Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the combined test, especially in high-dimensional models considering composite hypotheses tests. We derive a mathematical framework to study standard {meta-analysis} testing approaches in the context of the many normal means model, which serves as the platform to investigate more complex models. We introduce a natural and mild restriction on the meta-level combination functions of the local trials. This allows us to mathematically quantify the cost of compressing $m$ trials into real-valued test statistics and combining these. We then derive minimax lower and matching upper bounds for the separation rates of standard combination methods for e.g. p-values and e-values, quantifying the loss relative to using the full, pooled data. We observe an elbow effect, revealing that in certain cases combining the locally optimal tests in each trial results in a sub-optimal {meta-analysis} method and develop approaches to achieve the global optima. We also explore the possible gains of allowing limited coordination between the trial designs. Our results connect meta-analysis with bandwidth constraint distributed inference and build on recent information theoretic developments in the latter field.
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In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for the arithmetic mean on the original scale of measurement. Central to the approach is a general variance-covariance function, derived by assuming multiplicative measurement error. Quasi-likelihood analysis of logit models for composition is then a general alternative to the use of multivariate linear models for log-ratio transformed measurements, and it has important advantages. These include robustness to secondary aspects of model specification, stability when there are zero-valued or near-zero measurements in the data, and more direct interpretation. The usual efficiency property of quasi-likelihood estimation applies even when the error covariance matrix is unspecified. We also indicate how the derived variance-covariance function can be used, instead of the variance-covariance matrix of log-ratios, with more general multivariate methods for the analysis of composition. A specific feature is that the notion of `null correlation' -- for compositional measurements on their original scale -- emerges naturally.
This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the condition of a stroke patient, which justifies adopting a linearized version of the complete electrode model as the forward model. The algorithm is based on finding a (locally) A-optimal measurement configuration via gradient descent with respect to the electrode positions. The efficient computation of the needed derivatives of the complete electrode model is one of the focal points. Two algorithms are introduced and numerically tested on a three-layer head model. The first one assumes a region of interest and a Gaussian prior for the conductivity in the brain, and it can be run offline, i.e., prior to taking any measurements. The second algorithm first computes a reconstruction of the conductivity anomaly caused by the stroke with an initial electrode configuration by combining lagged diffusivity iteration with sequential linearizations, which can be interpreted to produce an approximate Gaussian probability density for the conductivity perturbation. It then resorts to the first algorithm to find new, more informative positions for the available electrodes with the constructed density as the prior.
We study hypothesis testing under communication constraints, where each sample is quantized before being revealed to a statistician. Without communication constraints, it is well known that the sample complexity of simple binary hypothesis testing is characterized by the Hellinger distance between the distributions. We show that the sample complexity of simple binary hypothesis testing under communication constraints is at most a logarithmic factor larger than in the unconstrained setting and this bound is tight. We develop a polynomial-time algorithm that achieves the aforementioned sample complexity. Our framework extends to robust hypothesis testing, where the distributions are corrupted in the total variation distance. Our proofs rely on a new reverse data processing inequality and a reverse Markov inequality, which may be of independent interest. For simple $M$-ary hypothesis testing, the sample complexity in the absence of communication constraints has a logarithmic dependence on $M$. We show that communication constraints can cause an exponential blow-up leading to $\Omega(M)$ sample complexity even for adaptive algorithms.
Due to their cost, experiments for inertial confinement fusion (ICF) heavily rely on numerical simulations to guide design. As simulation technology progresses, so too can the fidelity of models used to plan for new experiments. However, these high-fidelity models are by themselves insufficient for optimal experimental design, because their computational cost remains too high to efficiently and effectively explore the numerous parameters required to describe a typical experiment. Traditionally, ICF design has relied on low-fidelity modeling to initially identify potentially interesting design regions, which are then subsequently explored via selected high-fidelity modeling. In this paper, we demonstrate that this two-step approach can be insufficient: even for simple design problems, a two-step optimization strategy can lead high-fidelity searching towards incorrect regions and consequently waste computational resources on parameter regimes far away from the true optimal solution. We reveal that a primary cause of this behavior in ICF design problems is the presence of low-fidelity optima in distinct regions of the parameter space from high-fidelity optima. To address this issue, we propose an iterative multifidelity Bayesian optimization method based on Gaussian Process Regression that leverages both low- and high-fidelity modelings. We demonstrate, using both two- and eight-dimensional ICF test problems, that our algorithm can effectively utilize low-fidelity modeling for exploration, while automatically refining promising designs with high-fidelity models. This approach proves to be more efficient than relying solely on high-fidelity modeling for optimization.
Spatial data can come in a variety of different forms, but two of the most common generating models for such observations are random fields and point processes. Whilst it is known that spectral analysis can unify these two different data forms, specific methodology for the related estimation is yet to be developed. In this paper, we solve this problem by extending multitaper estimation, to estimate the spectral density matrix function for multivariate spatial data, where processes can be any combination of either point processes or random fields. We discuss finite sample and asymptotic theory for the proposed estimators, as well as specific details on the implementation, including how to perform estimation on non-rectangular domains and the correct implementation of multitapering for processes sampled in different ways, e.g. continuously vs on a regular grid.
In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In particular, under certain causal conditions, this parameter corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose-response curve. We propose a debiased local linear estimator of the covariate-adjusted regression function, and demonstrate that our estimator converges pointwise to a mean-zero normal limit distribution. We use this result to construct asymptotically valid confidence intervals for function values and differences thereof. In addition, we use approximation results for the distribution of the supremum of an empirical process to construct asymptotically valid uniform confidence bands. Our methods do not require undersmoothing, permit the use of data-adaptive estimators of nuisance functions, and our estimator attains the optimal rate of convergence for a twice differentiable function. We illustrate the practical performance of our estimator using numerical studies and an analysis of the effect of air pollution exposure on cardiovascular mortality.
This paper proposes a specialized autonomous driving system that takes into account the unique constraints and characteristics of automotive systems, aiming for innovative advancements in autonomous driving technology. The proposed system systematically analyzes the intricate data flow in autonomous driving and provides functionality to dynamically adjust various factors that influence deep learning models. Additionally, for algorithms that do not rely on deep learning models, the system analyzes the flow to determine resource allocation priorities. In essence, the system optimizes data flow and schedules efficiently to ensure real-time performance and safety. The proposed system was implemented in actual autonomous vehicles and experimentally validated across various driving scenarios. The experimental results provide evidence of the system's stable inference and effective control of autonomous vehicles, marking a significant turning point in the development of autonomous driving systems.
With the proliferation of ever more complicated Deep Learning architectures, data synthesis is a highly promising technique to address the demand of data-hungry models. However, reliably assessing the quality of a 'synthesiser' model's output is an open research question with significant associated risks for high-stake domains. To address this challenge, we have designed a unique confident data synthesis algorithm that introduces statistical confidence guarantees through a novel extension of the Conformal Prediction framework. We support our proposed algorithm with theoretical proofs and an extensive empirical evaluation of five benchmark datasets. To show our approach's versatility on ubiquitous real-world challenges, the datasets were carefully selected for their variety of difficult characteristics: low sample count, class imbalance and non-separability, and privacy-sensitive data. In all trials, training sets extended with our confident synthesised data performed at least as well as the original, and frequently significantly improved Deep Learning performance by up to +65% F1-score.
Diverse studies have analyzed the quality of automatically generated test cases by using test smells as the main quality attribute. But recent work reported that generated tests may suffer a number of quality issues not necessarily considered in previous studies. Little is known about these issues and their frequency within generated tests. In this paper, we report on a manual analysis of an external dataset consisting of 2,340 automatically generated tests. This analysis aimed at detecting new quality issues, not covered by past recognized test smells. We use thematic analysis to group and categorize the new quality issues found. As a result, we propose a taxonomy of 13 new quality issues grouped in four categories. We also report on the frequency of these new quality issues within the dataset and present eight recommendations that test generators may consider to improve the quality and usefulness of the automatically generated tests.
Modeling excess remains to be an important topic in insurance data modeling. Among the alternatives of modeling excess, the Peaks Over Threshold (POT) framework with Generalized Pareto distribution (GPD) is regarded as an efficient approach due to its flexibility. However, the selection of an appropriate threshold for such framework is a major difficulty. To address such difficulty, we applied several accumulation tests along with Anderson-Darling test to determine an optimal threshold. Based on the selected thresholds, the fitted GPD with the estimated quantiles can be found. We applied the procedure to the well-known Norwegian Fire Insurance data and constructed the confidence intervals for the Value-at-Risks (VaR). The accumulation test approach provides satisfactory performance in modeling the high quantiles of Norwegian Fire Insurance data compared to the previous graphical methods.
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