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This paper proposes Bayesian Adaptive Trials (BAT) as both an efficient method to conduct trials and a unifying framework for evaluation social policy interventions, addressing limitations inherent in traditional methods such as Randomized Controlled Trials (RCT). Recognizing the crucial need for evidence-based approaches in public policy, the proposal aims to lower barriers to the adoption of evidence-based methods and align evaluation processes more closely with the dynamic nature of policy cycles. BATs, grounded in decision theory, offer a dynamic, ``learning as we go'' approach, enabling the integration of diverse information types and facilitating a continuous, iterative process of policy evaluation. BATs' adaptive nature is particularly advantageous in policy settings, allowing for more timely and context-sensitive decisions. Moreover, BATs' ability to value potential future information sources positions it as an optimal strategy for sequential data acquisition during policy implementation. While acknowledging the assumptions and models intrinsic to BATs, such as prior distributions and likelihood functions, the paper argues that these are advantageous for decision-makers in social policy, effectively merging the best features of various methodologies.

Quantum computers promise to surpass the most powerful classical supercomputers when it comes to solving many critically important practical problems, such as pharmaceutical and fertilizer design, supply chain and traffic optimization, or optimization for machine learning tasks. Because quantum computers function fundamentally differently from classical computers, the emergence of quantum computing technology will lead to a new evolutionary branch of statistical and data analytics methodologies. This review provides an introduction to quantum computing designed to be accessible to statisticians and data scientists, aiming to equip them with an overarching framework of quantum computing, the basic language and building blocks of quantum algorithms, and an overview of existing quantum applications in statistics and data analysis. Our goal is to enable statisticians and data scientists to follow quantum computing literature relevant to their fields, to collaborate with quantum algorithm designers, and, ultimately, to bring forth the next generation of statistical and data analytics tools., Comment: 2nd version: 1) fixed typos; 2) added two sections on "Birds-Eye View of Quantum Theory" and "Programming Quantum Computers"

Variational Bayes (VB) is a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning. The natural gradient is an essential component of efficient VB estimation, but it is prohibitively computationally expensive in high dimensions. We propose a computationally efficient regression-based method for natural gradient estimation, with convergence guarantees under standard assumptions. The method enables the use of quantum matrix inversion to further speed up VB. We demonstrate that the problem setup fulfills the conditions required for quantum matrix inversion to deliver computational efficiency. The method works with a broad range of statistical models and does not require special-purpose or simplified variational distributions.

We use time-dependent Hartree Fock approximation to study the collective mode spectra of nu=2 quantum Hall bilayers in tilted magnetic field allowing for charge imbalance as well as tunneling between the two layers. In a previous companion paper to this work, we studied the zero temperature global phase diagram of this system which was found to include a symmetric and ferromagnetic phases as well as a first order transition between two canted phases with spontaneously broken U(1) symmetry. We further found that this first order transition line ends in a quantum critical point within the canted region. In the current work, we study the excitation spectra of all of these phases and pay particular attention to the behavior of the collective modes near the phase transitions. We find, most interestingly, that the first order transition between the two canted phases is signaled by a near softening of a magnetoroton minimum. Many of the collective mode features explored here should be accessible experimentally in light scattering experiments.

We consider a bilayer quantum Hall system at total filling fraction nu=2 in tilted magnetic field allowing for charge imbalance as well as tunneling between the two layers. Using an "unrestricted Hartree Fock," previously discussed by Burkov and MacDonald (Phys Rev B 66 115323 2002), we examine the zero temperature global phase diagrams that would be accessed experimentally by changing the in-plane field and the bias voltage between the layers while keeping the tunneling between the two layers fixed. In accordance with previous work, we find symmetric and ferromagnetic phases as well as a first order transition between two canted phases with spontaneously broken U(1) symmetry. We find that these two canted phases are topologically connected in the phase diagram and, reminiscent of a first order liquid-gas transition, the first order transition line between these two phases ends in a quantum critical point. We develop a physical picture of these two phases and describe in detail the physics of the transition.

There is growing experimental and theoretical evidence that very clean two dimensional electron systems form unidirectional charge density waves (UCDW) or ``striped'' states at low temperatures and at Landau level filling fractions of the form nu = M + x with 4 < M < 10 an integer and 0.4 < x < 0.6. Following previous work, we model the striped state using a Hartree-Fock approach. We construct the low energy excitations of the system by making smooth deformations of the stripe edges analogous to the construction of edge state excitations of quantum Hall droplets. These low energy excitations are described as a coupled Luttinger liquid theory, as discussed previously by MacDonald and Fisher (PRB61 5724 2000). Here, we extend that work and explicitly derive all of the parameters of this low energy theory using a Hartree Fock approach. We also make contact with the equivalent low energy hydrodynamic approach of Fogler and Vinokur (PRL84 5828 2000) and similarly derive the parameters of this theory. As examples of the use of these results, we explicitly calculate the low-energy excitation spectrum and study tunneling into the striped state., Comment: RevTex, 14 pages, 4 figures (minor corrections)