Untangling the Evolution of the Receptor-Binding Motif of SARS-CoV-2.

The spike protein determines the host-range specificity of coronaviruses. In particular, the Receptor-Binding Motif in the spike protein from SARS-CoV-2 contains the amino acids involved in molecular recognition of the host Angiotensin Converting Enzyme 2. Therefore, to understand how SARS-CoV-2 acquired its capacity to infect humans it is necessary to reconstruct the evolution of this important motif. Early during the pandemic, it was proposed that the SARS-CoV-2 Receptor-Binding Domain was acquired via recombination with a pangolin infecting coronavirus. This proposal was challenged by an alternative explanation that suggested that the Receptor-Binding Domain from SARS-CoV-2 did not originated via recombination with a coronavirus from a pangolin. Instead, this alternative hypothesis proposed that the Receptor-Binding Motif from the bat coronavirus RaTG13, was acquired via recombination with an unidentified coronavirus. And as a consequence of this event, the Receptor-Binding Domain from the pangolin coronavirus appeared as phylogenetically closer to SARS-CoV-2. Recently, the genomes from coronaviruses from Cambodia (bat_RShST182/200) and Laos (BANAL-20-52/103/247) which are closely related to SARS-CoV-2 were reported. However, no detailed analysis of the evolution of the Receptor-Binding Motif from these coronaviruses was reported. Here we revisit the evolution of the Receptor-Binding Domain and Motif in the light of the novel coronavirus genome sequences. Specifically, we wanted to test whether the above coronaviruses from Cambodia and Laos were the source of the Receptor-Binding Domain from RaTG13. We found that the Receptor-Binding Motif from these coronaviruses is phylogenetically closer to SARS-CoV-2 than to RaTG13. Therefore, the source of the Receptor-Binding Domain from RaTG13 is still unidentified. In accordance with previous studies, our results are consistent with the hypothesis that the Receptor-Binding Motif from SARS-CoV-2 evolved by vertical inheritance from a bat-infecting population of coronaviruses.

Likelihood ratios for changepoints in categorical event data with applications in digital forensics.

We investigate likelihood ratio models motivated by digital forensics problems involving time-stamped user-generated event data from a device or account. Of specific interest are scenarios where the data may have been generated by a single individual (the device/account owner) or by two different individuals (the device/account owner and someone else), such as instances in which an account was hacked or a device was stolen before being associated with a crime. Existing likelihood ratio methods in this context require that a precise time is specified at which the device or account is purported to have changed hands (the changepoint)-this is the known changepoint likelihood ratio model. In this paper, we develop a likelihood ratio model that instead accommodates uncertainty in the changepoint using Bayesian techniques, that is, an unknown changepoint likelihood ratio model. We show that the likelihood ratio in this case can be calculated in closed form as an expression that is straightforward to compute. In experiments with simulated changepoints using real-world data sets, the results demonstrate that the unknown changepoint model attains comparable performance to the known changepoint model that uses a perfectly specified changepoint, and considerably outperforms the known changepoint model that uses a misspecified changepoint, illustrating the benefit of capturing uncertainty in the changepoint.

Refining Bayesian hierarchical MPT modeling: Integrating prior knowledge and ordinal expectations.

Multinomial processing tree (MPT) models are a broad class of statistical models used to test sophisticated psychological theories. The research questions derived from these theories often go beyond simple condition effects on parameters and involve ordinal expectations (e.g., the same-direction effect on the memory parameter is stronger in one experimental condition than another) or disordinal expectations (e.g., the effect reverses in one experimental condition). Here, we argue that by refining common modeling practices, Bayesian hierarchical models are well suited to estimate and test these expectations. Concretely, we show that the default priors proposed in the literature lead to nonsensical predictions for individuals and the population distribution, leading to problems not only in model comparison but also in parameter estimation. Rather than relying on these priors, we argue that MPT modelers should determine priors that are consistent with their theoretical knowledge. In addition, we demonstrate how Bayesian model comparison may be used to test ordinal and disordinal interactions by means of Bayes factors. We apply the techniques discussed to empirical data from Bell et al. Journal of Experimental Psychology: Learning, Memory, and Cognition, 41, 456-472 (2015).

Problematic meta-analyses: Bayesian and frequentist perspectives on combining randomized controlled trials and non-randomized studies.

PURPOSE: In the literature, the propriety of the meta-analytic treatment-effect produced by combining randomized controlled trials (RCT) and non-randomized studies (NRS) is questioned, given the inherent confounding in NRS that may bias the meta-analysis. The current study compared an implicitly principled pooled Bayesian meta-analytic treatment-effect with that of frequentist pooling of RCT and NRS to determine how well each approach handled the NRS bias. MATERIALS & METHODS: Binary outcome Critical-Care meta-analyses, reflecting the importance of such outcomes in Critical-Care practice, combining RCT and NRS were identified electronically. Bayesian pooled treatment-effect and 95% credible-intervals (BCrI), posterior model probabilities indicating model plausibility and Bayes-factors (BF) were estimated using an informative heavy-tailed heterogeneity prior (half-Cauchy). Preference for pooling of RCT and NRS was indicated for Bayes-factors > 3 or < 0.333 for the converse. All pooled frequentist treatment-effects and 95% confidence intervals (FCI) were re-estimated using the popular DerSimonian-Laird (DSL) random effects model. RESULTS: Fifty meta-analyses were identified (2009-2021), reporting pooled estimates in 44; 29 were pharmaceutical-therapeutic and 21 were non-pharmaceutical therapeutic. Re-computed pooled DSL FCI excluded the null (OR or RR = 1) in 86% (43/50). In 18 meta-analyses there was an agreement between FCI and BCrI in excluding the null. In 23 meta-analyses where FCI excluded the null, BCrI embraced the null. BF supported a pooled model in 27 meta-analyses and separate models in 4. The highest density of the posterior model probabilities for 0.333 < Bayes factor < 1 was 0.8. CONCLUSIONS: In the current meta-analytic cohort, an integrated and multifaceted Bayesian approach gave support to including NRS in a pooled-estimate model. Conversely, caution should attend the reporting of naïve frequentist pooled, RCT and NRS, meta-analytic treatment effects.

Transfer Learning in Multiple Hypothesis Testing.

In this investigation, a synthesis of Convolutional Neural Networks (CNNs) and Bayesian inference is presented, leading to a novel approach to the problem of Multiple Hypothesis Testing (MHT). Diverging from traditional paradigms, this study introduces a sequence-based uncalibrated Bayes factor approach to test many hypotheses using the same family of sampling parametric models. A two-step methodology is employed: initially, a learning phase is conducted utilizing simulated datasets encompassing a wide spectrum of null and alternative hypotheses, followed by a transfer phase applying this fitted model to real-world experimental sequences. The outcome is a CNN model capable of navigating the complex domain of MHT with improved precision over traditional methods, also demonstrating robustness under varying conditions, including the number of true nulls and dependencies between tests. Although indications of empirical evaluations are presented and show that the methodology will prove useful, more work is required to provide a full evaluation from a theoretical perspective. The potential of this innovative approach is further illustrated within the critical domain of genomics. Although formal proof of the consistency of the model remains elusive due to the inherent complexity of the algorithms, this paper also provides some theoretical insights and advocates for continued exploration of this methodology.

An Objective and Robust Bayes Factor for the Hypothesis Test One Sample and Two Population Means.

It has been over 100 years since the discovery of one of the most fundamental statistical tests: the Student's t test. However, reliable conventional and objective Bayesian procedures are still essential for routine practice. In this work, we proposed an objective and robust Bayesian approach for hypothesis testing for one-sample and two-sample mean comparisons when the assumption of equal variances holds. The newly proposed Bayes factors are based on the intrinsic and Berger robust prior. Additionally, we introduced a corrected version of the Bayesian Information Criterion (BIC), denoted BIC-TESS, which is based on the effective sample size (TESS), for comparing two population means. We studied our developed Bayes factors in several simulation experiments for hypothesis testing. Our methodologies consistently provided strong evidence in favor of the null hypothesis in the case of equal means and variances. Finally, we applied the methodology to the original Gosset sleep data, concluding strong evidence favoring the hypothesis that the average sleep hours differed between the two treatments. These methodologies exhibit finite sample consistency and demonstrate consistent qualitative behavior, proving reasonably close to each other in practice, particularly for moderate to large sample sizes.

"This behavior strikes us as ideal": assessment and anticipations of Huisman (2022).

Huisman (Psychonomic Bulletin & Review, 1-10. 2022) argued that a valid measure of evidence should indicate more support in favor of a true alternative hypothesis when sample size is large than when it is small. Bayes factors may violate this pattern and hence Huisman concluded that Bayes factors are invalid as a measure of evidence. In this brief comment we call attention to the following: (1) Huisman's purported anomaly is in fact dictated by probability theory; (2) Huisman's anomaly has been discussed and explained in the statistical literature since 1939; the anomaly was also highlighted in the Psychonomic Bulletin & Review article by Rouder et al. (2009), who interpreted the anomaly as "ideal": an interpretation diametrically opposed to that of Huisman. We conclude that when intuition clashes with probability theory, chances are that it is intuition that needs schooling.

Bayesian tests for random mating in polyploids.

Hardy-Weinberg proportions (HWP) are often explored to evaluate the assumption of random mating. However, in autopolyploids, organisms with more than two sets of homologous chromosomes, HWP and random mating are different hypotheses that require different statistical testing approaches. Currently, the only available methods to test for random mating in autopolyploids (i) heavily rely on asymptotic approximations and (ii) assume genotypes are known, ignoring genotype uncertainty. Furthermore, these approaches are all frequentist, and so do not carry the benefits of Bayesian analysis, including ease of interpretability, incorporation of prior information, and consistency under the null. Here, we present Bayesian approaches to test for random mating, bringing the benefits of Bayesian analysis to this problem. Our Bayesian methods also (i) do not rely on asymptotic approximations, being appropriate for small sample sizes, and (ii) optionally account for genotype uncertainty via genotype likelihoods. We validate our methods in simulations and demonstrate on two real datasets how testing for random mating is more useful for detecting genotyping errors than testing for HWP (in a natural population) and testing for Mendelian segregation (in an experimental S1 population). Our methods are implemented in Version 2.0.2 of the hwep R package on the Comprehensive R Archive Network https://cran.r-project.org/package=hwep.

Multibridge: an R package to evaluate informed hypotheses in binomial and multinomial models.

The multibridge R package allows a Bayesian evaluation of informed hypotheses [Formula: see text] applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions 𝜃: (a) hypotheses that postulate equality constraints (e.g., 𝜃1 = 𝜃2 = 𝜃3); (b) hypotheses that postulate inequality constraints (e.g., 𝜃1 < 𝜃2 < 𝜃3 or 𝜃1 > 𝜃2 > 𝜃3); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., 𝜃1 < 𝜃2 = 𝜃3); and (d) hypotheses that postulate combinations of (a)-(c) (e.g., 𝜃1 < (𝜃2 = 𝜃3),𝜃4). Any informed hypothesis [Formula: see text] may be compared against the encompassing hypothesis [Formula: see text] that all category proportions vary freely, or against the null hypothesis [Formula: see text] that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples.

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.

Differences between Japanese and British participants in self-reported verbal strategies to appear convincing.

We compared the self-reported verbal strategies employed to appear convincing when lying and truth telling from 101 British (a low-context culture) and 149 Japanese (a high-context culture) participants. They completed a web-based survey and rated the degree to which they would use 16 verbal strategies when telling the truth and lying. British participants were more concerned with providing innocent reasons and avoiding/denying incriminating evidence when lying than when truth telling (no veracity effect emerged for Japanese participants). Japanese participants were less concerned with avoiding hesitations and lack of consistency when lying than when truth telling (no veracity effect emerged for British participants). The findings suggest that it is important to examine whether interview protocols developed to determine veracity in low-context cultures, such as the Strategic Use of Evidence and Cognitive Credibility Assessment, are equally effective in high-context cultures.

Evaluating network-based missing protein prediction using p-values, Bayes Factors, and probabilities.

Some prediction methods use probability to rank their predictions, while some other prediction methods do not rank their predictions and instead use [Formula: see text]-values to support their predictions. This disparity renders direct cross-comparison of these two kinds of methods difficult. In particular, approaches such as the Bayes Factor upper Bound (BFB) for [Formula: see text]-value conversion may not make correct assumptions for this kind of cross-comparisons. Here, using a well-established case study on renal cancer proteomics and in the context of missing protein prediction, we demonstrate how to compare these two kinds of prediction methods using two different strategies. The first strategy is based on false discovery rate (FDR) estimation, which does not make the same naïve assumptions as BFB conversions. The second strategy is a powerful approach which we colloquially call "home ground testing". Both strategies perform better than BFB conversions. Thus, we recommend comparing prediction methods by standardization to a common performance benchmark such as a global FDR. And where this is not possible, we recommend reciprocal "home ground testing".

Bayes factor functions for reporting outcomes of hypothesis tests.

Bayes factors represent a useful alternative to P-values for reporting outcomes of hypothesis tests by providing direct measures of the relative support that data provide to competing hypotheses. Unfortunately, the competing hypotheses have to be specified, and the calculation of Bayes factors in high-dimensional settings can be difficult. To address these problems, we define Bayes factor functions (BFFs) directly from common test statistics. BFFs depend on a single noncentrality parameter that can be expressed as a function of standardized effects, and plots of BFFs versus effect size provide informative summaries of hypothesis tests that can be easily aggregated across studies. Such summaries eliminate the need for arbitrary P-value thresholds to define "statistical significance." Because BFFs are defined using nonlocal alternative prior densities, they provide more rapid accumulation of evidence in favor of true null hypotheses without sacrificing efficiency in supporting true alternative hypotheses. BFFs can be expressed in closed form and can be computed easily from z, t, χ2, and F statistics.

A Bayesian perspective on severity: risky predictions and specific hypotheses.

A tradition that goes back to Sir Karl R. Popper assesses the value of a statistical test primarily by its severity: was there an honest and stringent attempt to prove the tested hypothesis wrong? For "error statisticians" such as Mayo (1996, 2018), and frequentists more generally, severity is a key virtue in hypothesis tests. Conversely, failure to incorporate severity into statistical inference, as allegedly happens in Bayesian inference, counts as a major methodological shortcoming. Our paper pursues a double goal: First, we argue that the error-statistical explication of severity has substantive drawbacks; specifically, the neglect of research context and the specificity of the predictions of the hypothesis. Second, we argue that severity matters for Bayesian inference via the value of specific, risky predictions: severity boosts the expected evidential value of a Bayesian hypothesis test. We illustrate severity-based reasoning in Bayesian statistics by means of a practical example and discuss its advantages and potential drawbacks.

Are P-values and Bayes factors valid measures of evidential strength?

P-values and Bayes factors are commonly used as measures of the evidential strength of the data collected in hypothesis tests. It is not clear, however, that they are valid measures of that evidential strength; that is, whether they have the properties that we intuitively expect a measure of evidential strength to have. I argue here that measures of evidential strength should be stochastically ordered by both the effect size and the sample size. I consider the case that the data are normally distributed and show that, for that case, P-values are valid measures of evidential strength while Bayes factors are not. Specifically, I show that in a sharp Null hypothesis test the Bayes factor is stochastically ordered by the sample size only if the effect size or the sample size is sufficiently large. This lack of stochastic ordering lies at the root of the Jeffreys-Lindley paradox.

Optimizing representations for integrative structural modeling using Bayesian model selection.

Motivation: Integrative structural modeling combines data from experiments, physical principles, statistics of previous structures, and prior models to obtain structures of macromolecular assemblies that are challenging to characterize experimentally. The choice of model representation is a key decision in integrative modeling, as it dictates the accuracy of scoring, efficiency of sampling, and resolution of analysis. But currently, the choice is usually made ad hoc, manually. Results: Here, we report NestOR (Nested Sampling for Optimizing Representation), a fully automated, statistically rigorous method based on Bayesian model selection to identify the optimal coarse-grained representation for a given integrative modeling setup. Given an integrative modeling setup, it determines the optimal representations from given candidate representations based on their model evidence and sampling efficiency. The performance of NestOR was evaluated on a benchmark of four macromolecular assemblies. Availability: NestOR is implemented in the Integrative Modeling Platform (https://integrativemodeling.org) and is available at https://github.com/isblab/nestor.

G × EBLUP: A novel method for exploring genotype by environment interactions and genomic prediction.

Genotype by environment (G × E) interaction is fundamental in the biology of complex traits and diseases. However, most of the existing methods for genomic prediction tend to ignore G × E interaction (GEI). In this study, we proposed the genomic prediction method G × EBLUP by considering GEI. Meanwhile, G × EBLUP can also detect the genome-wide single nucleotide polymorphisms (SNPs) subject to GEI. Using comprehensive simulations and analysis of real data from pigs and maize, we showed that G × EBLUP achieved higher efficiency in mapping GEI SNPs and higher prediction accuracy than the existing methods, and its superiority was more obvious when the GEI variance was large. For pig and maize real data, compared with GBLUP, G × EBLUP showed improvement by 3% in the prediction accuracy for backfat thickness, while our findings indicated that the trait of days to 100 kg of pig was not affected by GEI and G × EBLUP did not improve the accuracy of genomic prediction for the trait. A significant advantage was observed for G × EBLUP in maize; the prediction accuracy was improved by ∼5.0 and 7.7% for grain weight and water content, respectively. Furthermore, G × EBLUP was not influenced by the number of environment levels. It could determine a favourable environment using SNP Bayes factors for each environment, implying that it is a robust and useful method for market-specific animal and plant breeding. We proposed G × EBLUP, a novel method for the estimation of genomic breeding value by considering GEI. This method identified the genome-wide SNPs that were susceptible to GEI and yielded higher genomic prediction accuracies and lower mean squared error compared with the GBLUP method.

A Bayesian Motivated Two-Sample Test Based on Kernel Density Estimates.

A new nonparametric test of equality of two densities is investigated. The test statistic is an average of log-Bayes factors, each of which is constructed from a kernel density estimate. Prior densities for the bandwidths of the kernel estimates are required, and it is shown how to choose priors so that the log-Bayes factors can be calculated exactly. Critical values of the test statistic are determined by a permutation distribution, conditional on the data. An attractive property of the methodology is that a critical value of 0 leads to a test for which both type I and II error probabilities tend to 0 as sample sizes tend to ∞. Existing results on Kullback-Leibler loss of kernel estimates are crucial to obtaining these asymptotic results, and also imply that the proposed test works best with heavy-tailed kernels. Finite sample characteristics of the test are studied via simulation, and extensions to multivariate data are straightforward, as illustrated by an application to bivariate connectionist data.

Cognitive Rigidity, Habitual Tendencies, and Obsessive-Compulsive Symptoms: Individual Differences and Compensatory Interactions.

Recent theories have posited a range of cognitive risk factors for obsessive-compulsive disorder (OCD), including cognitive inflexibility and a maladaptive reliance on habits. However, empirical and methodological inconsistencies have obscured the understanding of whether inflexibility and habitual tendencies indeed shape OCD symptoms in clinical and sub-clinical populations, and whether there are notable interactions amongst these traits. The present investigation adopted an interactionist individual differences approach to examine the associations between behaviorally-assessed cognitive flexibility and subclinical OCD symptomatology in a healthy population. It also explored the nature of the interactions between cognitive flexibility and habitual tendencies, and the degree to which these cognitive traits predict subclinical OCD symptomatology. Across two studies, including a preregistration, Bayesian and regression analyses revealed that cognitive inflexibility and compulsive habitual tendencies act as unique and independent predictors of subclinical OCD symptomatology in healthy populations. Furthermore, there was a significant interaction between cognitive rigidity and habitual compulsivity, which accounted for 49.4% of the variance in subclinical OCD symptomatology in Study 1, and 37.3% in Study 2. In-depth analyses revealed a compensatory effect between cognitive inflexibility and habitual compulsivity such that both are necessary for OCD symptomatology, but neither is sufficient. These results imply that in order to generate reliable and nuanced models of the endophenotype of OCD symptomatology, it is essential to account for interactions between psychological traits. Moreover, the present findings have important implications for theories on the cognitive roots of OCD, and potentially in the development of interventions that target both cognitive inflexibility and habitual compulsivity.

Lack of evolutionary changes identified in SARS-CoV-2 for the re-emerging outbreak of COVID-19 in Beijing, China.

Although significant achievements have shown that the coronavirus disease 2019 (COVID-19) resurgence in Beijing, China, was initiated by contaminated frozen products and transported via cold chain transportation, international travelers with asymptomatic symptoms or false-negative nucleic acid may have another possible transmission mode that spread the virus to Beijing. One of the key differences between these two assumptions was whether the virus actively replicated since, so far, no reports showed viruses could stop evolution in alive hosts. We studied severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequences in this outbreak by a modified leaf-dating method with the Bayes factor. The numbers of single nucleotide variants (SNVs) found in SARS-CoV-2 sequences were significantly lower than those called from B.1.1 records collected at the matching time worldwide (P = 0.047). In addition, results of the leaf-dating method showed ages of viruses sampled from this outbreak were earlier than their recorded dates of collection (Bayes factors > 10), while control sequences (selected randomly with ten replicates) showed no differences in their collection dates (Bayes factors < 10). Our results which indicated that the re-emergence of SARS-CoV-2 in Beijing in June 2020 was caused by a virus that exhibited a lack of evolutionary changes compared to viruses collected at the corresponding time, provided evolutionary evidence to the contaminated imported frozen food should be responsible for the reappearance of COVID-19 cases in Beijing. The method developed here might also be helpful to provide the very first clues for potential sources of COVID-19 cases in the future.