Informative Prior Distributions Research Articles

Atezolizumab in Combination with Bevacizumab for the Management of Patients with Hepatocellular Carcinoma in the First-Line Setting: Systematic Literature Review and Meta-Analysis

Background: In 2020, atezolizumab-bevacizumab became the new standard of care (SOC) for first-line unresectable hepatocellular carcinoma (HCC) patients, following a decade where sorafenib was the preferred first-line treatment. In the last few years, a number of novel systemic treatments with non-inferiority and superiority to sorafenib have been approved as first-line treatments. Objectives: The objective of this systematic literature review (SLR) and network meta-analysis (NMA) was to compare randomised controlled trial evidence for atezolizumab-bevacizumab with globally relevant pharmacological comparators for first-line treatment of patients with unresectable HCC. Methods: Randomised controlled trials investigating first-line treatment of HCC in adults with no prior systemic treatment were eligible for inclusion into the SLR and were retrieved from Embase, MEDLINE, and Evidence-Based Medicine (EBM) Reviews. Interventions of interest for the NMA included atezolizumab-bevacizumab, sorafenib, lenvatinib, durvalumab (including in combination with tremelimumab), cabozantinib (including in combination with atezolizumab), camrelizumab (including in combination with rivoceranib), pembrolizumab (including in combination with lenvatinib), and tislelizumab. Random effects NMA was conducted for survival endpoints within a Bayesian framework with an informative prior distribution for between-study heterogeneity. The hazard ratios for relative treatment effect were estimated with 95% credible intervals (CrIs). Results: The SLR identified 49 studies, of which eight formed a connected evidence network permitting the indirect treatment comparison of atezolizumab-bevacizumab with comparators of interest. The indirect comparisons suggested an improved overall survival (OS) with atezolizumab-bevacizumab versus most comparators. All indirect treatment comparison results for atezolizumab-bevacizumab included the null value within the 95% CrI (n = 1) for OS and progression-free survival (PFS). Conclusions: The results of the NMA indicate atezolizumab-bevacizumab is associated with superior or comparable OS and PFS together with a manageable safety profile compared with globally relevant comparators in the unresected HCC indication. The findings support that atezolizumab-bevacizumab remains SOC for the management of first-line unresectable HCC patients.

Multivariate receptor modeling with widely dispersed Lichens as bioindicators of air quality

AbstractBiomonitoring studies evaluating air quality via airborne element accumulation patterns in lichens typically control variability by focusing on narrow geographic regions and short time windows. Using samples of the widespread “rock‐posy” lichen sampled across the Intermountain Region of the United States, we investigate whether accumulation patterns of generic pollution sources are detectable on broad geographic and temporal scales. We develop a novel Bayesian multivariate receptor modeling (BMRM) approach that sharpens detection and discrimination of candidate pollution sources through (i) regularization of source contributions to each sample and (ii) incorporating estimated lichen secondary chemistry as a factor. Through a simulation study, we demonstrate a distinct advantage in shrinking contributions when they are truly sparse, as would be expected with heterogeneous samples from dispersed collection sites. We contrast analyses employing both standard and sparse BMRMs, and positive matrix factorization (PMF). The sparse model better maintains source identity, as specified though informative prior distributions on elemental profiles. We advocate quantitative profile matching, which reveals that PMF primarily captures variations of the baseline profile for lichen secondary chemistry. Both PMF and BMRM results suggest that the most detectable signatures relate to aeolian dust deposition, while spatial patterns hint at sporadic anthropogenic influence.

A Bayesian Interpretation of a Pediatric Cardiac Arrest Trial (THAPCA-OH)

BackgroundPediatric out-of-hospital cardiac arrest results in high morbidity and mortality. Currently, there are no recommended therapies beyond supportive care. The THAPCA-OH (Therapeutic Hypothermia after Pediatric Cardiac Arrest Out-of-Hospital) trial compared hypothermia (33.0°C) with normothermia (36.8°C) in 295 children. Good neurobehavioral outcome and survival at 1 year were higher in the hypothermia group (20 vs. 12% and 38 vs. 29%, respectively). These differences did not meet the planned statistical threshold of P<0.05. To ensure that a potentially efficacious therapy is not prematurely discarded, we reassessed THAPCA-OH using a Bayesian statistical perspective.MethodsWe performed a Bayesian analysis, interpreting the trial in probabilistic terms (i.e., the probability that therapeutic hypothermia had any benefit, and overall absolute improvements greater than 2%, 5%, and 10% for 1-year neurobehavioral outcome and survival). Our primary analyses used noninformative priors, meaning that the analyses were based on the observed trial data without any information added by the priors. In the absence of pediatric trials to derive informative prior distributions, we used: (1) downweighted priors from adult trials; and (2) a previously published set of critical care priors that span benefit, equipoise, and harm.ResultsIn the primary analyses, the probability of any benefit from hypothermia was 94% for both the neurobehavioral outcome and survival at 1 year. For both outcomes, the probability of benefit was >75% for all informative prior integrations with the THAPCA-OH results, except those with the most pessimistic priors.ConclusionsThere is a high probability that hypothermia provides a modest benefit in neurobehavioral outcome and survival at 1 year. (ClinicalTrials.gov number, NCT00878644.)

Bayesian Estimation of a Scale Parameter of the Gumbel-Lomax Distribution Using Informative and Non Informative Priors

Estimating the scale parameter of the Gumbel-Lomax Distribution using the Bayesian method of estimation and evaluating the estimators by assuming two non-informative prior distributions and one informative prior distribution is very important for the general application of the Gumbel-Lomax distribution. These estimators are obtained using the squared error loss function (SELF), Quadratic loss function (QLF) and precautionary loss function (PLF). The posterior distributions of the scale parameter of the Gumbel-Lomax distribution are derived and the Estimators are also obtained using the above mentioned priors and loss functions. Furthermore, a simulation using a package in R software is carried out to assess the performance of the estimators by making use of the Mean Squared Errors of the Estimators under the Bayesian approach and Maximum likelihood method. Our results show that Bayesian Method using PLF under all priors produces the best estimators of the scale parameter compared to estimators using the Maximum Likelihood method, SELF and QLF under all the priors irrespective of the values of the parameters and the different sample sizes. It is also discovered that the other parameters have no effect on the estimators of the scale parameter.

Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

This paper develops the problem of estimating stress-strength reliability for Gompertz lifetime distribution. First, the maximum likelihood estimation (MLE) and exact and asymptotic confidence intervals for stress-strength reliability are obtained. Then, Bayes estimators under informative and noninformative prior distributions are obtained by using Lindley approximation, Monte Carlo integration, and MCMC. Bayesian credible intervals are constructed under these prior distributions. Also, simulation studies are used to illustrate these inference methods. Finally, a real dataset is analyzed to show the implementation of the proposed methodologies.

Prognostic impact of secondary prevention medical therapy following myocardial infarction with non-obstructive coronary arteries: a Bayesian and frequentist meta-analysis.

Myocardial infarction with non-obstructive coronary arteries (MINOCA) is a clinical entity with several causes and pathophysiologic mechanisms. Secondary prevention with medical therapy used in patients with obstructive coronary artery disease has unclear benefits in MINOCA patients. A literature search was conducted until 8 March 2022. Random-effect frequentist and hierarchical Bayesian meta-analyses were performed to assess the clinical impact of medical therapy [renin-angiotensin-aldosterone system (RAAS) inhibitors, statins, dual antiplatelet therapy (DAPT), β-blockers] in MINOCA patients. Outcomes of interest were all-cause mortality and major adverse cardiovascular events (MACE). A total of 12 663 MINOCA patients among five observational studies were analysed. The mean follow-up ranged from 12 to 90 months across studies. In frequentist meta-analysis, statins and β-blockers were associated with a lower risk of all-cause mortality [pooled adjusted hazard ratios (aHRs) 0.53 and 0.81, with 95% confidence intervals (CIs) (0.37-0.76) and (0.67-0.97), respectively]. Only RAAS inhibitors were associated with a lower risk of MACE [pooled aHR: 0.69, with 95% CI (0.53-0.90)]. Bayesian meta-analysis based on informative prior assumptions offered strong evidence only for the benefit of statins on decreasing the risk of all-cause death [Bayes factor (BF): 33.2] and moderate evidence for the benefit of RAAS inhibitors on decreasing the risk of MACE (BF: 9); assigning less informative prior distributions did not affect the results, yet it downgraded the level of evidence to anecdotal. In this meta-analysis, statins and RAAS inhibitors were consistently associated with a lower risk of all-cause mortality and MACE, respectively, in patients with MINOCA. Neutral prognostic evidence was demonstrated for β-blockers and DAPT.

Inference for a general family of inverted exponentiated distributions under unified hybrid censoring with partially observed competing risks data

In this paper, statistical inference of a competing risks model is developed based on a unified hybrid censoring scheme when the latent failure times follow a general family of inverted exponentiated distributions, which covers a wide range of lifetime distributions. Point and interval estimation methods for estimating the model parameters based on maximum likelihood and Bayesian approaches under non-restricted and restricted parameter spaces are developed. The Bayes estimates are obtained under the squared error loss function with non-informative and informative prior distributions. The existence and uniqueness of the maximum likelihood estimates of the model parameters are proved. A Monte Carlo simulation study is carried out to evaluate the performance of the proposed estimation procedures. To illustrate the proposed inferential procedures, a real data analysis is provided. Finally, some concluding remarks and future research directions are presented.

On the Application of Probabilistic Decline Curve Analysis to Unconventional Reservoirs

Summary Several authors have worked on combining decline curve analysis (DCA) models and stochastic algorithms for probabilistic DCAs. However, there are no publications on the application of these probabilistic decline curve models to all the major shale basins in the United States. Also, several empirical and analytical decline curve models have been developed to fit historical production data better; there is no systematic investigation of the relevance of the efforts on new model development compared with the efforts to quantify the uncertainty associated with the “noise” in the historical data. This work compares the uncertainty associated with determining the best-fit model (epistemic uncertainty) with the uncertainty associated with the historical data (aleatoric uncertainty) and presents a procedure to find DCA-stochastic algorithm combinations that encompass the epistemic uncertainty. We investigated two Bayesian methods—the approximate Bayesian computation and the Gibbs sampler—and two frequentist methods—the conventional bootstrap (BS) and modified BS (MBS). These stochastic algorithms were combined with five empirical DCA models (Arps, Duong, power law, logistic growth, and stretched exponential decline) and the analytical Jacobi theta-2 model. We analyzed historical production data from 1,800 wells (300 wells from each of the six major shale basins studied) with historical data lengths ranging from 12 to 60 months. We show the errors associated with the assumption of a uniform distribution for the model parameters and present an approach for integrating informative prior (IP) probabilistic distributions instead of the noninformative prior (NIP) or uniform prior distributions. Our results indicate the superior performance of the Bayesian methods, especially at short hindcasts (12–24 months of production history). We observed that the duration of the historical production data was the most critical factor. Using long hindcasts (up to 60 months) leveled the performance of all probabilistic methods regardless of the decline curve model or statistical methodology used. Additionally, we showed that it is possible to find DCA-stochastic model combinations that reflect the epistemic uncertainty in most of the shale basins investigated. The novelty of this work lies in the development of IPs for the Bayesian methodologies and the development of a systematic approach to determine the combination of statistical methods and DCA models that encompasses the epistemic uncertainty. The proposed approach was implemented using open-source software packages to make our results reproducible and to facilitate its practical application in forecasting production in unconventional oil and gas reservoirs.

A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme

A new life performance index is proposed for evaluating the quality of lifetime products. The maximum likelihood estimation method and the Bayesian approaches using informative and non-informative prior distributions are utilized to infer the parameters of the Weibull distribution and the proposed new life performance index under a Type-I hybrid censoring scheme. Monte Carlo simulation results show that two Bayesian approaches outperform the maximum likelihood estimation method in terms of the measures of relative bias, relative mean square error, and coverage probability for the point and confidence interval estimators, respectively. The Bayesian approach using a non-informative prior distribution is recommended if the knowledge of setting up the hyper-parameters in the informative prior distribution is not available. Two real data sets are provided for illustration.

Borrowing strength from clinical trials in analysing longitudinal data from a treated cohort: investigating the effectiveness of acetylcholinesterase inhibitors in the management of dementia.

Health care professionals seek information about effectiveness of treatments in patients who would be offered them in routine clinical practice. Electronic medical records (EMRs) and randomized controlled trials (RCTs) can both provide data on treatment effects; however, each data source has limitations when considered in isolation. A novel modelling methodology which incorporates RCT estimates in the analysis of EMR data via informative prior distributions is proposed. A Bayesian mixed modelling approach is used to model outcome trajectories among patients in the EMR dataset receiving the treatment of interest. This model incorporates an estimate of treatment effect based on a meta-analysis of RCTs as an informative prior distribution. This provides a combined estimate of treatment effect based on both data sources. The superior performance of the novel combined estimator is demonstrated via a simulation study. The new approach is applied to estimate the effectiveness at 12 months after treatment initiation of acetylcholinesterase inhibitors in the management of the cognitive symptoms of dementia in terms of Mini-Mental State Examination scores. This demonstrated that estimates based on either trials data only (1.10, SE = 0.316) or cohort data only (1.56, SE = 0.240) overestimated this compared with the estimate using data from both sources (0.86, SE = 0.327). It is possible to combine data from EMRs and RCTs in order to provide better estimates of treatment effectiveness.

Nested Sampling for Non-Gaussian Inference in SLAM Factor Graphs

We present nested sampling for factor graphs (NSFG), a novel nested sampling approach to approximate inference for posterior distributions expressed over factor-graphs. Performing such inference is a key step in simultaneous localization and mapping (SLAM). Although the Gaussian approximation often works well, in other more challenging SLAM situations, the posterior distribution is non-Gaussian and cannot be explicitly represented with standard distributions. Our technique applies to settings where the posterior distribution is substantially non-Gaussian (e.g., multi-modal) and thus needs a more expressive representation. NSFG exploits nested sampling methods to directly sample the posterior to represent the distribution without parametric density models. While nested sampling methods are known for their powerful capability in sampling multi-modal distributions, the application of the methods to SLAM factor graphs is not straightforward. NSFG leverages the structure of factor graphs to construct informative prior distributions which are efficiently sampled and provide notable computational benefits for nested sampling methods. We present simulated experiments which demonstrate that NSFG is more robust and computes solutions over an order of magnitude faster than state-of-the-art sampling techniques. Similarly, we compare NSFG to state-of-the-art Gaussian and non-Gaussian SLAM approaches and demonstrate that NSFG is notably more robust in describing non-Gaussian posteriors.

Persons with physical disabilities and autonomous vehicles: The perspective of the driving status

• Non-drivers with physical disabilities (PD) more prefer to use autonomous vehicles (AV) than drivers. • Persons with PD who live in urban areas prefer to use AV over others. • Persons with PD’s intention to use AV predominantly depends on their view of AV, not their mobility habits. • AV have excellent potential to improve access to transportation and ensure transportation equity. • One solution is introducing AV in the public transport system following accessibility, reliability, and safety principles. Improving access to transportation and ensuring transportation equity for persons with physical disabilities is one of the global challenges. Autonomous vehicles are pointed out as the potential solution to these problems. The views of persons with physical disabilities about autonomous vehicles differed sharply and substantially compared to non-disabled and other persons with disabilities. Therefore, this paper investigates differences in acceptance of autonomous vehicles among different groups of persons with physical disabilities. The driving status criterion was used because this fact significantly impacts the quality of life and social status. The paper’s main contribution is to help create policies and practices related to autonomous vehicles following the real needs of persons with physical disabilities. The research was conducted in a country with vast problems of inclusion of persons with disabilities and transportation equity – Serbia. The Bayesian linear regression models were created with weakly informative prior distributions. We found that non-drivers with physical disabilities prefer to use autonomous vehicles more than drivers. The key issues of the successful introduction of autonomous vehicles are attitudes, accessibility, and trust. Autonomous vehicles present an excellent opportunity to improve mobility and transportation equity for non-drivers with physical disabilities. Transportation stakeholders, vehicle manufacturers, and representative associations of persons with disabilities should cooperate closely, respecting the concept „Nothing about us, without us.”. One solution for resolving recognized challenges is introducing autonomous vehicles in the public transport system following accessibility, reliability, and safety principles.

Bayesian Measurement of Diagnostic Accuracy of the RT-PCR Test for COVID-19

Reverse transcription polymerase chain reaction (RT-PCR) targeting select genes of the SARS-CoV-2 RNA has been the main diagnostic tool in the global response to the COVID-19 pandemic. It took several months after the development of these molecular tests to assess their diagnostic performance in the population. The objective of this study is to demonstrate that it was possible to measure the diagnostic accuracy of the RT-PCR test at an early stage of the pandemic despite the absence of a gold standard. The study design is a secondary analysis of published data on 1014 patients in Wuhan, China, of whom 59.3% tested positive for COVID-19 in RT-PCR tests and 87.6% tested positive in chest computerized tomography (CT) exams. Previously ignored expert opinions in the form of verbal probability classifications of patients with conflicting test results have been utilized here to derive the informative prior distribution of the infected proportion. A Bayesian implementation of the Dawid-Skene model, typically used in the context of crowd-sourced data, was used to reconstruct the sensitivity and specificity of the diagnostic tests without the need for specifying a gold standard. The sensitivity of the RT-PCR diagnostic test developed by China CDC was estimated to be 0.707 (95% Cr I: 0.664, 0.753), while the specificity was 0.861 (95% Cr I: 0.781, 0.956). In contrast, chest CT was found to have high sensitivity (95% Cr I: 0.969, 1.000) but low specificity (95% Cr I: 0.477, 0.742). This estimate is similar to estimates that were found later in studies designed specifically for measuring the diagnostic performance of the RT-PCR test. The developed methods could be applied to assess diagnostic accuracy of new variants of SARS-CoV-2 in the future.

State‐space model combining local camera data and regional administration data reveals population dynamics of wild boar

AbstractRecent increases in wildlife cause negative impacts on humans through both economic and ecological damage, as well as the spread of pathogens. Understanding the population dynamics of wildlife is crucial to develop effective management strategies. However, it is difficult to estimate accurate and precise population size over large spatial and temporal scales because of the limited data availability. We addressed these issues by first fitting a random encounter and staying time (REST) model based on camera trap data to construct an informative prior distribution for a capture rate parameter in a harvest‐based Bayesian state‐space model. We constructed a Bayesian state‐space model that integrated administration data on the number of captured wild boar with the prior distribution of capture efficiency estimated by camera trap data. The model with informative prior distribution from the REST model successfully estimated population dynamics, whereas the model using only the administration data did not, owing to a lack of parameter convergence. We identified areas where (1) wild boars exhibit a high potential population growth rate and a high carrying capacity, (2) current trapping efforts are effectively suppressing local populations, and (3) trapping reinforcement is required to control populations in the whole region. The model could be used to predict future trends in populations under the assumptions of ongoing trapping pressure. This will help identify spatially explicit trapping efforts to achieve target population levels.

ZELLNER’S G-PRIORS IN BAYESIAN MODEL AVERAGING OF LARGE MODEL SPACE USING MARKOV CHAIN MONTE CARLO MODEL COMPOSITION APPLICABLE UNDER BAYESIAN MODEL SAMPLING

Applied researchers are frequently faced with the issue of model uncertainty in situations where many possible models exist. For large model space in regression analysis, the challenge has always been how to select a single model among competing large model space when making inferences. Bayesian Model Averaging (BMA) is a technique designed to help account for the uncertainty inherent in the model selection process. Informative prior distributions related to a natural conjugate prior specification are investigated under a limited choice of a single scalar hyper parameter called g-prior which corresponds to the degree of prior uncertainty on regression coefficients. This study focuses on situations with extremely large model space made up of large set of regressors generated by a small number of observations, when estimating model parameters. A set of g-prior structures in literature are considered with a view to identify an improved g-prior specification for regression coefficients in Bayesian Model Averaging. The study demonstrates the sensitivity of posterior results to the choice of g-prior on simulated dataand real-life data. Markov Chain Monte Carlo (MCMC) are used to generate a process which moves through large model space to adequately identify the high posterior probability models using the Markov Chain Monte Carlo Model Composition (MC3), a method applicable under Bayesian Model Sampling (BMS). To assess the sensitivity and predictive ability of the g-priors,predictive criteria like Log Predictive Score (LPS) and Log Marginal Likelihood (LML) are employed. The results reveal a g-prior structure that exhibited equally competitive and consistent predictive ability among considered g-prior structures in literature.

Bayesian Approach for Confidence Intervals of Variance on the Normal Distribution

This research aims to compare estimating the confidence intervals of variance based on the normal distribution with the primary method and the Bayesian approach. The maximum likelihood is the well-known method to approximate variance, and the Chi-squared distribution performs the confidence interval. The central Bayesian approach forms the posterior distribution that makes the variance estimator, which depends on the probability and prior distributions. Most introductory prior information looks for the availability of the prior distribution, informative prior distribution, and noninformative prior distribution. The gamma, Chi-squared, and exponential distributions are defined in the prior distribution. The informative prior distribution uses the Markov Chain Monte Carlo (MCMC) method to draw the random sample from the posterior distribution. The Fisher information performs the Wald confidence interval as the noninformative prior distribution. The interval estimation of the Bayesian approach is obtained from the central limit theorem. The performance of these methods considers the coverage probability and minimum value of the average width. The Monte Carlo process simulates the data from a normal distribution with the true parameter of mean and several variances and the sample sizes. The R program generates the simulated data repeated 10,000 times in each situation. The results showed that the maximum likelihood method employed on the small sample sizes. The best confidence interval estimation was when sample sizes increased the Bayesian approach with an available prior distribution. Overall, the Wald confidence interval tended to outperform the large sample sizes. For application in real data, we expressed the reported airborne particulate matter of 2.5 in Bangkok, Thailand. We used the 10–1000 records to estimate the confidence interval of variance and evaluated the interval width. The results are similar to those of the simulation study.

Bayesian and non‐Bayesian inference of Weibull lifetime model based on partially observed competing risks data under unified hybrid censoring scheme

AbstractIn this paper, a competing risk model is analyzed based on unified hybrid censoring scheme (UHCS). It is assumed that the latent failure times follow Weibull distributions with a common shape and different scale parameters. The maximum likelihood estimates (MLEs) and approximate confidence intervals (ACIs) of the distributional parameters are obtained. Sufficient conditions under which the MLEs exist (uniquely) have been studied. Further, the Bayes estimates are obtained with respect to symmetric and asymmetric loss functions. The non‐informative and informative prior distributions are considered for computing the approximate Bayes estimates. Furthermore, the highest posterior density (HPD) credible intervals have been obtained by using Markov Chain Monte Carlo (MCMC) method with the Gibbs sampling technique. The coverage probabilities for each confidence interval are computed. Then, hypothesis testing has been implemented using likelihood ratio statistic. A Monte Carlo simulation study is carried out to compare the performance of the proposed estimates. Finally, two real data sets are provided to illustrate the estimates.

Short-term Bayesian ETAS spatiotemporal forecasting of the Ölfus 2008 earthquake sequence in Iceland

Strong earthquakes occurring frequently in south Iceland are always characterized by intense aftershock activity. The aftershock sequences cause progressive damages to structures and considerable psychological strain on inhabitants as the threat of upcoming large earthquakes looms. In this study, we apply a Bayesian epidemiological spatiotemporal aftershock sequence (ETAS) clustering model to forecast the aftershock sequence that commenced with the damaging 29 May 2008 Mw6.3 Ölfus earthquake. The forecast is carried out manually but in a framework of a provisional operational earthquake forecasting (OEF) system and based on an informative set of ETAS parameters derived from the strong June 2000 sequence in the region. We show that the short-term forecasts are unreliable at the early stages of the ongoing seismic sequence due to incomplete aftershocks collected to feed the Bayesian updating procedure of the ETAS model parameters, mainly during the first hours after the Ölfus mainshock. In contrast, issuing 24-h long forecasts, starting 6–8 h after the mainshock gives the best forecasting results. We allow the daily forecasts to adapt to the ongoing 2008 sequence using the adaptive prior estimation method, i.e., by assigning an informative prior distribution to ETAS parameters for the subsequent forecasting interval based on the preceding ETAS parameter posterior distributions. The parametric posteriors do not show narrow distributions, thus indicating inconsistent forecasting performance, both in stark contrast to the June 2000 sequence. Regardless, our results provide a quantitative estimate of the reliability of the forecasts which is a prerequisite for evaluating their usefulness to civil protection.

Modelagem bayesiana das vazões máximas do reservatório de Furnas

The objective of this work was to predict the maximum flow of the Furnas reservoir in the dry and wet periods. The generalized distribution of extreme values (GEV) was used with parameter estimation via Bayesian inference. Data on average daily streamflows corresponding to the years 1965 to 2017 were obtained from Hidroweb, by the National Agency for Water and Basic Sanitation (Agência Nacional de Águas e Saneamento Básico – ANA), from which maximum values were extracted, by period and in each year. Accuracy and mean error of prediction of maximum streamflows were analyzed, comparing the estimates provided by the Bayesian inference, with informative and non-informative prior distributions. Information from a series of maximum streamflows from the Camargos reservoir was used to elicit the informative prior distribution. The use of prior information provided an increase in the precision and accuracy of the maximum streamflow estimates. Thus, the GEV model, with informative a priori distribution, was used to predict the return levels of Furnas maximum streamflow with their respective high posterior density intervals considering several return times.

Spatial Correlation Aware Compressed Sensing for User Activity Detection and Channel Estimation in Massive MTC

Grant-free access is considered as a key enabler for massive machine-type communications (mMTC) as it promotes energy-efficiency and small signalling overhead. Due to the sporadic user activity in mMTC, joint user identification and channel estimation (JUICE) is a main challenge. This paper addresses the JUICE in single-cell mMTC with single-antenna users and a multi-antenna base station (BS) under spatially correlated fading channels. In particular, by leveraging the sporadic user activity, we solve the JUICE in a multi measurement vector compressed sensing (CS) framework under two different cases, with and without the knowledge of prior channel distribution information (CDI) at the BS. First, for the case without prior information, we formulate the JUICE as an iterative reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm minimization problem. Second, when the CDI is known to the BS, we exploit the available information and formulate the JUICE from a Bayesian estimation perspective as a maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> probability (MAP) estimation problem. For both JUICE formulations, we derive efficient iterative solutions based on the alternating direction method of multipliers (ADMM). The numerical experiments show that the proposed solutions achieve higher channel estimation quality and activity detection accuracy with shorter pilot sequences compared to existing algorithms.