Sequential Bayesian Model Research Articles

Estimation of the basic reproduction number of Alpha and Delta variants of COVID-19 pandemic in Iran.

Estimating the basic reproduction number of a pandemic and the changes that appear on this value over time provide a good understanding of the contagious nature of the virus and efficiency of the controlling strategies. In this paper, we focus on studying the basic reproduction number (R0) for two important variants of COVID-19 pandemic in Iran: Alpha and Delta variants. We use four different methods, three statistical models and one mathematical model, to compute R0: Exponential Growth Rate (EGR), Maximum Likelihood (ML), Sequential Bayesian (SB), and time-dependent SIR model. Alpha variant of COVID-19 was active in Iran from March 10, 2021 until June 10, 2021. Our computations indicate that total R0 of this variant according to EGR, ML, SB, and SIR model is respectively 0.9999 (95% CI: 0.9994-1), 1.046 (95% CI: 1.044-1.049), 1.06 (95% CI: 1.03-1.08), and 2.79 (95% CI: 2.77-2.81) in the whole active time interval. Moreover, during the time interval from April 3, 2021 to April 9, 2021 in which this variant was in its exponential growth in Iran, R0 of Alpha variant in Iran according to SB, EGR, ML, and SIR model is respectively 2.26 (95% CI: 2.04-2.49), 2.64 (95% CI: 2.58-2.7), 11.38 (95% CI: 11.28-11.48), and 12.13 (95% CI: 12.12-12.14). Delta variant was active in Iran during the time interval from June 22, 2021 until September 22, 2021. Our computations show that during the time interval from July 3, 2021 to July 8, 2021 in which this variant was in its exponential growth in Iran, R0 of Delta variant in Iran according to SB, EGR, ML, and SIR model is respectively 3 (95% CI: 2.34-3.66), 3.1 (95% CI: 3.02-3.17), 12 (95% CI: 11.89-12.12), and 23.3 (95% CI: 23.19-23.41). Further, total R0 of Delta variant in Iran in the whole active time interval according to EGR, ML, SB, and SIR model is respectively 1.042 (95% CI: 1.04-1.043), 1.053 (95% CI: 1.051-1.055), 0.79 (95% CI: 0.63-0.95), and 5.65 (95% CI: 5.6-5.7). As the results show Delta variant was more severe than Alpha variant in Iran. Chasing the changes in R0 during each variant shows that the controlling strategies applied were effective in controlling the virus spread.

Bridge Digital Twinning Using an Output-Only Bayesian Model Updating Method and Recorded Seismic Measurements.

Rapid post-earthquake damage diagnosis of bridges can guide decision-making for emergency response management and recovery. This can be facilitated using digital technologies to remove the barriers of manual post-event inspections. Prior mechanics-based Finite Element (FE) models can be used for post-event response simulation using the measured ground motions at nearby stations; however, the damage assessment outcomes would suffer from uncertainties in structural and soil material properties, input excitations, etc. For instrumented bridges, these uncertainties can be reduced by integrating sensory data with prior models through a model updating approach. This study presents a sequential Bayesian model updating technique, through which a linear/nonlinear FE model, including soil-structure interaction effects, and the foundation input motions are jointly identified from measured acceleration responses. The efficacy of the presented model updating technique is first examined through a numerical verification study. Then, seismic data recorded from the San Rogue Canyon Bridge in California are used for a real-world case study. Comparison between the free-field and the foundation input motions reveals valuable information regarding the soil-structure interaction effects at the bridge site. Moreover, the reasonable agreement between the recorded and estimated bridge responses shows the potentials of the presented model updating technique for real-world applications. The described process is a practice of digital twinning and the updated FE model is considered as the digital twin of the bridge and can be used to analyze the bridge and monitor the structural response at element, section, and fiber levels to diagnose the location and severity of any potential damage mechanism.

Comparison of Different Approaches in Estimating Initial Reproduction Number of SARS-CoV-2 in the Islamic Republic of Iran

Background: The basic reproduction number (R0) is an epidemic threshold parameter that indicates the magnitude of disease transmission and thus allows suggestions for the planning of control measures. Objectives: Our aim in this study was to compare different approaches for estimating R0 in the early stage of the SARS-CoV-2 outbreak and discern the best-fitting model. Methods: The dataset was derived from cumulative laboratory-confirmed COVID-19 cases from 26th February to 30th May 2020 in Iran. The methods of exponential growth (EG) rate, maximum likelihood (ML), time-dependent (TD) reproduction number, attack rate (AR), and sequential Bayesian (SB) model were used. The gamma distribution (mean 4.41 ± 3.17 days) was used for serial interval (SI) distribution. The best-fitting method was selected according to the lowest root mean square error (RMSE). Results: We obtained the following estimated R0 [95% confidence interval]: 1.55 [1.54; 1.55], 1.46 [1.45; 1.46], 1.31 [1.30; 1.32], and 1.40 [1.39; 1.41] using EG, ML, TD, and SB methods, respectively. Additionally, the EG and ML methods showed an overestimation of R0, and the SB method showed to be under-fitting in the estimation of R0. The AR method estimated R0 equal to one. The TD method had the lowest RMSE. Conclusions: The simulated and actual R0 of TD showed that this method had a good fit for actual data and the lowest RMSE. Therefore, the TD method is the most appropriate method with the best performance in estimating actual R0 values.

A Sequential Bayesian Updated Wiener Process Model for Remaining Useful Life Prediction

Wiener processes have been extensively used to model the degradation processes exhibiting a linear trend for predicting the remaining useful life (RUL) of degrading components. To incorporate the real-time degradation monitoring information into degradation modeling, the Bayesian method has been frequently utilized to update the model parameter, particularly for the drift parameter in Wiener process. However, due to the inherent independent increment and Markov properties of Wiener process, the Bayesian updated drift parameter only utilizes the current degradation measurement and cannot incorporate the whole degradation measurements up to now. As such, once the updated degradation model in this way is used to predict the RUL, the obtained result may be dominated by partial degradation observations or lower the prognosis accuracy. In this paper, we propose a sequential Bayesian updated Wiener process model for RUL prediction. First, a Wiener process model with random drift efficient is used to model the degradation process with the linear trend. To estimate the model parameters, the historical degradation measurements are used to determine the initial model parameters based on the maximum likelihood estimation (MLE) method. Then, for the degrading component in service, a sequential Bayesian method is proposed to update the random drift parameter in Wiener process model. Differing from existing studies using the Bayesian method, the proposed sequential method uses the Bayesian estimate for random drift parameter in the last time as the prior of the next time. As such, the Bayesian estimate for random drift parameter in the current time is dependent on the whole degradation measurements up to current time, and thus the problem of depending only on the current degradation measurement is solved. Finally, we derive the analytical expressions of the RUL distribution based on the concept of the first passage time (FPT). Two case studies associated with the gyroscope drift data and lithium-ion battery data are provided to show the effectiveness and superiority of the proposed method. The results indicate that the proposed method can improve the RUL prediction accuracy.

Sequential Bayesian Analysis of Bernoulli Opinion Polls; a Simulation-Based Approach

In this paper we apply sequential Bayesian approach to compare the outcome of the presidential polls in Kenya. We use the previous polls to form the prior for the current polls. Even though several authors have used non-Bayesian models for countrywide polling data to forecast the outcome of the presidential race we propose a Bayesian approach in this case. As such the question of how to treat the previous and current pre-election polls data is inevitable. Some researchers consider only the most recent poll others Combine all previous polls up the present time and treat it as a single sample, weighting only by sample size, while others Combine all previous polls but adjust the sample size according to a weight function depending on the day the poll is taken. In this paper we apply a sequential Bayesian model (as an advancement of the latter which is time sensitive) where the previous measure is used as the prior of the current measure. Our concern is to model the proportion of votes between two candidates, incumbent and challenger. A Bayesian model of our binomial variable of interest will be applied sequentially to the Kenya opinion poll data sets in order to arrive at a posterior probability statement. The simulation results show that the eventual winner must lead consistently and constantly in at least 60% of the opinions polls. In addition, a candidate demonstrating high variability is more likely to lose the polls.

A Bayesian decision support sequential model for severity of illness predictors and intensive care admissions in pneumonia

BackgroundCommunity-acquired pneumonia (CAP) is one of the leading causes of morbidity and mortality in the USA. Our objective was to assess the predictive value on critical illness and disposition of a sequential Bayesian Model that integrates Lactate and procalcitonin (PCT) for pneumonia.MethodsSensitivity and specificity of lactate and PCT attained from pooled meta-analysis data. Likelihood ratios calculated and inserted in Bayesian/ Fagan nomogram to calculate posttest probabilities. Bayesian Diagnostic Gains (BDG) were analyzed comparing pre and post-test probability. To assess the value of integrating both PCT and Lactate in Severity of Illness Prediction we built a model that combined CURB65 with PCT as the Pre-Test markers and later integrated the Lactate Likelihood Ratio Values to generate a combined CURB 65 + Procalcitonin + Lactate Sequential value.ResultsThe BDG model integrated a CUBR65 Scores combined with Procalcitonin (LR+ and LR-) for Pre-Test Probability Intermediate and High with Lactate Positive Likelihood Ratios. This generated for the PCT LR+ Post-test Probability (POSITIVE TEST) Posterior probability: 93% (95% CI [91,96%]) and Post Test Probability (NEGATIVE TEST) of: 17% (95% CI [15–20%]) for the Intermediate subgroup and 97% for the high risk sub-group POSITIVE TEST: Post-Test probability:97% (95% CI [95,98%]) NEGATIVE TEST: Post-test probability: 33% (95% CI [31,36%]) . ANOVA analysis for CURB 65 (alone) vs CURB 65 and PCT (LR+) vs CURB 65 and PCT (LR+) and Lactate showed a statistically significant difference (P value = 0.013).ConclusionsThe sequential combination of CURB 65 plus PCT with Lactate yielded statistically significant results, demonstrating a greater predictive value for severity of illness thus ICU level care.

A Socratic epistemology for verbal emotional intelligence

We describe and experimentally validate a question-asking framework for machine-learned linguistic knowledge about human emotions. Using the Socratic method as a theoretical inspiration, we develop an experimental method and computational model for computers to learn subjective information about emotions by playing emotion twenty questions (EMO20Q), a game of twenty questions limited to words denoting emotions. Using human–human EMO20Q data we bootstrap a sequential Bayesian model that drives a generalized pushdown automaton-based dialog agent that further learns from 300 human–computer dialogs collected on Amazon Mechanical Turk. The human–human EMO20Q dialogs show the capability of humans to use a large, rich, subjective vocabulary of emotion words. Training on successive batches of human–computer EMO20Q dialogs shows that the automated agent is able to learn from subsequent human–computer interactions. Our results show that the training procedure enables the agent to learn a large set of emotion words. The fully trained agent successfully completes EMO20Q at 67% of human performance and 30% better than the bootstrapped agent. Even when the agent fails to guess the human opponent’s emotion word in the EMO20Q game, the agent’s behavior of searching for knowledge makes it appear human-like, which enables the agent to maintain user engagement and learn new, out-of-vocabulary words. These results lead us to conclude that the question-asking methodology and its implementation as a sequential Bayes pushdown automaton are a successful model for the cognitive abilities involved in learning, retrieving, and using emotion words by an automated agent in a dialog setting.

Sequential Bayesian Model Selection of Regular Vine Copulas

Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student's t copula. This paper presents two contributions related to model selection of regular vine copulas. First, our pair copula family selection procedure extends existing Bayesian family selection methods by allowing pair families to be chosen from an arbitrary set of candidate families. Second, our method represents the first Bayesian model selection approach to include the regular vine density construction in its scope of inference. The merits of our approach are established in a simulation study that benchmarks against methods suggested in current literature. A real data example about forecasting of portfolio asset returns for risk measurement and investment allocation illustrates the viability and relevance of the proposed scheme.

Application of time dependent probabilistic collision state checkers in highly dynamic environments.

When computing the trajectory of an autonomous vehicle, inevitable collision states must be avoided at all costs, so no harm comes to the device or pedestrians around it. In dynamic environments, considering collisions as binary events is risky and inefficient, as the future position of moving obstacles is unknown. We introduce a time-dependent probabilistic collision state checker system, which traces a safe route with a minimum collision probability for a robot. We apply a sequential Bayesian model to calculate approximate predictions of the movement patterns of the obstacles, and define a time-dependent variation of the Dijkstra algorithm to compute statistically safe trajectories through a crowded area. We prove the efficiency of our methods through experimentation, using a self-guided robotic device.

Computational prediction and validation of an expert's evaluation of chemical probes.

In a decade with over half a billion dollars of investment, more than 300 chemical probes have been identified to have biological activity through NIH funded screening efforts. We have collected the evaluations of an experienced medicinal chemist on the likely chemistry quality of these probes based on a number of criteria including literature related to the probe and potential chemical reactivity. Over 20% of these probes were found to be undesirable. Analysis of the molecular properties of these compounds scored as desirable suggested higher pKa, molecular weight, heavy atom count, and rotatable bond number. We were particularly interested whether the human evaluation aspect of medicinal chemistry due diligence could be computationally predicted. We used a process of sequential Bayesian model building and iterative testing as we included additional probes. Following external validation of these methods and comparing different machine learning methods, we identified Bayesian models with accuracy comparable to other measures of drug-likeness and filtering rules created to date.

Information Acquisition and Voluntary Disclosure in an Export‐Processing System

We study a strategic information management problem in the export‐processing trade, where the buyer controls the raw material input and sales and the producer is responsible for production. The production is vulnerable to random yield risk. The producer can exert a costly effort to acquire the private yield rate information and discretionarily share it with the buyer. We develop a sequential Bayesian game model that captures three key features of the system—endogenous information endowment, voluntary disclosure, and ex post information sharing—a significant departure from the literature. The optimal disclosure strategy is driven by the trade‐off between the gains from Pareto efficiency improvement and self‐interested overproduction. It is specified by two thresholds on yield rate: only the middle‐yield producers (with yield rate between these two thresholds) share private information to improve supply‐demand match; the low‐ and high‐yield producers withhold information to extract excess input from the buyer. The buyer in response penalizes nondisclosure with reduced input and rewards information sharing with a larger order. This strategic interaction is further exacerbated by the double marginalization effect from decentralization, resulting in severe efficiency loss. We examine the effectiveness of three corrective mechanisms—vertical integration, mandatory disclosure, and production restriction—and reveal the costs of information suppressive effect and overinvestment incentive and the benefit from concessions on the processing fee. Our study endogenizes the asymmetric supply risk and provides the first attempt to rationalize the strategic interactions of informational and operational incentives in the export‐processing system.

Non Pegilated Liposomal Doxorubicin (TLC-D99; Myocet ™) Can Be Safely and Effectively Used As Part of the R-COMP Regimen in Patients with Diffuse Large B-Cell Lymphoma Who Show Contraindications to Anthracyclines Due to Concomitant Moderate/Severe Heart Disease. Results of the HEART01 Phase II trial by the Fondazione Italiana Linfomi (NCT01009970)

AbstractAbstract 3644 Background:R-CHOP is the standard treatment for Diffuse Large B-Cell Lymphoma (DLBCL) but is usually contraindicated in patients with concomitant heart disease due to the unsafe cardiac profile of doxorubicin. The encapsulation of doxorubicin into liposomes modifies its pharmacokinetic reducing its concentration in the heart. We conducted a multicenter phase II trial investigating activity and safety of R-COMP regimen where conventional doxorubicin was substituted with non-pegilated liposomal doxorubicin (TLC-D99; Myocet ™) in patients with DLBCL presenting with moderate/severe concomitant heart disease. Methods:Main inclusion criteria were: age >18 years, diagnosis of DLBCL, no previous oncological treatments. Patients were also required to have cardiac disorder defined by at least one of the following: left ventricular ejection fraction (LVEF) < 50%, left ventricular hypertrophy, uncontrolled moderate/severe arterial hypertension, history of ischemic cardiopathy, clinically significant ventricular arrhythmia, atrial fibrillation (AF), pulmonary hypertension, moderate/severe mitral valvular disorder, moderate aortic valvular disorder. Enrolled patients received 6 courses of 3-weekly R-COMP (rituximab 375 mg/m2, cyclophosphamide 750 mg/m2, vincristine 1.4 mg/m2, TLC-D99 50 mg/m2, prednisone 40 mg/m2/day day 1–5). Cardiac function was monitored with LVEF and electrocardiogram (ECG) after cycle 3, at the end of treatment, and during follow-up. It was adopted a Bayesian sequential design that required the monitoring of complete reponse (CR) and cardiac events (CE) rates defined as primary endpoints. Response was defined according to international criteria (Cheson 2007). CE were defined as a LVEF < 25%, a LVEF reduction > 20% from baseline, or occurrence of significant cardiac disorder. Initial study assumptions were a CR rate of at least 70% and a rate of CE below 20%; with a power of 80% and a level of significance of 5%, the study sample was fixed at 50 patients. The proposed strategy would be considered as active and safe if at least 26 CRs and no more than 14 CEs were recorded at the end of the study. Results:Between 2009 and 2011, 51 patients were enrolled. One patient was excluded after registration due to violation of inclusion criteria. Median age was 77 years (range 53 – 91 years), 69% were male and 33% had stage IV disease. IPI score at study entry was 0–1 in 25%, 2 in 25%, and 3–5 in 50%. Sixty-three cardiac disorders were identified at baseline; the most frequent was ischemic cardiopathy (40%), followed by AF (17%), baseline LVEF <50% (16%), left ventricular hypertrophy (16%); 2 and 3 concomitant cardiac disorders were described in 4 patients; altered profiles at baseline ECG were detected in 38% patients. Median baseline LVEF was 58%. Treatment was completed in 76% of patients with a median dose intensity for TLC-D99 of 98%. R-COMP was interrupted prematurely due to lack of response (n=1), CEs (n=5), severe infection (n=2), deep venous thrombosis (n=1), renal failure (n=1), other toxicity (n=1), and patient’s decision (n=1). As requested by the sequential Bayesian model, the CR rate and the rate of CE never fell outside activity and safety boundaries. In fact, 27 patients achieved a CR (55%; 95%CI=42–72%) and 6 CE were observed, which included significant LVEF reduction (2 patients), clinically significant s-troponine increase (2), hearth failure (1), and cardiac arrest (1). Median LVEF after cycle 3 and at the end of treatment was 59% (range 25–72%) and 56% (30–69%), without significant modifications from baseline values. Grade 3–4 hematological toxicity included neutropenia in 67% of pcases, anemia and thrombocytopenia in 10% each, and infections in 4%.With a median follow-up of 13 months (range 1–28) 6 patients had lymphoma progression, 6 experienced relapse and 6 died without signs of lymphoma relapse/progression. Overall, 10 patients died due to lymphoma (2), severe infection (2), second cancer (1), hemorrhage (1), myocardial infarction (1), renal insufficiency (1), respiratory insufficiency (1), and unknown cause (1). The 1-year OS and PFS were 76% (95%CI: 58–87%) and 60% (95%CI: 42–74%), respectively. Conclusions:The substitution of conventional doxorubicin with non pegilated liposomal doxorubicin (TLCD99-Myocet™) in the R-CHOP regimen is a safe and active option for patients with DLBCL presenting with concomitant moderate/severe cardiac disorders. Disclosures:No relevant conflicts of interest to declare.

Toward reduction of model uncertainty: Integration of Bayesian model averaging and data assimilation

Multimodeling in hydrologic forecasting has proved to improve upon the systematic bias and general limitations of a single model. This is typically done by establishing a new model as a linear combination or a weighted average of several models with weights on the basis of individual model performance in previous time steps. The most commonly used multimodeling method, Bayesian model averaging (BMA), assumes a fixed probability distribution around individual models' forecast in establishing the prior and uses a calibration period to determine static weights for each individual model. More recent work has focused on a sequential Bayesian model selection technique with weights that are adjusted at each time step in an attempt to accentuate the dynamics of an individual model's performance with respect to the system's response. However, these approaches still assume a fixed distribution around the individual models' forecast. A new sequential Bayesian model‐averaging technique is developed incorporating a sliding window of individual model performance around the forecast. Additionally, this new technique relaxes the fixed distribution assumption in establishing the prior utilizing a particle filter data assimilation method that reflects both the performance dynamics of the models' forecasts along with their uncertainty. A comparative analysis of the different BMA strategies is performed across different rates of change in the hydrograph. Results show that methods employing the particle filter show higher probabilistic skill in high ranges of volatility but are overconfident in medium and low ranges of volatility.

Melody Tracking Based on Sequential Bayesian Model

This paper proposes a melody tracking algorithm based on the state-space equation of the parameters that define melody. The parameters that consist of melody pitch and harmonic amplitudes are assumed to follow two uncoupled first-order Markov processes, and the polyphonic audio is related to the parameters such that the current framed segment of the polyphonic audio is conditionally independent of other framed segments given the parameters. The transition probability of the melody pitch is defined based on a number of statistical characteristics of music that account for small and large variation in melody, and for reasons of mathematical tractability, the transition probability of harmonic amplitude is assumed to be Gaussian. To estimate and track the parameters, the sequential Monte Carlo method is utilized. Experimental results show that the performance of the proposed algorithm is better than or comparable to other well-known melody extraction algorithms in terms of the raw pitch accuracy (RPA) and the raw chroma accuracy (RCA).

Information Acquisition and Voluntary Disclosure in an Export-Processing System

We study a strategic information management problem in the export-processing trade, where the buyer controls the raw material input and sales and the producer is responsible for production. The production is vulnerable to random yield risk. The producer can exert a costly effort to acquire the private yield rate information and discretionarily share it with the buyer. We develop a sequential Bayesian game model that captures three key features of the system --- endogenous information endowment, voluntary disclosure, and ex post information sharing --- a significant departure from the literature. The optimal disclosure strategy is driven by the trade-off between the gains from Pareto efficiency improvement and self-interested overproduction. It is specified by two thresholds on yield rate: only the middle producers with yield rate between these two thresholds share private information to improve supply-demand match; the low- and high-yield producers withhold information to extract excess input from the buyer. The buyer in response penalizes nondisclosure with reduced input and rewards information sharing with a larger order. This strategic interaction is further exacerbated by the double marginalization effect from decentralization, resulting in severe efficiency loss. We examine the effectiveness of three corrective mechanisms --- vertical integration, mandatory disclosure, and production restriction --- and reveal the costs of information suppressive effect and overinvestment incentive, and the benefit from concessions on processing fee. Our study endogenizes the asymmetric supply risk and provides the first attempt to rationalize the strategic interactions of informational and operational incentives in the export-processing system.

A Sequential Bayesian Control Model for Influenza-Like Illnesses and Early Detection of Intentional Outbreaks

ABSTRACT Data pertaining to influenza and influenza-like illnesses (ILI) are being used in the United States and around the globe to assess evidence of influenza activity, whether it is the natural course of the flu or intentional release of a biological agent with flu-like symptoms. These data, used in surveillance, are unstable, serially correlated, and non-stationary. An important goal is to detect, as soon as possible, either emergence of an epidemic or release of biological agent whose symptoms may be initially classified as ILI. Statistical methodologies for analyzing these data are currently short of being able to capture all their important structural details and are generally deficient. Tools from statistical process control (SPC) are, on the face of it, ideally suited for the task since they address a problem of detecting sudden shift against a background of random variability. However, traditional SPC methods are generally deficient in assuming exact knowledge of the background prevalence and in relying on over simplified models. The objective of this article is to use a Bayesian model to find statistical and data-driven evidence for a surveillance problem based on the U.S. Sentinel ILI data. Bayesian statistical methodologies applied to SPC are very well suited for this setting of partial but imperfect information on the parameters describing these data. This article provides a control algorithm capable to act in detect-to-warn fashion on near-real-time data, to increase the ability to detect unusual surges in the prevalence of ILIs. We defined a model that uses sequential update methods to chart the discrepancy between the observed and predicted incidence of ILI.

Use of sequential Bayesian model in diagnosis of jaundice by computer.

A sequential Bayesian model has been developed for a computer and used to diagnose jaundiced patients admitted to hospital. Up to 102 items of information from the history, physical examination, and special investigations available within 48 hours of admission were collected on 309 patients. The results from these patients were used to calculate the probabilities of 11 possible diseases in 65 new patients and also to place patients into groups for medical or surgical treatment.The overall accuracy of the model in diagnosing patients as having one of 11 diseases was 69%, and where the final probability reached > 0.96, it was 89%. The overall accuracy in making a medical or surgical decision was 89%, and where the final probability reached > 0.96 it was 94%.Improvement in accuracy should result as the number of cases seen with rare conditions increases, and probably a similar model could be developed and used to make most use of those indicants with the highest cost-effectiveness.