function of the sample size when data arrive sequentially. While the $θ_{0}$-posterior is monotonically increasing (i.e., it is a submartingale) when the data are generated under that same $θ_{0}$, it need not be monotonically decreasing in general, not even in terms of its overall expectation, when the data are generated under a different $θ_{1}.$ In fact, it may keep going up and down many times, even in simple cases such as iid coin tosses. We obtain precise asymptotic rates when the data come from the wide class of exponential families of distributions; these rates imply in particular that the expectation of the $θ_{0}$-posterior under $θ_{1}\neqθ_{0}$ is eventually strictly decreasing. Finally, we show that in a number of interesting cases this expectation is a log-concave function of the sample size, and thus unimodal. In the Bernoulli case we obtain this by developing an inequality that is related to Turán's inequality for Legendre polynomials.

math.ST↗

arXiv2022

On Tournaments and Negative Dependence

Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations, the rate of increase of the maximum, and more. In the study of probability models of tournaments, negative dependence of participants' outcomes arises naturally with application to various asymptotic results. In particular, the property of negative orthant dependence was proved in several articles for different tournament models, with a special proof for each model. In this note we unify these results by proving a stronger property, negative association, a generalization leading to a very simple proof. We also present a natural example of a knockout tournament where the scores are negatively orthant dependent but not negatively associated. The proof requires a new result on a preservation property of negative orthant dependence that is of independent interest.

math.PR↗

arXiv2022

Optimal designs for the development of personalized treatment rules

We study the design of multi-armed parallel group clinical trials to estimate personalized treatment rules that identify the best treatment for a given patient with given covariates. Assuming that the outcomes in each treatment arm are given by a homoscedastic linear model, with possibly different variances between treatment arms, and that the trial subjects form a random sample from an unselected overall population, we optimize the (possibly randomized) treatment allocation allowing the allocation rates to depend on the covariates. We find that, for the case of two treatments, the approximately optimal allocation rule does not depend on the value of the covariates but only on the variances of the responses. In contrast, for the case of three treatments or more, the optimal treatment allocation does depend on the values of the covariates as well as the true regression coefficients. The methods are illustrated with a recently published dietary clinical trial.

math.ST↗

arXiv2021

A procedure for multiple testing of partial conjunction hypotheses based on a hazard rate inequality

The partial conjunction null hypothesis is tested in order to discover a signal that is present in multiple studies. The standard approach of carrying out a multiple test procedure on the partial conjunction (PC) $p$-values can be extremely conservative. We suggest alleviating this conservativeness, by eliminating many of the conservative PC $p$-values prior to the application of a multiple test procedure. This leads to the following two step procedure: first, select the set with PC $p$-values below a selection threshold; second, within the selected set only, apply a family-wise error rate or false discovery rate controlling procedure on the conditional PC $p$-values. The conditional PC $p$-values are valid if the null p-values are uniform and the combining method is Fisher. The proof of their validity is based on a novel inequality in hazard rate order of partial sums of order statistics which may be of independent interest. We also provide the conditions for which the false discovery rate controlling procedures considered will be below the nominal level. We demonstrate the potential usefulness of our novel method, CoFilter (conditional testing after filtering), for analyzing multiple genome wide association studies of Crohn's disease.

stat.ME↗

arXiv2021

Adjusting Queries to Statistical Procedures Under Differential Privacy

We consider a dataset $S$ held by an agency, and a vector query of interest, $f(S) \in \mathbb{R}^k$, to be posed by an analyst, which contains the information required for certain planned statistical inference. The agency releases the requested vector query with noise that guarantees a given level of Differential Privacy -- DP$(\varepsilon,δ)$ -- using the well-known Gaussian mechanism. The analyst can choose to pose the vector query $f(S)$ or to adjust it by a suitable transformation that can make the agency's response more informative. For any given level of privacy DP$(\varepsilon,δ)$ decided by the agency, we study natural situations where the analyst can achieve better statistical inference by adjusting the query with a suitable simple explicit transformation.

cs.CR↗

arXiv2021

Optimal selection of sample-size dependent common subsets of covariates for multi-task regression prediction

An analyst is given a training set consisting of regression datasets $D_j$ of different sizes, which are distributed according to some $G_j$, $j=1,\ldots,\cal J$, where the distributions $G_j$ are assumed to form a random sample generated by some common source. In particular, the $D_j$'s have a common set of covariates and they are all labeled. The training set is used by the analyst for selection of subsets of covariates denoted by ${P}^*(n)$, whose role is described next. The multi-task problem we consider is as follows: given a number of random labeled datasets (which may be in the training set or not) $D_{J_k}$ of size $n_k$, $k=1,\ldots,K$, estimate separately for each dataset the regression coefficients on the subset of covariates ${P}^*(n_k)$ and then predict future dependent variables given their covariates. Naturally, a large sample size $n_k$ of $D_{J_k}$ allows a larger subset of covariates, and the dependence of the size of the selected covariate subsets on $n_k$ is needed in order to achieve good prediction and avoid overfitting. Subset selection is notoriously difficult and computationally demanding, and requires large samples; using all the regression datasets in the training set together amounts to borrowing strength toward better selection under suitable assumptions. Furthermore, using common subsets for all regressions having a given sample size standardizes and simplifies the data collection and avoids having to select and use a different subset for each prediction task. Our approach is efficient when the relevant covariates for prediction are common to the different regressions, while the models' coefficients may vary between different regressions.

math.ST↗

arXiv2021

Statistical Aspects of the Quantum Supremacy Demonstration

The notable claim of quantum supremacy presented by Google's team in 2019 consists of demonstrating the ability of a quantum circuit to generate, albeit with considerable noise, bitstrings from a distribution that is considered hard to simulate on classical computers. Verifying that the generated data is indeed from the claimed distribution and assessing the circuit's noise level and its fidelity is a purely statistical undertaking. The objective of this paper is to explain the relations between quantum computing and some of the statistical aspects involved in demonstrating quantum supremacy in terms that are accessible to statisticians, computer scientists, and mathematicians. Starting with the statistical analysis in Google's demonstration, which we explain, we study various estimators of the fidelity, and different approaches to testing the distributions generated by the quantum computer. We propose different noise models, and discuss their implications. A preliminary study of the Google data, focusing mostly on circuits of 12 and 14 qubits is discussed throughout the paper.

quant-ph↗

arXiv2018

A BKR operation for events occurring for disjoint reasons with high probability

Given events $A$ and $B$ on a product space $S=\prod_{i=1}^n S_i$, the set $A \Box B$ consists of all vectors ${\bf x}=(x_1,\ldots,x_n) \in S$ for which there exist disjoint coordinate subsets $K$ and $L$ of $\{1,\ldots,n\}$ such that given the coordinates $x_i, i \in K$ one has that ${\bf x} \in A$ regardless of the values of ${\bf x}$ on the remaining coordinates, and likewise that ${\bf x} \in B$ given the coordinates {$x_j, j \in L$}. For a finite product of discrete spaces endowed with a product measure, the BKR inequality $$ P(A \Box B) \le P(A)P(B) \quad (1) $$ was conjectured by van den Berg and Kesten [3] and proved by Reimer [13]. In [7] inequality (1) was extended to general product probability spaces, replacing $A \Box B$ by the set $A \Box_{11} B$ consisting of those outcomes ${\bf x}$ which only assure with probability one that ${\bf x} \in A$ and ${\bf x} \in B$ based only on the revealed coordinates in $K$ and $L$ as above. A strengthening of the original BKR inequality (1) results, due to the fact that $A \Box B \subseteq A \Box_{11} B$. In particular, it may be the case that $A \Box B$ is empty, while $A \Box_{11} B$ is not. We propose the further extension $A \Box_{st} B$ depending on probability thresholds $s$ and $t$, where $A \Box_{11} B$ is the special case where both $s$ and $t$ take the value one. The outcomes ${\bf x}$ in $A \Box_{st} B$ are those for which disjoint sets of coordinates $K$ and $L$ exist such that given the values of $\bf x$ on the revealed set of coordinates $K$, the probability that $A$ occurs is at least $s$, and given the coordinates of $\bf x$ in $L$, the probability of $B$ is at least $t$. We provide simple examples that illustrate the utility of these extensions.

math.PR↗

arXiv2015

Functional van den Berg-Kesten-Reimer Inequalities and their Duals, with Applications

The BKR inequality conjectured by van den Berg and Kesten in [11], and proved by Reimer in [8], states that for $A$ and $B$ events on $S$, a finite product of finite sets $S_i,i=1,\ldots,n$, and $P$ any product measure on $S$, $$ P(A \Box B) \le P(A)P(B),$$ where the set $A \Box B$ consists of the elementary events which lie in both $A$ and $B$ for `disjoint reasons.' Precisely, with ${\bf n}:=\{1,\ldots,n\}$ and $K \subset {\bf n}$, for ${\bf x} \in S$ letting $[{\bf x}]_K=\{{\bf y} \in S: y_i = x_i, i \in K\}$, the set $A \Box B$ consists of all ${\bf x} \in S$ for which there exist disjoint subsets $K$ and $L$ of ${\bf n}$ for which $[{\bf x}]_K \subset A$ and $[{\bf x}]_L \subset B$. The BKR inequality is extended to the following functional version on a general finite product measure space $(S,\mathbb{S})$ with product probability measure $P$, $$E\left\{ \max_{\stackrel{K \cap L = \emptyset}{K \subset {\bf n}, L \subset {\bf n}}} \underline{f}_K({\bf X})\underline{g}_L({\bf X})\right\} \leq E\left\{f({\bf X})\right\}\,E\left\{g({\bf X})\right\},$$ where $f$ and $g$ are non-negative measurable functions, $\underline{f}_K({\bf x}) = {\rm ess} \inf_{{\bf y} \in [{\bf x}]_K}f({\bf y})$ and $\underline{g}_L({\bf x}) = {\rm ess} \inf_{{\bf y} \in [{\bf x}]_L}g({\bf y}).$ The original BKR inequality is recovered by taking $f({\bf x})={\bf 1}_A({\bf x})$ and $g({\bf x})={\bf 1}_B({\bf x})$, and applying the fact that in general ${\bf 1}_{A \Box B} \le \max_{K \cap L = \emptyset} \underline{f}_K({\bf x}) \underline{g}_L({\bf x})$. Related formulations, and functional versions of the dual inequality on events by Kahn, Saks, and Smyth [6], are also considered. Applications include order statistics, assignment problems, and paths in random graphs.

math.PR↗

arXiv2012

A Colonel Blotto Gladiator Game

We consider a stochastic version of the well-known Blotto game, called the gladiator game. In this zero-sum allocation game two teams of gladiators engage in a sequence of one-to-one fights in which the probability of winning is a function of the gladiators' strengths. Each team's strategy consists of the allocation of its total strength among its gladiators. We find the Nash equilibria and the value of this class of games and show how they depend on the total strength of teams and the number of gladiators in each team. To do this, we study interesting majorization-type probability inequalities concerning linear combinations of Gamma random variables. Similar inequalities have been used in models of telecommunications and research and development.

cs.GT↗

arXiv2011

Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators

We compare estimators of the (essential) supremum and the integral of a function $f$ defined on a measurable space when $f$ may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their levels of stratification of the domain, with the result that more refined stratification is better with respect to different criteria. The emphasis is on criteria related to stochastic orders. For example, rather than compare estimators of the integral of $f$ by their variances (for unbiased estimators), or mean square error, we attempt the stronger comparison of convex order when possible. For the supremum, the criterion is based on the stochastic order of estimators.

math.ST↗

arXiv2011

Are adaptive allocation designs beneficial for improving power in binary response trials?

We consider the classical problem of selecting the best of two treatments in clinical trials with binary response. The target is to find the design that maximizes the power of the relevant test. Many papers use a normal approximation to the power function and claim that Neyman allocation that assigns subjects to treatment groups according to the ratio of the responses' standard deviations, should be used. As the standard deviations are unknown, an adaptive design is often recommended. The asymptotic justification of this approach is arguable, since it uses the normal approximation in tails where the error in the approximation is larger than the estimated quantity. We consider two different approaches for optimality of designs that are related to Pitman and Bahadur definitions of relative efficiency of tests. We prove that the optimal allocation according to the Pitman criterion is the balanced allocation and that the optimal allocation according to the Bahadur approach depends on the unknown parameters. Exact calculations reveal that the optimal allocation according to Bahadur is often close to the balanced design, and the powers of both are comparable to the Neyman allocation for small sample sizes and are generally better for large experiments. Our findings have important implications to the design of experiments, as the balanced design is proved to be optimal or close to optimal and the need for the complications involved in following an adaptive design for the purpose of increasing the power of tests is therefore questionable.

math.ST↗