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It is argued that all model based approaches to the selection of covariates in linear regression have failed. This applies to frequentist approaches based on P-values and to Bayesian approaches although for different reasons. In the first part of the paper 13 model based procedures are compared to the model-free Gaussian covariate procedure in terms of the covariates selected and the time required. The comparison is based on seven data sets and three simulations. There is nothing special about these data sets which are often used as examples in the literature. All the model based procedures failed. In the second part of the paper it is argued that the cause of this failure is the very use of a model. If the model involves all the available covariates standard P-values can be used. The use of P-values in this situation is quite straightforward. As soon as the model specifies only some unknown subset of the covariates the problem being to identify this subset the situation changes radically. There are many P-values, they are dependent and most of them are invalid. The P-value based approach collapses. The Bayesian paradigm also assumes a correct model but although there are no conceptual problems with a large number of covariates there is a considerable overhead causing computational and allocation problems even for moderately sized data sets. The Gaussian covariate procedure is based on P-values which are defined as the probability that a random Gaussian covariate is better than the covariate being considered. These P-values are exact and valid whatever the situation. The allocation requirements and the algorithmic complexity are both linear in the size of the data making the procedure capable of handling large data sets. It outperforms all the other procedures in every respect.

This paper considers a single-cell massive MIMO (multiple-input multiple-output) system with dual-polarized antennas at both the base station and users. We study a channel model that takes into account several practical aspects that arise when utilizing dual-polarization, such as channel cross-polar discrimination (XPD) and cross-polar correlations (XPC) at the transmitter and receiver. We analyze uplink and downlink achievable spectral efficiencies (SE) with and without successive interference cancellation (SIC) for the linear minimum mean squared error (MMSE), zero-forcing (ZF), and maximum ratio (MR) combining/precoding schemes. In addition, we derive the statistical properties of the MMSE channel estimator for the dual-polarized channel model. These estimates are used to implement different precoding and combining schemes when the uplink and downlink SE expressions are calculated for the case. Closed-form uplink and downlink SE expressions for MR combining/precoding are derived. Based on these results, we also provide power control algorithms to maximize the uplink and downlink sum SEs. Moreover, we compare the SEs achieved in dual-polarized and uni-polarized setups numerically and evaluate the impact of XPD and XPC.

In this paper we investigate the problem of stochastic multi-armed bandits (MAB) in the (local) differential privacy (DP/LDP) model. Unlike previous results that assume bounded/sub-Gaussian reward distributions, we focus on the setting where each arm's reward distribution only has $(1+v)$-th moment with some $v\in (0, 1]$. In the first part, we study the problem in the central $\epsilon$-DP model. We first provide a near-optimal result by developing a private and robust Upper Confidence Bound (UCB) algorithm. Then, we improve the result via a private and robust version of the Successive Elimination (SE) algorithm. Finally, we establish the lower bound to show that the instance-dependent regret of our improved algorithm is optimal. In the second part, we study the problem in the $\epsilon$-LDP model. We propose an algorithm that can be seen as locally private and robust version of SE algorithm, which provably achieves (near) optimal rates for both instance-dependent and instance-independent regret. Our results reveal differences between the problem of private MAB with bounded/sub-Gaussian rewards and heavy-tailed rewards. To achieve these (near) optimal rates, we develop several new hard instances and private robust estimators as byproducts, which might be used to other related problems. Finally, experiments also support our theoretical findings and show the effectiveness of our algorithms.

Explicit knowledge of total community-level immune seroprevalence is critical to developing policies to mitigate the social and clinical impact of SARS-CoV-2. Publicly available vaccination data are frequently cited as a proxy for population immunity, but this metric ignores the effects of naturally-acquired immunity, which varies broadly throughout the country and world. Without broad or random sampling of the population, accurate measurement of persistent immunity post natural infection is generally unavailable. To enable tracking of both naturally-acquired and vaccine-induced immunity, we set up a synthetic random proxy based on routine hospital testing for estimating total Immunoglobulin G (IgG) prevalence in the sampled community. Our approach analyzes viral IgG testing data of asymptomatic patients who present for elective procedures within a hospital system. We apply multilevel regression and poststratification to adjust for demographic and geographic discrepancies between the sample and the community population. We then apply state-based vaccination data to categorize immune status as driven by natural infection or by vaccine. We have validated the model using verified clinical metrics of viral and symptomatic disease incidence to show the expected biological correlation of these entities with the timing, rate, and magnitude of seroprevalence. In mid-July 2021, the estimated immunity level was 74% with the administered vaccination rate of 45% in the two counties. The metric improves real-time understanding of immunity to COVID-19 as it evolves and the coordination of policy responses to the disease, toward an inexpensive and easily operational surveillance system that transcends the limits of vaccination datasets alone.

This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that will allow us to define numerical approximation methods in several dimensions adapted to discontinuities.

Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting of multiple contests. We study the tradeoff between two risks in this setting: (1) the threat of early clinch when the title has been clinched before the last contest(s) of the competition take place; (2) the danger of winning the competition without finishing first in any contest. In particular, four historical points scoring systems of the Formula One World Championship are compared with the family of geometric scoring rules, recently proposed by an axiomatic approach. The schemes used in practice are found to be competitive with respect to these goals, and the current rule seems to be a reasonable compromise close to the Pareto frontier. Our results shed more light on the evolution of the Formula One points scoring systems and contribute to the issue of choosing the set of point values.

Preferential sampling provides a formal modeling specification to capture the effect of bias in a set of sampling locations on inference when a geostatistical model is used to explain observed responses at the sampled locations. In particular, it enables modification of spatial prediction adjusted for the bias. Its original presentation in the literature addressed assessment of the presence of such sampling bias while follow on work focused on regression specification to improve spatial interpolation under such bias. All of the work in the literature to date considers the case of a univariate response variable at each location, either continuous or modeled through a latent continuous variable. The contribution here is to extend the notion of preferential sampling to the case of bivariate response at each location. This exposes sampling scenarios where both responses are observed at a given location as well as scenarios where, for some locations, only one of the responses is recorded. That is, there may be different sampling bias for one response than for the other. It leads to assessing the impact of such bias on co-kriging. It also exposes the possibility that preferential sampling can bias inference regarding dependence between responses at a location. We develop the idea of bivariate preferential sampling through various model specifications and illustrate the effect of these specifications on prediction and dependence behavior. We do this both through simulation examples as well as with a forestry dataset that provides mean diameter at breast height (MDBH) and trees per hectare (TPH) as the point-referenced bivariate responses.

Ensemble methods based on subsampling, such as random forests, are popular in applications due to their high predictive accuracy. Existing literature views a random forest prediction as an infinite-order incomplete U-statistic to quantify its uncertainty. However, these methods focus on a small subsampling size of each tree, which is theoretically valid but practically limited. This paper develops an unbiased variance estimator based on incomplete U-statistics, which allows the tree size to be comparable with the overall sample size, making statistical inference possible in a broader range of real applications. Simulation results demonstrate that our estimators enjoy lower bias and more accurate confidence interval coverage without additional computational costs. We also propose a local smoothing procedure to reduce the variation of our estimator, which shows improved numerical performance when the number of trees is relatively small. Further, we investigate the ratio consistency of our proposed variance estimator under specific scenarios. In particular, we develop a new "double U-statistic" formulation to analyze the Hoeffding decomposition of the estimator's variance.

In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of the data fitting in this formulation allows for reasonable assumptions to be made about the solution that can improve the computational performance further. In particular, we employ a well known dual formulation of this problem and solve the corresponding equations in a restricted domain. We present experimental results that explore the dependence of the solution on this restriction and quantify imrovements in the computational performance. This approach can be extended to analogous methods simply and could provide an efficient alternative for problems of this type.

Privacy is a major good for users of personalized services such as recommender systems. When applied to the field of health informatics, privacy concerns of users may be amplified, but the possible utility of such services is also high. Despite availability of technologies such as k-anonymity, differential privacy, privacy-aware recommendation, and personalized privacy trade-offs, little research has been conducted on the users' willingness to share health data for usage in such systems. In two conjoint-decision studies (sample size n=521), we investigate importance and utility of privacy-preserving techniques related to sharing of personal health data for k-anonymity and differential privacy. Users were asked to pick a preferred sharing scenario depending on the recipient of the data, the benefit of sharing data, the type of data, and the parameterized privacy. Users disagreed with sharing data for commercial purposes regarding mental illnesses and with high de-anonymization risks but showed little concern when data is used for scientific purposes and is related to physical illnesses. Suggestions for health recommender system development are derived from the findings.