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A Test for Shared Patterns in Cross-modal Brain Activation Analysis

Determining the extent to which different cognitive modalities (understood here as the set of cognitive processes underlying the elaboration of a stimulus by the brain) rely on overlapping neural representations is a fundamental issue in cognitive neuroscience. In the last decade, the identification of shared activity patterns has been mostly framed as a supervised learning problem. For instance, a classifier is trained to discriminate categories (e.g. faces vs. houses) in modality I (e.g. perception) and tested on the same categories in modality II (e.g. imagery). This type of analysis is often referred to as cross-modal decoding. In this paper we take a different approach and instead formulate the problem of assessing shared patterns across modalities within the framework of statistical hypothesis testing. We propose both an appropriate test statistic and a scheme based on permutation testing to compute the significance of this test while making only minimal distributional assumption. We denote this test cross-modal permutation test (CMPT). We also provide empirical evidence on synthetic datasets that our approach has greater statistical power than the cross-modal decoding method while maintaining low Type I errors (rejecting a true null hypothesis). We compare both approaches on an fMRI dataset with three different cognitive modalities (perception, imagery, visual search). Finally, we show how CMPT can be combined with Searchlight analysis to explore spatial distribution of shared activity patterns.

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A Bayesian Statistics Course for Undergraduates: Bayesian Thinking, Computing, and Research

We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern Bayesian computing techniques not only for implementing Bayesian methods, but also to deepen students' understanding of the methods. Collaborative case studies further enrich students' learning and provide experience to solve open-ended applied problems. The course has an emphasis on undergraduate research, where accessible academic journal articles are read, discussed, and critiqued in class. With increased confidence and familiarity, students take the challenge of reading, implementing, and sometimes extending methods in journal articles for their course projects.

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\texttt{code::proof}: Prepare for \emph{most} weather conditions

Computational tools for data analysis are being released daily on repositories such as the Comprehensive R Archive Network. How we integrate these tools to solve a problem in research is increasingly complex and requiring frequent updates. To mitigate these \emph{Kafkaesque} computational challenges in research, this manuscript proposes \emph{toolchain walkthrough}, an opinionated documentation of a scientific workflow. As a practical complement to our proof-based argument~(Gray and Marwick, arXiv, 2019) for reproducible data analysis, here we focus on the practicality of setting up a reproducible research compendia, with unit tests, as a measure of \texttt{code::proof}, confidence in computational algorithms.

stat.OT↗

Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper Scoring Rules

In recent years, probabilistic forecasting is an emerging topic, which is why there is a growing need of suitable methods for the evaluation of multivariate predictions. We analyze the sensitivity of the most common scoring rules, especially regarding quality of the forecasted dependency structures. Additionally, we propose scoring rules based on the copula, which uniquely describes the dependency structure for every probability distribution with continuous marginal distributions. Efficient estimation of the considered scoring rules and evaluation methods such as the Diebold-Mariano test are discussed. In detailed simulation studies, we compare the performance of the renowned scoring rules and the ones we propose. Besides extended synthetic studies based on recently published results we also consider a real data example. We find that the energy score, which is probably the most widely used multivariate scoring rule, performs comparably well in detecting forecast errors, also regarding dependencies. This contradicts other studies. The results also show that a proposed copula score provides very strong distinction between models with correct and incorrect dependency structure. We close with a comprehensive discussion on the proposed methodology.

stat.ME↗

Improved error rates for sparse (group) learning with Lipschitz loss functions

We study a family of sparse estimators defined as minimizers of some empirical Lipschitz loss function -- which include the hinge loss, the logistic loss and the quantile regression loss -- with a convex, sparse or group-sparse regularization. In particular, we consider the L1 norm on the coefficients, its sorted Slope version, and the Group L1-L2 extension. We propose a new theoretical framework that uses common assumptions in the literature to simultaneously derive new high-dimensional L2 estimation upper bounds for all three regularization schemes. %, and to improve over existing results. For L1 and Slope regularizations, our bounds scale as $(k^*/n) \log(p/k^*)$ -- $n\times p$ is the size of the design matrix and $k^*$ the dimension of the theoretical loss minimizer $\Bβ^*$ -- and match the optimal minimax rate achieved for the least-squares case. For Group L1-L2 regularization, our bounds scale as $(s^*/n) \log\left( G / s^* \right) + m^* / n$ -- $G$ is the total number of groups and $m^*$ the number of coefficients in the $s^*$ groups which contain $\Bβ^*$ -- and improve over the least-squares case. We show that, when the signal is strongly group-sparse, Group L1-L2 is superior to L1 and Slope. In addition, we adapt our approach to the sub-Gaussian linear regression framework and reach the optimal minimax rate for Lasso, and an improved rate for Group-Lasso. Finally, we release an accelerated proximal algorithm that computes the nine main convex estimators of interest when the number of variables is of the order of $100,000s$.

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Incomplete Reparameterizations and Equivalent Metrics

Reparameterizing a probabilisitic system is common advice for improving the performance of a statistical algorithm like Markov chain Monte Carlo, even though in theory such reparameterizations should leave the system, and the performance of any algorithm, invariant. In this paper I show how the reparameterizations common in practice are only incomplete reparameterizations which result in different interactions between a target probabilistic system and a given algorithm. I then consider how these changing interactions manifest in the context of Markov chain Monte Carlo algorithms defined on Riemannian manifolds. In particular I show how any incomplete reparameterization is equivalent to modifying the metric geometry directly.

stat.OT↗

baymedr: An R Package and Web Application for the Calculation of Bayes Factors for Superiority, Equivalence, and Non-Inferiority Designs

Clinical trials often seek to determine the superiority, equivalence, or non-inferiority of an experimental condition (e.g., a new drug) compared to a control condition (e.g., a placebo or an already existing drug). The use of frequentist statistical methods to analyze data for these types of designs is ubiquitous even though they have several limitations. Bayesian inference remedies many of these shortcomings and allows for intuitive interpretations. In this article, we outline the frequentist conceptualization of superiority, equivalence, and non-inferiority designs and discuss its disadvantages. Subsequently, we explain how Bayes factors can be used to compare the relative plausibility of competing hypotheses. We present baymedr, an R package and web application, that provides user-friendly tools for the computation of Bayes factors for superiority, equivalence, and non-inferiority designs. Instructions on how to use baymedr are provided and an example illustrates how already existing results can be reanalyzed with baymedr.

stat.OT↗

Jump balls, rating falls, and elite status: A sensitivity analysis of three quarterback rating statistics

Quarterback performance can be difficult to rank, and much effort has been spent in creating new rating systems. However, the input statistics for such ratings are subject to randomness and factors outside the quarterback's control. To investigate this variance, we perform a sensitivity analysis of three quarterback rating statistics: the Traditional 1971 rating by Smith, the Burke, and the Wages of Wins ratings. The comparisons are made at the team level for the 32 NFL teams from 2002-2015, thus giving each case an even 16 games. We compute quarterback ratings for each offense with 1-5 additional touchdowns, 1-5 fewer interceptions, 1-5 additional sacks, and a 1-5 percent increase in the passing completion rate. Our sensitivity analysis provides insight into whether an elite passing team could seem mediocre or vice versa based on random outcomes. The results indicate that the Traditional rating is the most sensitive statistic with respect to touchdowns, interceptions, and completions, whereas the Burke rating is most sensitive to sacks. The analysis suggests that team passing offense rankings are highly sensitive to aspects of football that are out of the quarterback's hands (e.g., deflected passes that lead to interceptions). Thus, on the margins, we show arguments about whether a specific quarterback has entered the elite or remains mediocre are irrelevant.

stat.OT↗

Multivariate Time-Between-Events Monitoring -- An overview and some (overlooked) underlying complexities

We review methods for monitoring multivariate time-between-events (TBE) data. We present some underlying complexities that have been overlooked in the literature. It is helpful to classify multivariate TBE monitoring applications into two fundamentally different scenarios. One scenario involves monitoring individual vectors of TBE data. The other involves the monitoring of several, possibly correlated, temporal point processes in which events could occur at different rates. We discuss performance measures and advise the use of time-between-signal based metrics for the design and comparison of methods. We re-evaluate an existing multivariate TBE monitoring method, offer some advice and some directions for future research.

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Machine Learning for high speed channel optimization

Design of printed circuit board (PCB) stack-up requires the consideration of characteristic impedance, insertion loss and crosstalk. As there are many parameters in a PCB stack-up design, the optimization of these parameters needs to be efficient and accurate. A less optimal stack-up would lead to expensive PCB material choices in high speed designs. In this paper, an efficient global optimization method using parallel and intelligent Bayesian optimization is proposed for the stripline design.

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Item Response Theory based Ensemble in Machine Learning

In this article, we propose a novel probabilistic framework to improve the accuracy of a weighted majority voting algorithm. In order to assign higher weights to the classifiers which can correctly classify hard-to-classify instances, we introduce the Item Response Theory (IRT) framework to evaluate the samples' difficulty and classifiers' ability simultaneously. Three models are created with different assumptions suitable for different cases. When making an inference, we keep a balance between the accuracy and complexity. In our experiment, all the base models are constructed by single trees via bootstrap. To explain the models, we illustrate how the IRT ensemble model constructs the classifying boundary. We also compare their performance with other widely used methods and show that our model performs well on 19 datasets.

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Online detection of cascading change-points

We propose an online detection procedure for cascading failures in the network from sequential data, which can be modeled as multiple correlated change-points happening during a short period. We consider a temporal diffusion network model to capture the temporal dynamic structure of multiple change-points and develop a sequential Shewhart procedure based on the generalized likelihood ratio statistics based on the diffusion network model assuming unknown post-change distribution parameters. We also tackle the computational complexity posed by the unknown propagation. Numerical experiments demonstrate the good performance for detecting cascade failures.

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Sharp hypotheses and bispatial inference

A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for example, be the value that indicates the absence of an effect. Standard ways of tackling problems of this type, including the Bayesian method, are often highly inadequate in practice. To address this issue, an inferential framework called bispatial inference is put forward, which can be viewed as both a generalisation and radical reinterpretation of existing approaches to inference that are based on P values. It is shown that to obtain an appropriate post-data density function for a given parameter, it is often convenient to combine a special type of bispatial inference, which is constructed around one-sided P values, with a previously outlined form of fiducial inference. Finally, by using what are called post-data opinion curves, this bispatial-fiducial theory is naturally extended to deal with the general scenario in which any number of parameters may be unknown. The application of the theory is illustrated in various examples, which are especially relevant to the analysis of clinical trial data.

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The Scenario Culture

Scenario Analysis is a risk assessment tool that aims to evaluate the impact of a small number of distinct plausible future scenarios. In this paper, we provide an overview of important aspects of Scenario Analysis including when it is appropriate, the design of scenarios, uncertainty and encouraging creativity. Each of these issues is discussed in the context of climate, energy and legal scenarios.

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Inference for Synthetic Control Methods with Multiple Treated Units

Although the Synthetic Control Method (SCM) is now widely applied, its most commonly-used inference method, placebo test, is often problematic, especially when the treatment is not uniquely assigned. This paper discuss the problems with the placebo test under multivariate treatment case. And, to improve the power of inferences, I further propose an Andrews-type procedure as it potentially solve some drawbacks of placebo test. Simulations are conducted to show the Andrews' test is often valid and powerful, compared with the placebo test.

stat.ME↗

The limits of the sample spiked eigenvalues for a high-dimensional generalized Fisher matrix and its applications

A generalized spiked Fisher matrix is considered in this paper. We establish a criterion for the description of the support of the limiting spectral distribution of high-dimensional generalized Fisher matrix and study the almost sure limits of the sample spiked eigenvalues where the population covariance matrices are arbitrary which successively removed an unrealistic condition posed in the previous works, that is, the covariance matrices are assumed to be diagonal or diagonal block-wise structure. In addition, we also give a consistent estimator of the population spiked eigenvalues. A series of simulations are conducted that support the theoretical results and illustrate the accuracy of our estimators.

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Variable selection for transportability

Transportability provides a principled framework to address the problem of applying study results to new populations. Here, we consider the problem of selecting variables to include in transport estimators. We provide a brief overview of the transportability framework and illustrate that while selection diagrams are a vital first step in variable selection, these graphs alone identify a sufficient but not strictly necessary set of variables for generating an unbiased transport estimate. Next, we conduct a simulation experiment assessing the impact of including unnecessary variables on the performance of the parametric g-computation transport estimator. Our results highlight that the types of variables included can affect the bias, variance, and mean squared error of the estimates. We find that addition of variables that are not causes of the outcome but whose distributions differ between the source and target populations can increase the variance and mean squared error of the transported estimates. On the other hand, inclusion of variables that are causes of the outcome (regardless of whether they modify the causal contrast of interest or differ in distribution between the populations) reduces the variance of the estimates without increasing the bias. Finally, exclusion of variables that cause the outcome but do not modify the causal contrast of interest does not increase bias. These findings suggest that variable selection approaches for transport should prioritize identifying and including all causes of the outcome in the study population rather than focusing on variables whose distribution may differ between the study sample and target population.

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Parametric mode regression for bounded responses

We propose new parametric frameworks of regression analysis with the conditional mode of a bounded response as the focal point of interest. Covariate effects estimation and prediction based on the maximum likelihood method under two new classes of regression models are demonstrated. We also develop graphical and numerical diagnostic tools to detect various sources of model misspecification. Predictions based on different central tendency measures inferred using various regression models are compared using synthetic data in simulations. Finally, we conduct regression analysis for data from the Alzheimer's Disease Neuroimaging Initiative to demonstrate practical implementation of the proposed methods. Supplementary materials that contain technical details, and additional simulation and data analysis results are available online.

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