BridgePRS leverages shared genetic effects across ancestries to increase polygenic risk score portability

Here we present BridgePRS, a novel Bayesian polygenic risk score (PRS) method that leverages shared genetic effects across ancestries to increase PRS portability. We evaluate BridgePRS via simulations and real UK Biobank data across 19 traits in individuals of African, South Asian and East Asian ancestry, using both UK Biobank and Biobank Japan genome-wide association study summary statistics; out-of-cohort validation is performed in the Mount Sinai (New York) BioMe biobank. BridgePRS is compared with the leading alternative, PRS-CSx, and two other PRS methods. Simulations suggest that the performance of BridgePRS relative to PRS-CSx increases as uncertainty increases: with lower trait heritability, higher polygenicity and greater between-population genetic diversity; and when causal variants are not present in the data. In real data, BridgePRS has a 61% larger average R2 than PRS-CSx in out-of-cohort prediction of African ancestry samples in BioMe (P = 6 × 10-5). BridgePRS is a computationally efficient, user-friendly and powerful approach for PRS analyses in non-European ancestries.

Sparse Bayesian Learning for End-to-End EEG Decoding

Decoding brain activity from non-invasive electroencephalography (EEG) is crucial for brain-computer interfaces (BCIs) and the study of brain disorders. Notably, end-to-end EEG decoding has gained widespread popularity in recent years owing to the remarkable advances in deep learning research. However, many EEG studies suffer from limited sample sizes, making it difficult for existing deep learning models to effectively generalize to highly noisy EEG data. To address this fundamental limitation, this paper proposes a novel end-to-end EEG decoding algorithm that utilizes a low-rank weight matrix to encode both spatio-temporal filters and the classifier, all optimized under a principled sparse Bayesian learning (SBL) framework. Importantly, this SBL framework also enables us to learn hyperparameters that optimally penalize the model in a Bayesian fashion. The proposed decoding algorithm is systematically benchmarked on five motor imagery BCI EEG datasets ( N=192) and an emotion recognition EEG dataset ( N=45), in comparison with several contemporary algorithms, including end-to-end deep-learning-based EEG decoding algorithms. The classification results demonstrate that our algorithm significantly outperforms the competing algorithms while yielding neurophysiologically meaningful spatio-temporal patterns. Our algorithm therefore advances the state-of-the-art by providing a novel EEG-tailored machine learning tool for decoding brain activity.

Assessment of generalised Bayesian structural equation models for continuous and binary data

The paper proposes a novel model assessment paradigm aiming to address shortcoming of posterior predictivep -values, which provide the default metric of fit for Bayesian structural equation modelling (BSEM). The model framework presented in the paper focuses on the approximate zero approach (Psychological Methods, 17, 2012, 313), which involves formulating certain parameters (such as factor loadings) to be approximately zero through the use of informative priors, instead of explicitly setting them to zero. The introduced model assessment procedure monitors the out-of-sample predictive performance of the fitted model, and together with a list of guidelines we provide, one can investigate whether the hypothesised model is supported by the data. We incorporate scoring rules and cross-validation to supplement existing model assessment metrics for BSEM. The proposed tools can be applied to models for both continuous and binary data. The modelling of categorical and non-normally distributed continuous data is facilitated with the introduction of an item-individual random effect. We study the performance of the proposed methodology via simulation experiments as well as real data on the 'Big-5' personality scale and the Fagerstrom test for nicotine dependence.

HPOSS: A hierarchical portfolio optimization stacking strategy to reduce the generalization error of ensembles of models

Surrogate models are frequently used to replace costly engineering simulations. A single surrogate is frequently chosen based on previous experience or by fitting multiple surrogates and selecting one based on mean cross-validation errors. A novel stacking strategy will be presented in this paper. This new strategy results from reinterpreting the model selection process based on the generalization error. For the first time, this problem is proposed to be translated into a well-studied financial problem: portfolio management and optimization. In short, it is demonstrated that the individual residues calculated by leave-one-out procedures are samples from a given random variable ϵi, whose second non-central moment is the i-th model's generalization error. Thus, a stacking methodology based solely on evaluating the behavior of the linear combination of the random variables ϵi is proposed. At first, several surrogate models are calibrated. The Directed Bubble Hierarchical Tree (DBHT) clustering algorithm is then used to determine which models are worth stacking. The stacking weights can be calculated using any financial approach to the portfolio optimization problem. This alternative understanding of the problem enables practitioners to use established financial methodologies to calculate the models' weights, significantly improving the ensemble of models' out-of-sample performance. A study case is carried out to demonstrate the applicability of the new methodology. Overall, a total of 124 models were trained using a specific dataset: 40 Machine Learning models and 84 Polynomial Chaos Expansion models (which considered 3 types of base random variables, 7 least square algorithms for fitting the up to fourth order expansion's coefficients). Among those, 99 models could be fitted without convergence and other numerical issues. The DBHT algorithm with Pearson correlation distance and generalization error similarity was able to select a subgroup of 23 models from the 99 fitted ones, implying a reduction of about 77% in the total number of models, representing a good filtering scheme which still preserves diversity. Finally, it has been demonstrated that the weights obtained by building a Hierarchical Risk Parity (HPR) portfolio perform better for various input random variables, indicating better out-of-sample performance. In this way, an economic stacking strategy has demonstrated its worth in improving the out-of-sample capabilities of stacked models, which illustrates how the new understanding of model stacking methodologies may be useful.

clusterBMA: Bayesian model averaging for clustering

Various methods have been developed to combine inference across multiple sets of results for unsupervised clustering, within the ensemble clustering literature. The approach of reporting results from one 'best' model out of several candidate clustering models generally ignores the uncertainty that arises from model selection, and results in inferences that are sensitive to the particular model and parameters chosen. Bayesian model averaging (BMA) is a popular approach for combining results across multiple models that offers some attractive benefits in this setting, including probabilistic interpretation of the combined cluster structure and quantification of model-based uncertainty. In this work we introduce clusterBMA, a method that enables weighted model averaging across results from multiple unsupervised clustering algorithms. We use clustering internal validation criteria to develop an approximation of the posterior model probability, used for weighting the results from each model. From a combined posterior similarity matrix representing a weighted average of the clustering solutions across models, we apply symmetric simplex matrix factorisation to calculate final probabilistic cluster allocations. In addition to outperforming other ensemble clustering methods on simulated data, clusterBMA offers unique features including probabilistic allocation to averaged clusters, combining allocation probabilities from 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation. This method is implemented in an accompanying R package of the same name. We use simulated datasets to explore the ability of the proposed technique to identify robust integrated clusters with varying levels of separation between subgroups, and with varying numbers of clusters between models. Benchmarking accuracy against four other ensemble methods previously demonstrated to be highly effective in the literature, clusterBMA matches or exceeds the performance of competing approaches under various conditions of dimensionality and cluster separation. clusterBMA substantially outperformed other ensemble methods for high dimensional simulated data with low cluster separation, with 1.16 to 7.12 times better performance as measured by the Adjusted Rand Index. We also explore the performance of this approach through a case study that aims to identify probabilistic clusters of individuals based on electroencephalography (EEG) data. In applied settings for clustering individuals based on health data, the features of probabilistic allocation and measurement of model-based uncertainty in averaged clusters are useful for clinical relevance and statistical communication.

Statistical inference with exchangeability and martingales

In this paper, we start by reviewing exchangeability and its relevance to the Bayesian approach. We highlight the predictive nature of Bayesian models and the symmetry assumptions implied by beliefs of an underlying exchangeable sequence of observations. By taking a closer look at the Bayesian bootstrap, the parametric bootstrap of Efron and a version of Bayesian thinking about inference uncovered by Doob based on martingales, we introduce a parametric Bayesian bootstrap. Martingales play a fundamental role. Illustrations are presented as is the relevant theory. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

Information acquisition and decision strategies in intertemporal choice

Intertemporal decision models describe choices between outcomes with different delays. While these models mainly focus on predicting choices, they make implicit assumptions about how people acquire and process information. A link between information processing and choice model predictions is necessary for a complete mechanistic account of decision making. We establish this link by fitting 18 intertemporal choice models to experimental datasets with both choice and information acquisition data. First, we show that choice models have highly correlated fits: people that behave according to one model also behave according to other models that make similar information processing assumptions. Second, we develop and fit an attention model to information acquisition data. Critically, the attention model parameters predict which type of intertemporal choice models best describes a participant's choices. Overall, our results relate attentional processes to models of intertemporal choice, providing a stepping stone towards a complete mechanistic account of intertemporal decision making.

BridgePRS : A powerful trans-ancestry Polygenic Risk Score method

Polygenic Risk Scores (PRS) have huge potential to contribute to biomedical research and to a future of precision medicine, but to date their calculation relies largely on Europeanancestry GWAS data. This global bias makes most PRS substantially less accurate in individuals of non-European ancestry. Here we present BridgePRS , a novel Bayesian PRS method that leverages shared genetic effects across ancestries to increase the accuracy of PRS in non-European populations. The performance of BridgePRS is evaluated in simulated data and real UK Biobank (UKB) data across 19 traits in African, South Asian and East Asian ancestry individuals, using both UKB and Biobank Japan GWAS summary statistics. BridgePRS is compared to the leading alternative, PRS-CSx , and two single-ancestry PRS methods adapted for trans-ancestry prediction. PRS trained in the UK Biobank are then validated out-of-cohort in the independent Mount Sinai (New York) Bio Me Biobank. Simulations reveal that BridgePRS performance, relative to PRS-CSx , increases as uncertainty increases: with lower heritability, higher polygenicity, greater between-population genetic diversity, and when causal variants are not present in the data. Our simulation results are consistent with real data analyses in which BridgePRS has better predictive accuracy in African ancestry samples, especially in out-of-cohort prediction (into Bio Me ), which shows a 60% boost in mean R 2 compared to PRS-CSx ( P = 2 × 10 -6 ). BridgePRS performs the full PRS analysis pipeline, is computationally efficient, and is a powerful method for deriving PRS in diverse and under-represented ancestry populations.

Bayes Factors for Mixed Models: Perspective on Responses

In van Doorn et al. (2021), we outlined a series of open questions concerning Bayes factors for mixed effects model comparison, with an emphasis on the impact of aggregation, the effect of measurement error, the choice of prior distributions, and the detection of interactions. Seven expert commentaries (partially) addressed these initial questions. Surprisingly perhaps, the experts disagreed (often strongly) on what is best practice-a testament to the intricacy of conducting a mixed effect model comparison. Here, we provide our perspective on these comments and highlight topics that warrant further discussion. In general, we agree with many of the commentaries that in order to take full advantage of Bayesian mixed model comparison, it is important to be aware of the specific assumptions that underlie the to-be-compared models.

Inference about quantitative traits under selection: a Bayesian revisitation for the post-genomic era

BACKGROUND

Selection schemes distort inference when estimating differences between treatments or genetic associations between traits, and may degrade prediction of outcomes, e.g., the expected performance of the progeny of an individual with a certain genotype. If input and output measurements are not collected on random samples, inferences and predictions must be biased to some degree. Our paper revisits inference in quantitative genetics when using samples stemming from some selection process. The approach used integrates the classical notion of fitness with that of missing data. Treatment is fully Bayesian, with inference and prediction dealt with, in an unified manner. While focus is on animal and plant breeding, concepts apply to natural selection as well. Examples based on real data and stylized models illustrate how selection can be accounted for in four different situations, and sometimes without success.

RESULTS

Our flexible "soft selection" setting helps to diagnose the extent to which selection can be ignored. The clear connection between probability of missingness and the concept of fitness in stylized selection scenarios is highlighted. It is not realistic to assume that a fixed selection threshold t holds in conceptual replication, as the chance of selection depends on observed and unobserved data, and on unequal amounts of information over individuals, aspects that a "soft" selection representation addresses explicitly. There does not seem to be a general prescription to accommodate potential distortions due to selection. In structures that combine cross-sectional, longitudinal and multi-trait data such as in animal breeding, balance is the exception rather than the rule. The Bayesian approach provides an integrated answer to inference, prediction and model choice under selection that goes beyond the likelihood-based approach, where breeding values are inferred indirectly.

CONCLUSIONS

The approach used here for inference and prediction under selection may or may not yield the best possible answers. One may believe that selection has been accounted for diligently, but the central problem of whether statistical inferences are good or bad does not have an unambiguous solution. On the other hand, the quality of predictions can be gauged empirically via appropriate training-testing of competing methods.

Ionization states for the multipetawatt laser-QED regime

A paradigm shift in the physics of laser-plasma interactions is approaching with the commissioning of multipetawatt laser facilities worldwide. Radiation reaction processes will result in the onset of electron-positron pair cascades and, with that, the absorption and partitioning of the incident laser energy, as well as the energy transport throughout the irradiated targets. To accurately quantify these effects, one must know the focused intensity on target in situ. In this work, a way of measuring the focused intensity on target is proposed based upon the ionization of xenon gas at low ambient pressure. The field ionization rates from two works [Phys. Rev. A 59, 569 (1999)1050-294710.1103/PhysRevA.59.569 and Phys. Rev. A 98, 043407 (2018)2469-992610.1103/PhysRevA.98.043407], where the latter rate has been derived using quantum mechanics, have been implemented in the particle-in-cell code SMILEI [Comput. Phys. Commun. 222, 351 (2018)0010-465510.1016/j.cpc.2017.09.024]. A series of one- and two-dimensional simulations are compared and shown to reproduce the charge states without presenting visible differences when increasing the simulation dimensionality. They provide a way to accurately verify the intensity on target using in situ measurements.

Bayesian imputation of COVID-19 positive test counts for nowcasting under reporting lag

Obtaining up to date information on the number of UK COVID-19 regional infections is hampered by the reporting lag in positive test results for people with COVID-19 symptoms. In the UK, for 'Pillar 2' swab tests for those showing symptoms, it can take up to five days for results to be collated. We make use of the stability of the under reporting process over time to motivate a statistical temporal model that infers the final total count given the partial count information as it arrives. We adopt a Bayesian approach that provides for subjective priors on parameters and a hierarchical structure for an underlying latent intensity process for the infection counts. This results in a smoothed time-series representation nowcasting the expected number of daily counts of positive tests with uncertainty bands that can be used to aid decision making. Inference is performed using sequential Monte Carlo.

Predicting Brazilian Court Decisions

Predicting case outcomes is useful for legal professionals to understand case law, file a lawsuit, raise a defense, or lodge appeals, for instance. However, it is very hard to predict legal decisions since this requires extracting valuable information from myriads of cases and other documents. Moreover, legal system complexity along with a huge volume of litigation make this problem even harder. This paper introduces an approach to predicting Brazilian court decisions, including whether they will be unanimous. Our methodology uses various machine learning algorithms, including classifiers and state-of-the-art Deep Learning models. We developed a working prototype whose F1-score performance is ~80.2% by using 4,043 cases from a Brazilian court. To our knowledge, this is the first study to present methods for predicting Brazilian court decision outcomes.

Brain signals of a Surprise-Actor-Critic model: Evidence for multiple learning modules in human decision making

Learning how to reach a reward over long series of actions is a remarkable capability of humans, and potentially guided by multiple parallel learning modules. Current brain imaging of learning modules is limited by (i) simple experimental paradigms, (ii) entanglement of brain signals of different learning modules, and (iii) a limited number of computational models considered as candidates for explaining behavior. Here, we address these three limitations and (i) introduce a complex sequential decision making task with surprising events that allows us to (ii) dissociate correlates of reward prediction errors from those of surprise in functional magnetic resonance imaging (fMRI); and (iii) we test behavior against a large repertoire of model-free, model-based, and hybrid reinforcement learning algorithms, including a novel surprise-modulated actor-critic algorithm. Surprise, derived from an approximate Bayesian approach for learning the world-model, is extracted in our algorithm from a state prediction error. Surprise is then used to modulate the learning rate of a model-free actor, which itself learns via the reward prediction error from model-free value estimation by the critic. We find that action choices are well explained by pure model-free policy gradient, but reaction times and neural data are not. We identify signatures of both model-free and surprise-based learning signals in blood oxygen level dependent (BOLD) responses, supporting the existence of multiple parallel learning modules in the brain. Our results extend previous fMRI findings to a multi-step setting and emphasize the role of policy gradient and surprise signalling in human learning.

Bayesian Criterion Based Variable Selection

Bayesian approaches for criterion based selection include the marginal likelihood based highest posterior model (HPM) and the deviance information criterion (DIC). The DIC is popular in practice as it can often be estimated from sampling based methods with relative ease and DIC is readily available in various Bayesian software. We find that sensitivity of DIC based selection can be high, in the range of 90 - 100%. However, correct selection by DIC can be in the range of 0 - 2%. These performances persist consistently with increase in sample size. We establish that both marginal likelihood and DIC asymptotically disfavor under-fitted models, explaining the high sensitivities of both criteria. However, mis-selection probability of DIC remains bounded below by a positive constant in linear models with g -priors whereas mis-selection probability by marginal likelihood converges to 0 under certain conditions. A consequence of our results is that not only the DIC cannot asymptotically differentiate between the data-generating and an over-fitted model, but, in fact, it cannot asymptotically differentiate between two over-fitted models as well. We illustrate these results in multiple simulation studies and in a biomarker selection problem on cancer cachexia of non-small cell lung cancer patients. We further study performances of HPM and DIC in generalized linear model as practitioners often choose to use DIC that is readily available in software in such non-conjugate settings.

Novelty is not surprise: Human exploratory and adaptive behavior in sequential decision-making

Classic reinforcement learning (RL) theories cannot explain human behavior in the absence of external reward or when the environment changes. Here, we employ a deep sequential decision-making paradigm with sparse reward and abrupt environmental changes. To explain the behavior of human participants in these environments, we show that RL theories need to include surprise and novelty, each with a distinct role. While novelty drives exploration before the first encounter of a reward, surprise increases the rate of learning of a world-model as well as of model-free action-values. Even though the world-model is available for model-based RL, we find that human decisions are dominated by model-free action choices. The world-model is only marginally used for planning, but it is important to detect surprising events. Our theory predicts human action choices with high probability and allows us to dissociate surprise, novelty, and reward in EEG signals.

Large-scale model selection in misspecified generalized linear models

Model selection is crucial both to high-dimensional learning and to inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work implicitly assumes that the models are correctly specified or have fixed dimensionality, yet both model misspecification and high dimensionality are prevalent in practice. In this paper, we exploit the framework of model selection principles under the misspecified generalized linear models presented in Lv & Liu (2014), and investigate the asymptotic expansion of the posterior model probability in the setting of high-dimensional misspecified models. With a natural choice of prior probabilities that encourages interpretability and incorporates the Kullback–Leibler divergence, we suggest using the high-dimensional generalized Bayesian information criterion with prior probability for large-scale model selection with misspecification. Our new information criterion characterizes the impacts of both model misspecification and high dimensionality on model selection. We further establish the consistency of covariance contrast matrix estimation and the model selection consistency of the new information criterion in ultrahigh dimensions under some mild regularity conditions. Our numerical studies demonstrate that the proposed method enjoys improved model selection consistency over its main competitors.