Bayesian Hierarchical Model for Large-Scale Covariance Matrix Estimation

Improved hierarchical Bayesian modeling framework with arbitrary polynomial chaos for probabilistic model updating

In this brief, a hierarchical Bayesian network modeling framework is formulated for large-scale process monitoring and decision making, which includes a basic layer and a functional layer. First, the whole process is decomposed into different units, where local Bayesian networks are constructed, providing monitoring information and decision-making capability for the upper layer. The network structure is determined automatically based on the process data in each local unit of the basic layer. Then, through incorporating the topological structure of the process, a functional Bayesian network is further constructed to infer the information from the basic layer, which can be customized according to user demands, such as fault detection, fault diagnosis, and classification of operating status. The performance of the proposed method is evaluated through a benchmark process.

Mitochondrial dysfunction is involved in many complex diseases. Efficient and accurate evaluation of mitochondrial functionality is crucial for understanding pathology as well as facilitating novel therapeutic developments. As a popular platform, Seahorse extracellular flux (XF) analyzer is widely used for measuring mitochondrial oxygen consumption rate (OCR) in living cells. A hidden feature of Seahorse XF OCR data is that it has a complex data structure, caused by nesting and crossing between measurement cycles, wells and plates. Surprisingly, statistical analysis of Seahorse XF data has not received sufficient attention, and current methods completely ignore the complex data structure, impairing the robustness of statistical inference. To rigorously incorporate the complex structure into data analysis, here we developed a Bayesian hierarchical modeling framework, OCRbayes, and demonstrated its applicability based on analysis of published data sets. We showed that OCRbayes can analyze Seahorse XF OCR experimental data derived from either single or multiple plates. Moreover, OCRbayes has potential to be used for diagnosing patients with mitochondrial diseases.

Psychedelic drugs are re-emerging as promising scientific and clinical tools. However, despite a rapidly expanding literature on their therapeutic value, the neural mechanisms underlying psychedelic effects remain unclear. Resting-state functional magnetic resonance imaging studies of acute psychedelic effects, conducted independently by several research groups, have so far yielded fragmented and sometimes inconsistent findings. Here, to help facilitate greater convergence, we conducted a ‘mega-analysis’ integrating 11 independent resting-state functional magnetic resonance imaging datasets across five psychedelic drugs (psilocybin, lysergic acid diethylamide, mescaline, N,N-dimethyltryptamine and ayahuasca) from research groups spanning three continents and five countries. By applying a uniform preprocessing pipeline and a Bayesian hierarchical modeling framework, we discovered several common features in the induced alterations to brain function across drugs and sites. Most prominently, we identified a core signature of increased functional connectivity between transmodal (default, frontoparietal and limbic) and unimodal networks (visual and somatomotor), with subnetwork specificity. Furthermore, key subcortical regions (thalamus, caudate and putamen) and the cerebellum exhibited altered coupling with sensorimotor networks. In contrast to several single-site reports, Bayesian modeling revealed weak-to-moderate and selective reductions in within-network functional connectivity, with substantial variability across drugs and networks. Together, these findings extend past work by demonstrating that psychedelics reconfigure large-scale cortical organization while selectively engaging subcortical circuitry. This study provides the most comprehensive synthesis of psychedelic brain action to date, helping resolve inconsistencies and offering a probabilistic map of how psychedelics alter large-scale brain organization. We hereby provide a cornerstone to benchmark and shepherd future psychedelic neuroimaging research.

Thetdistribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lassotregression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat thetdistribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesiantregression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers.

Distinguishing driver mutations from the large background of passenger mutations remains a major challenge in cancer genomics. Evidence-based approaches to nominate driver mutations are often limited by the availability of experimental or clinical validation for specific variants. As clinical sequencing becomes integrated into patient care, computational methods provide powerful opportunities to analyze expanding genomic datasets and identify functional candidates beyond the current knowledge base. Among various analytical frameworks, mutual exclusivity, the observation that mutations in two or more genes tend not to co-occur within the same tumor, has been particularly attractive. Building on this principle, we propose BayesMAGPIE, a refined version of a statistical method, MAGPIE, developed previously for identifying driver genes within oncogenic pathways. The new method introduces two key innovations. First, it incorporates information on mutation type using a Bayesian hierarchical modeling framework, enabling the distinction between potential differences in functional effects among variants within the same gene, thereby improving the accuracy of driver identification. Second, it models gene-specific driver frequencies with a Dirichlet prior which effectively controls the sparsity of the inferred driver set and aligns with the biological expectation that most tumor types are driven by a small number of genes. We evaluate BayesMAGPIE through extensive simulation studies to assess its estimation bias and accuracy in driver identification, and benchmark its performance against MAGPIE using TCGA data from eight cancer types.

The Soyang Dam is a main multi-purpose dam for preventing floods and supplying water to the metropolitan area, including Seoul, located in the Han River basin. This research explored the predictability of streamflow that plays a critical role in the reservoir operation of the Soyang Dam in South Korea. A novel stochastic approach was used to offer skillful season-ahead streamflow forecasting during the monsoon season (June-July-August, JJA) using climate state variables (e.g., SST, SLP, and wind anomalies) and dynamic climate forecasts simulated from global climate models (GCMs), as predictors. Further, we employes autoregressive exogenous stochastic volatility(ARXSV) model for streamflow prediction with the predictors that were identified within a Hierarchical Bayesian modeling framework. A cross-validation experiment under different synoptic patterns is performed to test the efficacy of the proposed modeling process. Finally, this study will investigate the effectiveness of streamflow forecasts as a precursor of the hydrological drought condition for the upcoming season. AcknowledgementThis research was supported by a grant(2022-MOIS63-001) of Cooperative Research Method and Safety Management Technology in National Disaster funded by Ministry of Interior and Safety(MOIS, Korea). This work was partially funded by the Korea Meteorological Administration Research and Development Program under Grant KMI 2018-07010.

The near-shore ocean ecosystem is influenced by catchment runoff. The Great Barrier Reef has been experiencing significant water quality deterioration over the past 150 years, due in part to agricultural intensification and urban settlement in adjacent catchments (Thorburn et al., 2013). There is a need for us to understand the influences of catchment characteristics on stream water quality, with an aim to mitigate and manage the water quality issue in the terrestrial stream runoff derived from the adjacent Great Barrier Reef catchments. The event-based water quality monitoring data set from the Paddock to Reef Integrated Monitoring Program across six Natural Management Regions provides a potential opportunity to develop a data-driven understanding of catchment characteristics affecting water quality at the catchment scale. This requires a robust and reliable modelling tool to relate the monitoring data to anthropogenic and natural processes. In this study, monitoring data of Total Suspended Solids (TSS) and dissolved Oxidised Nitrogen (NOX) from 32 sites across the Great Barrier Reef catchments are selected as case study constituents due to the high risk they pose to reef health when exported from catchments to the receiving marine environment. Also, these two constituents have distinct biogeochemical processes in catchments. Specifically, TSS is typically conserved (although mobilized and deposited) while travelling through river systems; while NOX can be potentially processed and removed from the system altogether. A Bayesian hierarchical linear modelling framework is adopted, due to its ability to borrow strength among sites, allowing information to be transferred across space, and due to its ability to provide uncertainty of the predictions. The Bayesian hierarchical linear regression model in this study is developed to evaluate the significance of various catchment characteristics (e.g., land uses, catchment topography and geology) on spatial variation in water quality. The main findings of this study are listed as follows, • Sites located in the Burdekin and Fitzroy Natural Management Regions tend to have greater TSS concentrations, illustrated by the modelled site-specific spatial random effects (deviation from the overall average concentration). Additionally, grazing and dry land agriculture land uses are positively correlated with the spatial random effect on TSS. The complexity of interaction between different catchment characteristics (e.g., land use and topography) can potentially result in a negative spatial random effect on TSS, which is reduced in the relatively steeper Great Barrier Reef catchments with a denser stream network. • Sugar cane is one of the most significant NOX contributors according to the modelling results, likely partially due to the excessive application of fertilizers; however, conservation land use has limited effect on NOX removal, indicating denitrification process alone may not be sufficient to remove NOX. The modelling results demonstrate different land management strategies are required for the purpose of reducing different constituents. This work will provide scientific insights for water quality management at the catchment scale.

Earth and Space Science Open Archive Presented WorkOpen AccessYou are viewing the latest version by default [v1]A space–time Bayesian hierarchical modeling framework for projection of seasonal high flow riskAuthorsÁlvaroOssandóniDBalajiRajagopalanSee all authors Álvaro OssandóniDCorresponding Author• Submitting AuthorUniversity of Colorado at BoulderiDhttps://orcid.org/0000-0003-2165-8736view email addressThe email was not providedcopy email addressBalaji RajagopalanUniversity of Colorado at Boulderview email addressThe email was not providedcopy email address

We develop a space‐time Bayesian hierarchical modeling (BHM) framework for two flood risk attributes—seasonal daily maximum flow and the number of events that exceed a threshold during a season (NEETM)—at a suite of gauge locations on a river network. The model uses generalized extreme value (GEV) and Poisson distributions as marginals for these flood attributes with non‐stationary parameters. The rate parameters of the Poisson distribution and location, scale, and shape parameters of the GEV are modeled as linear functions of suitable covariates. Gaussian copulas are applied to capture the spatial dependence. The best covariates are selected using the Watanabe‐Akaike information criterion (WAIC). The modeling framework results in the posterior distribution of the flood attributes at all the gauges and various lead times. We demonstrate the utility of this modeling framework to forecast the flood risk attributes during the summer peak monsoon season (July‐August) at five gauges in the Narmada River basin (NRB) of West‐Central India for several lead times (0–3 months). As potential covariates, we consider climate indices such as El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), and the Pacific Warm Pool Region (PWPR) from antecedent seasons, which have shown strong teleconnections with the Indian monsoon. We also include new indices related to the East Pacific and West Indian Ocean regions depending on the lead times. We show useful long lead skill from this modeling approach which has a strong potential to enable robust risk‐based flood mitigation and adaptation strategies 3 months before flood occurrences.

An Empirical Analysis of Search Engine Advertising: Sponsored Search in Electronic Markets

Abstract. The Atlantic Meridional Overturning Circulation (AMOC) is a major climate element subject to possible ongoing loss of stability. Recent studies have found evidence of a gradual weakening in circulation, including early warning signals (EWSs), such as increased fluctuations and correlation time of the system, which are both known to be indicators of a possible forthcoming tipping point. To assess these changes in statistical behavior, we propose a robust and general statistical model based on a second-order autoregressive process with time-dependent parameters. This allows for the statistical changes from increased external variability and destabilization to be accounted for separately. We estimate the time evolution of the correlation parameters using a hierarchical Bayesian modeling framework, which also yields uncertainty quantification through the posterior distribution. To assess possible changes in AMOC stability, we apply the model to an AMOC fingerprint proxy based on the subpolar gyre and the global mean temperature anomaly. We find statistically significant EWSs, which suggests that AMOC is indeed undergoing a loss of stability and is getting closer to a tipping point. The methodology developed in this study is made publicly available as an extension of the R-package INLA.ews.

Hierarchical Bayesian modelling for spatial analysis of the number of avalanche occurrences at the scale of the township

The phenomenon of sponsored search advertising—where advertisers pay a fee to Internet search engines to be displayed alongside organic (nonsponsored) Web search results—is gaining ground as the largest source of revenues for search engines. Using a unique six-month panel data set of several hundred keywords collected from a large nationwide retailer that advertises on Google, we empirically model the relationship between different sponsored search metrics such as click-through rates, conversion rates, cost per click, and ranking of advertisements. Our paper proposes a novel framework to better understand the factors that drive differences in these metrics. We use a hierarchical Bayesian modeling framework and estimate the model using Markov Chain Monte Carlo methods. Using a simultaneous equations model, we quantify the relationship between various keyword characteristics, position of the advertisement, and the landing page quality score on consumer search and purchase behavior as well as on advertiser's cost per click and the search engine's ranking decision. Specifically, we find that the monetary value of a click is not uniform across all positions because conversion rates are highest at the top and decrease with rank as one goes down the search engine results page. Though search engines take into account the current period's bid as well as prior click-through rates before deciding the final rank of an advertisement in the current period, the current bid has a larger effect than prior click-through rates. We also find that an increase in landing page quality scores is associated with an increase in conversion rates and a decrease in advertiser's cost per click. Furthermore, our analysis shows that keywords that have more prominent positions on the search engine results page, and thus experience higher click-through or conversion rates, are not necessarily the most profitable ones—profits are often higher at the middle positions than at the top or the bottom ones. Besides providing managerial insights into search engine advertising, these results shed light on some key assumptions made in the theoretical modeling literature in sponsored search.

In this paper, we focus on a multi-task sparse Bayesian learning (SBL) theory that simultaneously utilizes multiple measurement vectors that are marked by a similar sparseness profile. Joint learning for sparse representations of multiple tasks has been mostly overlooked, although it is a useful tool for exploiting data redundancy by modeling the statistical relationships within groups of measurements. We first present a hierarchical Bayesian model and Bayesian inference framework for the multi-task SBL algorithm. Then we investigate the application of the multi-task SBL for model updating in structural health monitoring. The results verify that exploiting common information among multiple related tasks leads to better performance of the Bayesian inversion