Empirical Bayesian Model Research Articles

Improving Bayesian optimization via hierarchical variation modeling for combinatorial experiments given limited runs guided by process knowledge

Active learning based on Bayesian optimization (BO) is a popular black-box combinatorial search method, particularly effective for autonomous experimentation. However, existing BO methods did not consider the joint variation caused by the process degradation over time and input-dependent variation. The challenge is more significant when the affordable experimental runs are very limited. State-of-the-art approaches did not address allocating limited experimental runs that can jointly cover (1) representative inputs over large search space for identifying the best combination, (2) replicates reflecting the true input-dependent testing variation, and (3) process variations that increase over time due to process degradation. This paper proposed Empirical Bayesian Hierarchical Variation Modeling in Bayesian Optimization (EHVBO) guided by the process knowledge to maximize the exploration of potential combinations in sequential experiments given limited experimental runs. The method first mitigates the process degradation effect through generalized linear modeling of grouped variations, guided by the knowledge of the re-calibration cycle of process conditions. Then, EHVBO introduces an empirical Bayesian hierarchical model to reduce the replicates for learning the input-dependent variation, leveraging the process knowledge of the common structure shared across different testing combinations. This way can reduce the necessary replicates for each input condition. Furthermore, the paper developed a heuristics-based strategy incorporated in EHVBO to improve search efficiency by selectively refining the search space over pivotal regions and excluding less-promising regions. A case study based on real experimental data demonstrates that the proposed method outperforms testing results from various optimization models.

DO CHILDHOOD MEMORIES INFLUENCE THE THERAPEUTIC RELATIONSHIP? AN EMPIRICAL BAYESIAN SEM APPROACH.

This study aims to explore the interplay of these concepts in a sample patients diagnosed with schizophrenia and related psychotic disorders. Hence, the potentially mediating role of countertransference in the relationship between recalled parenting styles, childhood trauma and therapeutic working alliance was examined. A total sample of 30 patients (Age: 38.60; SD = 16.37; 50% female) treated for psychotic disorders in an inpatient setting were assessed. Pathways between the variables Recalled Parental Styles, Childhood Trauma, Countertransference and Working Alliance were estimated via frequentist and empirical Bayesian Structural Equation Modeling (EBSEM). Both maximum likelihood and EBSEM derived results suggested direct effects of remembered parental style on childhood trauma, as well as of childhood trauma on negative countertransference. Positive and negative countertransference were associated with working alliance. Furthermore, the findings suggested indirect effects of remembered parental style on negative countertransference via childhood trauma, as well as remembered parental style with working alliance mediated via childhood trauma and negative countertransference. Childhood trauma showed a significant indirect effect on working alliance via negative countertransference. The results provide preliminary support for the idea that traumatic memories from the past influence the therapeutic relationship in the present. In correspondence to this, the clinical significance of concepts like reverie and containment are discussed.

Altered Effective Connectivity During Threat Anticipation in Individuals With Alcohol Use Disorder

BackgroundA developing theory and recent research suggest that heightened reactivity to uncertain stressors or threats may be an important individual difference factor that facilitates excessive drinking as a means of avoidance-based coping and characterizes individuals with current and past alcohol use disorder (AUD). Neuroimaging studies of unpredictable threat processing have repeatedly demonstrated activation of the anterior insula, anteromedial thalamus, and dorsal anterior cingulate cortex. In the current study, we aimed to understand how these 3 regions function as a network during anticipation of unpredictable threat (and predictable threat). MethodsParticipants were 43 adults (ages 21–30) with AUD and 26 healthy control participants. Functional magnetic resonance imaging and dynamic causal modeling were used to study interregional effective connectivities and predictable and unpredictable threat-related modulations thereof within this network. Parametric empirical Bayesian modeling was used to conduct between-group comparisons in effective connectivities. ResultsDuring unpredictable threat trials, the increased projection from the right anteromedial thalamus to the right anterior insula was significantly present only in the AUD group. This directional influence was stronger among individuals who consumed more drinks per week on average. As expected, we found no group differences in modulatory changes to effective connectivities during predictable threat trials. ConclusionsTo our knowledge, this is the first study to examine directional interactions between key frontolimbic regions during anticipation of unpredictable and predictable threat and demonstrate the importance of bottom-up thalamic-insular projections during unpredictable threat processing in AUD. Prospective studies are warranted to determine whether this association is causal.

Development of a population pharmacokinetic model for the novel long-acting injectable antipsychotic risperidone ISM®.

The aims of this study were to develop a population pharmacokinetic (PK) model for risperidone ISM® and to investigate the relationships between active moiety exposure, as described by apparent clearance (CL40), and several covariates using all data from five clinical studies. A population PK model was developed using active moiety concentrations from a study in healthy volunteers and two studies in patients with schizophrenia. Data from a comparative bioavailability study in medically stable patients and a Phase III study in patients with acute exacerbation of schizophrenia were then incorporated, using empirical Bayesian feedback and model refinement in NONMEM. Finally, covariate analysis was performed on CL40. The final model adequately described the pharmacokinetics of 6288 active moiety concentrations in 17 healthy volunteers and 430 patients with schizophrenia. This one-compartment disposition model had a complex absorption process, combining a small amount immediately entering the central active moiety compartment, two first-order absorption processes and a combined zero-order and first order process, with first-order elimination from the central compartment. Significant covariates on CL40 were BMI and sex. Goodness-of-fit (GOF) plots and visual predictive checks (VPC) confirmed acceptable description of the data. The population PK model adequately described active moiety concentrations from five clinical studies after risperidone ISM® administration. Relationships between active moiety exposure and covariates were defined in order to facilitate simulations for future studies. The model showed that risperidone ISM® rapidly achieves therapeutic plasma levels within the first hours after the first injection that are maintained sustainedly throughout the whole dosing interval following once-monthly gluteal injections of 100 mg and 75 mg.

Estimating Forest Aboveground Biomass Using a Combination of Geographical Random Forest and Empirical Bayesian Kriging Models

Accurately estimating forest aboveground biomass (AGB) is imperative for comprehending carbon cycling, calculating carbon budgets, and formulating sustainable forest management plans. Currently, random forest (RF) and other machine learning models are widely used to estimate forest AGB, as they can effectively handle nonlinear relationships. However, by constructing a global model using all the samples collected from a study area, these models fail to account for the spatial heterogeneity in the AGB and cannot correct the prediction biases, thereby constraining the estimation accuracy. To overcome these limitations, we proposed a novel approach termed geographical random forest and empirical Bayesian kriging (GRFEBK). This hybrid model combines the localized modeling capability of geographical random forest (GRF) with the bias correction strength of empirical Bayesian kriging (EBK). GRF adapts RF to account for the spatial heterogeneity of the AGB, while EBK utilizes the spatial autocorrelation of residuals to correct the prediction deviations. This study was conducted in Hainan Island, utilizing spectral bands, vegetation indices, tasseled cap components derived from Landsat-8 imagery, backscattering coefficients from ALOS-2 synthetic aperture radar, topographic features, and the forest canopy height as the explanatory variables. A total of 195 forest aboveground biomass (AGB) samples were collected for modeling and assessing the predictive accuracy. The results demonstrate that, among the tested models, including GRFEBK, RF, support vector machine (SVM), k-nearest neighbor (KNN), geographically weighted regression (GWR), GRF, and EBK, GRFEBK attains the highest R2 (0.78) and the lowest RMSE (36.04 Mg/ha) and RRMSE (22.87%), significantly outperforming the conventional models and using GRF or EBK alone. These results demonstrate that by accounting for local non-stationarity in AGB and correcting prediction biases, GRFEBK achieves significantly higher accuracy than conventional RF and other models. While the results are promising, the computational cost of GRFEBK and its performance under varying geographical conditions warrant further investigation at larger scales to assess its broader applicability. Nevertheless, GRFEBK provides an innovative and more reliable approach for accurate forest AGB estimation with great potential to support global forest resource monitoring.

Spatial-temporal pattern of colorectal cancer mortality in a Northeastern Brazilian State.

Colorectal cancer (CRC) is one of the most common cancer types worldwide. Its increasing mortality trends, especially in emerging countries, are a concern. The aim of this study was to analyse mortality trends and spatial patterns of CRC in the state of Sergipe, Brazil, from 1990 to 2019. Trends were calculated using data from the Online Mortality Atlas and Joinpoint Regression Program 4.8.0.1. Spatial analyses were performed using the empirical Bayesian model and Moran indices calculated by TerraView 4.2.2 between 1990 to 1999, 2000 to 2009 and 2010 to 2019. A total of 1585 deaths were recorded during the study period, with 58.42% among females. Trends were increasing and constant for both sexes and all age groups studied. The highest mean annual percent change was 6.2 {95% Confidence interval (CI) 3.4;9.0} for males aged +65 years and 4.5 (95% CI 3.2;5.8) for females aged 50-64 years. There was positive spatial autocorrelation for both sexes in all periods studied when using the Moran index for Bayesian rates. In summary, a consistent trend of increasing colorectal cancer (CRC) mortality has been observed overall. Nevertheless, an altered spatial distribution among males has emerged over the studied period.

Ensemble Bayesian Model Averaging Projections of Wind‐Speed Extremes for Wind Energy Applications Over China Under Climate Change

AbstractWind energy has grown rapidly in recent years as a measure to control carbon emissions and mitigate climate change. Extreme wind can damage wind turbines, cause losses to wind power plants, limit economic benefits of wind energy facilities, and disrupt regional grid balance. Therefore, an accurate assessment of extreme wind speeds at wind turbine hub height and their spatiotemporal variation under climate change is critical for the planning of wind energy and for guaranteeing regional energy security. In this study, the 100‐m extreme wind speeds in China are estimated using an empirical downscaling and Bayesian model averaging ensemble method with the latest ERA5 reanalysis and 20 global climate models (GCMs) from the Coupled Model Intercomparison Project phase 6 (CMIP6). Two shared socioeconomic pathways (SSP), that is, SSP2‐4.5 and SSP5‐8.5, are considered to account for the uncertainty in anthropogenic emissions. According to the results, the highest extreme wind speeds are primarily found in Inner Mongolia, northeast China, western Tibet, and the eastern coastal region. Extreme wind speeds in central and southeastern China are projected to increase by approximately 2% in the middle (2031–2060) and the end (2071–2100) of the 21st century relative to the baseline period (1985–2014). Summer extreme wind speeds in northwestern Tibet are expected to increase by more than 9% at the end of the century. The findings of this study indicate that it is important to take the present and projected changes in local wind extremes into account when choosing locations for wind power plants and wind energy installations.

Associations of long-term exposure to air pollution with prevalence of pulmonary nodules: A cross-sectional study in Shijiazhuang, China

A complete understanding of the associations of ambient air pollution with prevalence of pulmonary nodule is lacking. We aimed to investigate the associations of ambient air pollutants with prevalence of pulmonary nodule. A total of 9991 health examination participants was enrolled and 3166 was elected in the final in Shijiazhuang between April 1st, 2018, and December 31st, 2018. 107 participants were diagnosed in pulmonary nodule while 3059 participants were diagnosed in non-pulmonary (named control). The individual exposure of participants was evaluation by Empirical Bayesian Kriging model according to their residential or work addresses. The pulmonary nodules were found and diagnosed by health examination through chest x-ray detection. Our results suggested that there were positive associations between prevalence of pulmonary nodules and PM2.5 (OR = 1.06, 95% CI: 1.02, 1.11) as well as O3 (OR = 1.49, 95% CI: 1.35, 1.66) levels. The platelet count (PLT) acted as the mediator of pulmonary nodules related with the PM2.5 exposure, while the neutrophil-to-lymphocyte ratio (NLR) as well as platelet-to-lymphocyte ratio (PLR) were the mediators of pulmonary nodules related with the O3 exposure. This study suggests that long-term exposure to PM2.5 and O3 may significantly associated with prevalence of pulmonary nodules, and the above associations are mediated by PLT, NLR and PLR.

A Bayesian hierarchical age model for optical dating of single grains of quartz

In optical dating, the last time that a sample of sediment was exposed to sunlight is determined by dividing its equivalent dose (De) by the dose rate. For single-grain dating, the sample De is based on the statistical analysis of the distribution of De values estimated for individual grains, whereas the dose rate is usually determined from measurements of the environmental radioactivity of the bulk sample, together with allowances for radiation sources internal to the grains and cosmic rays. Conventionally, the De and dose rate are measured and analysed separately to produce an estimate of the depositional age of a sample, but this approach may result in loss of information because distributions of single-grain De values are influenced by several factors. Existing statistical models do not incorporate all the key information contributing to age estimation, such as the pattern and scale of dispersion of single-grain De values and dose rates, the associated measurement uncertainties, the effect of natural variability among grains, and the outlier probabilities of De and dose rate estimates. Here we propose an empirical Bayesian hierarchical age model (BHAM) for optical dating of quartz samples that incorporates the above information to estimate their depositional ages. The BHAM is based on the implementation of standardised growth curve and LnTn methods to integrate information on the full distribution of single-grain De values, sources of measurement uncertainty, beta-dose heterogeneity (observed or modelled), and detection of outliers. We present the results of validation tests using data sets of optically stimulated luminescence measurements and dose rates obtained for quartz samples dated previously from Denisova Cave (Russia) and for simulated samples. We conclude that the BHAM represents a robust and flexible approach to dealing with data for single grains of quartz within a Bayesian hierarchical framework and is suitable for application to sediments deposited in a variety of depositional settings.

Technical Comment on "Policy impacts of statistical uncertainty and privacy".

Steed et al. (1) illustrates the crucial impact that the quality of official statistical data products may exert on the accuracy, stability, and equity of policy decisions on which they are based. The authors remind us that data, however responsibly curated, can be fallible. With this comment, we underscore the importance of conducting principled quality assessment of official statistical data products. We observe that the quality assessment procedure employed by Steed et al. needs improvement, due to (i) the inadmissibility of the estimator used, and (ii) the inconsistent probability model it induces on the joint space of the estimator and the observed data. We discuss the design of alternative statistical methods to conduct principled quality assessments for official statistical data products, showcasing two simulation-based methods for admissible minimax shrinkage estimation via multilevel empirical Bayesian modeling. For policymakers and stakeholders to accurately gauge the context-specific usability of data, the assessment should take into account both uncertainty sources inherent to the data and the downstream use cases, such as policy decisions based on those data products.

Integration of simultaneous fMRI and EEG source localization in emotional decision problems

Simultaneous EEG-fMRI has been a powerful technique to understand the mechanism of the brain in recent years. In this paper, we develop an integrating method by integrating the EEG data into the fMRI data based on the parametric empirical Bayesian (PEB) model to improve the accuracy of the brain source location. The gambling task, a classic paradigm, is used for the emotional decision-making study in this paper. The proposed method was conducted on 21 participants, including 16 men and 5 women. Contrary to the previous method that only localizes the area widely distributed across the ventral striatum and orbitofrontal cortex, the proposed method localizes accurately at the orbital frontal cortex during the process of the brain's emotional decision-making. The activated brain regions extracted by source localization were mainly located in the prefrontal and orbitofrontal lobes; the activation of the temporal pole regions unrelated to reward processing disappeared, and the activation of the somatosensory cortex and motor cortex was significantly reduced. The log evidence shows that the integration of simultaneous fMRI and EEG method based on synchronized data evidence is 22,420, the largest value among the three methods. The integration method always takes on a larger value of log evidence and describes a better performance in analysis associated with source localization. Data availabilityThe data used in the current study are available from the corresponding author upon on reasonable request.

Temporal trend, spatial analysis and spatiotemporal clusters of infant mortality associated with congenital toxoplasmosis in Brazil: Time series from 2000 to 2020.

To analyse the spatial, temporal and spatial-temporal patterns of infant mortality associated with congenital toxoplasmosis in Brazil between the years 2000 and 2020. Ecological study of time series, with spatial analysis and spatiotemporal scan of infant mortality associated with congenital toxoplasmosis from the records of deaths of the Mortality Information System of the Brazilian Ministry of Health. The rates were smoothed by the Local Empirical Bayesian model. The Global Moran Index, Global Geary's Contiguity and Getis-Ord General statistics were calculated for spatial autocorrelation assessment. The trends were evaluated by the Joinpoint method. We identified 1183 infant deaths associated with congenital toxoplasmosis in Brazil between 2000 and 2020. The predominant characteristics were male sex (52.1%), post-neonatal age group (51.9%), white race/colour (45.7%), and Southeast region of residence (40.0%). The infant mortality rate associated with congenital toxoplasmosis showed an increasing trend in the country in the years analysed. The spatial analysis showed heterogeneous distribution of mortality in the Brazilian territory and found no evidence of spatial autocorrelation; but spatial-temporal analysis identified three risk clusters involving 703 municipalities. Infant mortality associated with congenital toxoplasmosis is a persistent public health problem in Brazil. The risk factors male sex, indigenous race/colour, early neonatal age, North and Northeast regions and risk clusters mapped in this study should be observed for future analysis and planning of health care policies in the control of infant deaths associated with congenital toxoplasmosis. Health surveillance strategies and public health policies need to be strengthened.

A space-time analysis of mortality in older people living with HIV/AIDS in the state of São Paulo, Brazil.

To analyze the spatiotemporal distribution of mortality in older people living with the human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS) in the state of São Paulo, Brazil. This is an ecological study with temporal and spatial approaches to analyze mortality from HIV/AIDS in the older adult population in the 2010-2020 period in the state of São Paulo, Brazil. Analysis of temporal trends was performed using the joinpoint regression, and spatial analysis was carried out using the Moran's index and the local empirical Bayesian model. We identified a total of 3,070 deaths from HIV/AIDS among older adults and a mortality rate of 51.71 per 100 thousand inhabitants during the study period. The joinpoint method showed a growing trend for the age groups from 70 to 79 years (annual percent change [APC]=3.45; p=0.01) and ≥80 years (APC=6.60; p=0.006) and stability for the general older adult population (APC=0.99; p=0.226). The spatial distribution of the crude mortality rate was diffuse throughout the state. After smoothing by the Bayesian estimator, we observed greater concentration in the eastern mesoregions. In Moran's analysis, we observed clusters of lower mortality rates in more central regions; and of higher rates in the southern and northern regions of the state. We found a major growing trend in mortality from HIV/AIDS in the age group of older adults over 69 years during the 2010-2020 period. Clusters of high mortality rates were located in regions further to the south and north of the state, where places of greater social inequalities are concentrated.

An Empirical Bayesian Approach to Quantify Multi-Scale Spatial Structural Diversity in Remote Sensing Data

Landscape structure is as much a driver as a product of environmental and biological interactions and it manifests as scale-specific, but also as multi-scale patterns. Multi-scale structure affects processes on smaller and larger scales and its detection requires information from different scales to be combined. Herein, we propose a novel method to quantify multi-scale spatial structural diversity in continuous remote sensing data. We combined information from different extents with an empirical Bayesian model and we applied a new entropy metric and a value co-occurrence approach to capture heterogeneity. We tested this method on Normalized Difference Vegetation Index data in northern Eurasia and on simulated data and we also tested the effect of coarser pixel resolution. We find that multi-scale structural diversity can reveal itself as patches and linear landscape features, which persist or become apparent across spatial scales. Multi-scale line features reveal the transition zones between spatial regimes and multi-scale patches reveal those areas within transition zones where values are most different from each other. Additionally, spatial regimes themselves can be distinguished. We also find the choice of scale need not be informed by typical length-scales, which makes the method easy to implement. The proposed multi-scale approach can be applied to other contexts, following the roadmap we pave out in this study and using the tools available in the accompanying R package StrucDiv.

Fluoride Contamination of Groundwater from Semi-Arid Regions of Western India

A study on fluoride risk assessment was carried out in the semi-arid region of North Gujarat, India. The intricate link between groundwater fluoride and human health, lack of awareness, limited access to fluoride treatment facilities, and poor socio-economic conditions of the ~5.0 million rural population in the studied region make them vulnerable to fluoride. This study aimed to evaluate non-carcinogenic health risk, its severity, and the total population at risk in these regions due to chronic fluoride exposure. Fluoride in our samples (n=132) exhibits large spatial variability, and it ranges from ~0.13-8.64 mg.L-1 (average: 1.64 ± 1.50 mg.L-1) and 43% of them are more than the WHO limit of 1.5 mg.L-1. Hazard Quotient (HQ) was used to assess health risks through the ingestion exposure route. The comparison of the range (0.1-8.55 versus 0.06-4.11), average (1.63 ± 1.49 versus 0.78 ± 0.72), and median (1.26 versus 0.60) of HQ between children and adults highlights that the former are at more risk compared to latter. Our conservative estimates suggest that ~0.45 million children and ~1.06 million adult population, ~55% and ~20% of the respective population classes, of the region, are potentially at risk. The empirical Bayesian Kriging model was used to produce risk-assessments maps. These can help policymakers in prioritizing the application of mitigation funding and resources, and in increasing testing efforts in high-risk areas. We believe this study should guide policymakers to adopt strategies in ensuring the public health safety of the rural population, children in particular, of the studied region.

COVID-19 spatialization by empirical Bayesian model in São Paulo, Brazil.

The new Acute Respiratory Syndrome, COVID-19, has affected the health and the economy worldwide. Therefore, scientists have been looking for ways to understand this disease. In this context, the main objective of this study was the spatialization of COVID-19, thinking in distinguishing areas with high transmissibility yet, verifying if these areas were associated with the elderly population occurrence. The work was delineated, supposing that spatialization could support the decision-making to combat the outbreak and that the same method could be used for spatialization and prevent other diseases. The study area was a municipality near Sao Paulo Metropolis, one of Brazil's main disease epicenters. Using official data and an empirical Bayesian model, we spatialized people infected by region, including older people, obtaining reasonable adjustment. The results showed a weak correlation between regions infected and older adults. Thus, we define a robust model that can support the definition of actions aiming to control the COVID-19 spread.

A resource for integrated genomic analysis of the human liver

In this study, we generated whole-transcriptome RNA-Seq from n = 192 genotyped liver samples and used these data with existing data from the GTEx Project (RNA-Seq) and previous liver eQTL (microarray) studies to create an enhanced transcriptomic sequence resource in the human liver. Analyses of genotype-expression associations show pronounced enrichment of associations with genes of drug response. The associations are primarily consistent across the two RNA-Seq datasets, with some modest variation, indicating the importance of obtaining multiple datasets to produce a robust resource. We further used an empirical Bayesian model to compare eQTL patterns in liver and an additional 20 GTEx tissues, finding that MHC genes, and especially class II genes, are enriched for liver-specific eQTL patterns. To illustrate the utility of the resource to augment GWAS analysis with small sample sizes, we developed a novel meta-analysis technique to combine several liver eQTL data sources. We also illustrate its application using a transcriptome-enhanced re-analysis of a study of neutropenia in pancreatic cancer patients. The associations of genotype with liver expression, including splice variation and its genetic associations, are made available in a searchable genome browser.

Topological dissimilarities of hierarchical resting networks in type 2 diabetes mellitus and obesity

Type 2 diabetes mellitus (T2DM) is reported to cause widespread changes in brain function, leading to cognitive impairments. Research using resting-state functional magnetic resonance imaging data already aims to understand functional changes in complex brain connectivity systems. However, no previous studies with dynamic causal modelling (DCM) tried to investigate large-scale effective connectivity in diabetes. We aimed to examine the differences in large-scale resting state networks in diabetic and obese patients using combined DCM and graph theory methodologies. With the participation of 70 subjects (43 diabetics, 27 obese), we used cross-spectra DCM to estimate connectivity between 36 regions, subdivided into seven resting networks (RSN) commonly recognized in the literature. We assessed group-wise connectivity of T2DM and obesity, as well as group differences, with parametric empirical Bayes and Bayesian model reduction techniques. We analyzed network connectivity globally, between RSNs, and regionally. We found that average connection strength was higher in T2DM globally and between RSNs, as well. On the network level, the salience network shows stronger total within-network connectivity in diabetes (8.07) than in the obese group (4.02). Regionally, we measured the most significant average decrease in the right middle temporal gyrus (-0.013 Hz) and the right inferior parietal lobule (-0.01 Hz) relative to the obese group. In comparison, connectivity increased most notably in the left anterior prefrontal cortex (0.01 Hz) and the medial dorsal thalamus (0.009 Hz). In conclusion, we find the usage of complex analysis of large-scale networks suitable for diabetes instead of focusing on specific changes in brain function.

Forecasting of monthly precipitation based on ensemble empirical mode decomposition and Bayesian model averaging

Precipitation prediction is crucial for water resources management and agricultural production. We deployed a hybrid model based on ensemble empirical mode decomposition (EEMD) and Bayesian model averaging (BMA), called EEMD-BMA, for monthly precipitation series data at Kunming station from January 1951 to December 2020. Firstly, the monthly precipitation data series was decomposed into multiple Intrinsic Mode Functions (IMFs) and a residue with EEMD. Next, autoregressive integrated moving average (ARIMA), support vector regression (SVR) and long short-term memory (LSTM) models are used to predict components respectively. The prediction results of EEMD-ARIMA, EEMD-SVR and EEMD-LSTM are obtained by summing the prediction results of each component. Finally, BMA is used to combine the prediction results of the EEMD-ARIMA, EEMA-SVR and EEMD-LSTM models, whose weights are calculated by birth-death Markov Chain Monte Carlo algorithm. The results show that the proposed EEMD-BMA model provides more accurate precipitation predictions than the individual models; the RMSE is 17.2811 mm, the MAE is 12.6999 mm and the R2 is 0.9573. Moreover, the coverage probability (CP) and mean width (MW) of the 90% confidence interval for the predicted values of the EEMD-BMA model are 0.9375 and 60.315 mm, respectively. Therefore, the proposed EEMD-BMA model has good application prospects and can provide a basis for decision makers to develop measures against potential disasters.

Intelligent Optimization of Dosing Uniformity in Ion Implantation Systems

Spatial dose non-uniformity is a key variation of concern in ion implantation. These non-uniformities are often compensated for by adjusting the implantation times spent at each point on the wafer: areas with a low uncompensated dose are assigned more implantation time, while those with a greater dose are assigned reduced times. In this paper, we present a machine learning based method that rapidly learns a set of compensating implantation times in order to achieve a desired uniformity.We propose an iterative tuning approach comprised of two components. The first component is an empirical Bayesian forward model that infers the relationship between the implantation times and the implantation dose profile. The model is updated as new implantations are performed and measured, enabling progressive accuracy improvements during tuning. The second component is an optimization method that selects compensating times by solving a constrained optimization problem. When tuning a process, we alternate between these two components, repeatedly selecting compensating times, measuring the resulting dose profile and updating the model until the desired uniformity is achieved. Our proposed method is compared to the conventional non-Bayesian industry method of record, and converges to a desired uniformity in significantly fewer iterations. Finally, the solutions found by our method result in a greater total dose given the same total implantation time and uniformity, increasing the throughput of implantation with no added cost.