Examinations of any experiment involving living organisms require justifications of the need and moral defensibleness of the study. Statistical planning, design and sample size calculation of the experiment are no less important review criteria than general medical and ethical points to consider. Errors made in the statistical planning and data evaluation phase can have severe consequences on both results and conclusions. They might proliferate and thus impact future trials-an unintended outcome of fundamental research with profound ethical consequences. Therefore, any trial must be efficient in both a medical and statistical way in answering the questions of interests to be considered as approvable. Unified statistical standards are currently missing for animal review boards in Germany. In order to accompany, we developed a biometric form to be filled and handed in with the proposal at the local authority on animal welfare. It addresses relevant points to consider for biostatistical planning of animal experiments and can help both the applicants and the reviewers in overseeing the entire experiment(s) planned. Furthermore, the form might also aid in meeting the current standards set by the 3+3R's principle of animal experimentation Replacement, Reduction, Refinement as well as Robustness, Registration and Reporting. The form has already been in use by the local authority of animal welfare in Berlin, Germany. In addition, we provide reference to our user guide giving more detailed explanation and examples for each section of the biometric form. Unifying the set of biostatistical aspects will help both the applicants and the reviewers to equal standards and increase quality of preclinical research projects, also for translational, multicenter, or international studies.
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Harnessing distributed computing environments to build scalable inference algorithms for very large data sets is a core challenge across the broad mathematical sciences. Here we provide a theoretical framework to do so along with fully implemented examples of scalable algorithms with performance guarantees. We begin by formalizing the class of statistics which admit straightforward calculation in such environments through independent parallelization. We then show how to use such statistics to approximate arbitrary functional operators, thereby providing practitioners with a generic approximate inference procedure that does not require data to reside entirely in memory. We characterize the $L^2$ approximation properties of our approach, and then use it to treat two canonical examples that arise in large-scale statistical analyses: sample quantile calculation and local polynomial regression. A variety of avenues and extensions remain open for future work.
We propose a general statistical mechanics framework for the collective motion of animals. The framework considers the principle of maximum entropy, the interaction, boundary, and desire effects, as well as the time-delay effect. These factors provide the ability to describe and solve dynamic and non-equilibrium problems under this framework. We show that the Vicsek model, the social force model, and some of their variants can be considered special cases of this framework. Furthermore, this framework can be extended to the maximum caliber setting. We demonstrate the potential of this framework for model comparisons and parameter estimations by applying the model to observed data from a field study of the emergent behavior of termites. Finally, we demonstrate the flexibility of the framework by simulating some collective moving phenomena for birds and ants.
Approximate message passing (AMP) is a promising technique for unknown signal reconstruction of certain high-dimensional linear systems with non-Gaussian signaling. A distinguished feature of the AMP-type algorithms is that their dynamics can be rigorously described by state evolution. However, state evolution does not necessarily guarantee the convergence of iterative algorithms. To solve the convergence problem of AMP-type algorithms in principle, this paper proposes a memory AMP (MAMP) under a sufficient statistic condition, named sufficient statistic MAMP (SS-MAMP). We show that the covariance matrices of SS-MAMP are L-banded and convergent. Given an arbitrary MAMP, we can construct an SS-MAMP by damping, which not only ensures the convergence of MAMP but also preserves the orthogonality of MAMP, i.e., its dynamics can be rigorously described by state evolution. As a byproduct, we prove that the Bayes-optimal orthogonal/vector AMP (BO-OAMP/VAMP) is an SS-MAMP. As a result, we reveal two interesting properties of BO-OAMP/VAMP for large systems: 1) the covariance matrices are L-banded and are convergent in BO-OAMP/VAMP, and 2) damping and memory are useless (i.e., do not bring performance improvement) in BO-OAMP/VAMP. As an example, we construct a sufficient statistic Bayes-optimal MAMP (BO-MAMP), which is Bayes optimal if its state evolution has a unique fixed point and its MSE is not worse than the original BO-MAMP. Finally, simulations are provided to verify the validity and accuracy of the theoretical results.
We propose two-stage and sequential procedures to construct prescribed proportional closeness confidence intervals for the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative-binomial experiment having the same p
Research in the past few decades has discussed the concept of "spatial confounding" but has provided conflicting definitions and proposed solutions, some of which do not address the issue of confounding as it is understood in the field of causal inference. We give a clear account of spatial confounding as the existence of an unmeasured confounding variable with a spatial structure. Under certain conditions, including the smoothness of the confounder as a function of space, we show that spatial covariates (e.g., latitude and longitude) can be handled as typical covariates by algorithms popular in causal inference. We focus on "double machine learning" (DML) by which flexible models are fit for both the exposure and outcome variables to arrive at a causal estimator with favorable convergence properties. These models avoid restrictive assumptions, such as linearity and heterogeneity, which are present in linear models typically employed in spatial statistics and which can lead to strong bias when violated. We demonstrate the advantages of the DML approach analytically and via extensive simulation studies.
Airports have been constantly evolving and adopting digital technologies to improve operational efficiency, enhance passenger experience, generate ancillary revenues and boost capacity from existing infrastructure. The COVID-19 pandemic has also challenged airports and aviation stakeholders alike to adapt and manage new operational challenges such as facilitating a contactless travel experience and ensuring business continuity. Digitalisation using Industry 4.0 technologies offers opportunities for airports to address short-term challenges associated with the COVID-19 pandemic while also preparing for future long-term challenges that ensue the crisis. Through a systematic literature review of 102 relevant articles, we discuss the current state of adoption of Industry 4.0 technologies in airports, the associated challenges as well as future research directions. The results of this review suggest that the implementation of Industry 4.0 technologies is slowly gaining traction within the airport environment, and shall continue to remain relevant in the digital transformation journeys in developing future airports.
The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesise finite element models with observed data. Through embedding uncertainty inside of the governing equations, finite element solutions are updated to give a posterior distribution which quantifies all sources of uncertainty associated with the model. However to incorporate all sources of uncertainty, one must integrate over the uncertainty associated with the model parameters, the known forward problem of uncertainty quantification. In this paper, we make use of Langevin dynamics to solve the statFEM forward problem, studying the utility of the unadjusted Langevin algorithm (ULA), a Metropolis-free Markov chain Monte Carlo sampler, to build a sample-based characterisation of this otherwise intractable measure. Due to the structure of the statFEM problem, these methods are able to solve the forward problem without explicit full PDE solves, requiring only sparse matrix-vector products. ULA is also gradient-based, and hence provides a scalable approach up to high degrees-of-freedom. Leveraging the theory behind Langevin-based samplers, we provide theoretical guarantees on sampler performance, demonstrating convergence, for both the prior and posterior, in the Kullback-Leibler divergence, and, in Wasserstein-2, with further results on the effect of preconditioning. Numerical experiments are also provided, for both the prior and posterior, to demonstrate the efficacy of the sampler, with a Python package also included.
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
This manuscript surveys reinforcement learning from the perspective of optimization and control with a focus on continuous control applications. It surveys the general formulation, terminology, and typical experimental implementations of reinforcement learning and reviews competing solution paradigms. In order to compare the relative merits of various techniques, this survey presents a case study of the Linear Quadratic Regulator (LQR) with unknown dynamics, perhaps the simplest and best studied problem in optimal control. The manuscript describes how merging techniques from learning theory and control can provide non-asymptotic characterizations of LQR performance and shows that these characterizations tend to match experimental behavior. In turn, when revisiting more complex applications, many of the observed phenomena in LQR persist. In particular, theory and experiment demonstrate the role and importance of models and the cost of generality in reinforcement learning algorithms. This survey concludes with a discussion of some of the challenges in designing learning systems that safely and reliably interact with complex and uncertain environments and how tools from reinforcement learning and controls might be combined to approach these challenges.
Like any large software system, a full-fledged DBMS offers an overwhelming amount of configuration knobs. These range from static initialisation parameters like buffer sizes, degree of concurrency, or level of replication to complex runtime decisions like creating a secondary index on a particular column or reorganising the physical layout of the store. To simplify the configuration, industry grade DBMSs are usually shipped with various advisory tools, that provide recommendations for given workloads and machines. However, reality shows that the actual configuration, tuning, and maintenance is usually still done by a human administrator, relying on intuition and experience. Recent work on deep reinforcement learning has shown very promising results in solving problems, that require such a sense of intuition. For instance, it has been applied very successfully in learning how to play complicated games with enormous search spaces. Motivated by these achievements, in this work we explore how deep reinforcement learning can be used to administer a DBMS. First, we will describe how deep reinforcement learning can be used to automatically tune an arbitrary software system like a DBMS by defining a problem environment. Second, we showcase our concept of NoDBA at the concrete example of index selection and evaluate how well it recommends indexes for given workloads.
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