Binomial Distribution Research Articles

Assessing the association between multiple parental alcohol events and the risk of being maltreated children in a New Zealand population-based birth cohort.

Child maltreatment is an important component of alcohol's harm to others. No previous studies have assessed the association between multiple parental alcohol events and child maltreatment. This study aimed to measure the impact of parental alcohol-attributable events on the incidence rate of child maltreatment events over the span of childhood and adolescence in New Zealand. Longitudinal analysis using the birth cohort data of all live births (n = 58 359) in New Zealand in 2000, with the cohort followed until age 17 years using linked data from the Statistics New Zealand Integrated Data Infrastructure (IDI) from 1995 to 2017. Zero-inflated negative binomial and count regression models were used to measure the association between the number of child maltreatment events [collected from publicly funded hospital discharges, Programme for the Integration of Mental Health Data (PRIMHD), Oranga Tamariki, Children's Action Plan (CAP) and police data sets] and parental exposure to alcohol-attributable hospitalization or service use for mental health/addiction. Potential confounders were included for parents and children. Of 58 359 children in the cohort, 86% (50 319) had not experienced any documented maltreatment events. Among those at risk of being maltreated children, the maltreatment incidence rate ratio increased by 35.2% (95% confidence interval = 18.1-55.6%) if a child was exposed to parental alcohol-attributable hospitalization or service use for mental health addiction events. For each additional parental alcohol-attributable hospitalization or service use for mental health or addiction, the risk of being maltreated children increased by 12.8%. In New Zealand, hazardous alcohol consumption by parents appears to be associated with child maltreatment alongside other contributing factors, in particular parental lower educational attainment.

Effects of Inpatient Hospice Care on Cost and Medication Use in Patients with Lung Cancer: A Population-Based Retrospective Study in South Korea.

Background: Inpatient hospices (IHs) can alleviate distress and address economic burdens on patients with terminal cancer. However, there have been inconsistent findings regarding IHs in terms of cost savings and medication use. Objective: We aimed to examine cost savings associated with IHs, according to the timing of first hospitalization before death, and analyze their use of medication, among Korean patients with terminal lung cancer. Methods: Using the South Korean national health insurance claim database, we identified 31,139 patients with lung cancer who died between 2017 and 2020. Their daily hospitalization costs were analyzed using a generalized linear model stratified by time of first hospitalization before death. Medication use was examined using a negative binomial model. Results: IHs spent $134, and $21 less on patients during days 1-7, and 8-30 before death, but $18, $44, $36, and $54 more during days 31-60, 61-90, and 91-180, respectively, compared with non-IHs (all p < 0.05). However, total hospitalization costs in the year preceding death did not differ (relative risk: 0.990, 95% confidence interval [CI]: 0.972-1.007, p > 0.05). IHs used 2.103 times more opioid analgesics (95% CI: 1.980-2.233, p < 0.001). They also used more antiemetics, delirium medications, and antianxiety agents, as well as fewer antidepressive agents, systemic steroids, diuretics, total parenteral nutrition, and antibiotics (all p < 0.05). Conclusions: Patients with terminal lung cancer in IHs in Korea were more likely to receive symptom-oriented medications and experienced reduced hospitalization costs only during the 30 days preceding death.

Probabilistic poly-Bernoulli numbers

ABSTRACT Assume that is Y a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study probabilistic poly-Bernoulli numbers associated with Y, as probabilistic extensions of poly-Bernoulli numbers. We derive explicit expressions, some related identities and a symmetric relation for those numbers. We also investigate explicit expressions for the modified probabilisitc Bernoulli numbers associated with Y, which are slightly different from probabilisitic Bernoulli numbers associated with Y. As special cases of Y, we treat the Poisson, gamma and Bernoulli random variables.

Long COVID and financial hardship: A disaggregated analysis at income and education levels.

To examine how long COVID is associated with financial hardship (food insecurity, inability to pay bills, or threat of losing service) across income and education levels, and to assess the role of employment loss or reduced work hours in this hardship. We used nationally representative data on 271,076 adults from the 2022 Behavioral Risk Factor Surveillance System (BRFSS). We used multivariable binomial logistic regression models to estimate the average marginal effect of long COVID on financial hardships across multiple income and education groups. In general, we found a significant positive association between long COVID and the three measures of financial hardships across income and education groups (1-11 percentage points increase, 95% CI 0.00-0.02 and 0.07-0.14, respectively). Mediation analysis showed that lost or reduced hours of employment accounted for a significant portion (6%-20%) of the changes in financial distress. Long COVID has affected the economic wellbeing of people from all socioeconomic statuses, although at a higher rate for lower income groups. Policy attention is needed to address its economic impacts across income and education levels.

Evaluation of RT-QuIC Diagnostic Performance for Chronic Wasting Disease Detection Using Elk (Cervus canadensis) Ear Punches.

Sensitive and specific antemortem diagnostic tests are a prerequisite for effective management of chronic wasting disease (CWD). Paired with readily accessible samples that accurately reflect CWD status, the real-time quaking-induced conversion (RT-QuIC) assay has the potential to enable more effective CWD surveillance and interventions. We evaluated the feasibility of RT-QuIC as a CWD diagnostic test using 6-mm ear tissue biopsies from elk (Cervus canadensis). First, we evaluated the effect of ear spatial location on seeding activity. We observed an effect of ear punch spatial location on the amyloid formation rate (AFR): Samples collected from the periphery of the ear evidenced a statistically significant increase in AFR relative to ear punches from the ventral midline. Gross microdissection of an ear pinna suggested that there was more small nerve innervation around the periphery of the ear. Second, we evaluated the diagnostic sensitivity, specificity, and predictive value of RT-QuIC using ear punches from elk that had been previously diagnosed via ELISA testing. We evaluated the impact of nonstatistical and statistical approaches on diagnostic accuracy. Specificity and positive predictive value were perfect when statistical analyses were used to evaluate the binomial distribution (CWD positive versus CWD negative) of the data. Conversely, sensitivity and negative predictive value were modest, independent of the application of statistical analysis, indicating that RT-QuIC may be susceptible to false-negative data in this context. Taken together, our data support the idea that RT-QuIC, when paired with US Department of Agriculture-approved diagnostic tests, may provide more time to stakeholders for making major management decisions.

A new web application for determining sample size in freedom-from-disease testing with imperfect tests

Veterinary surveillance frequently requires study design for freedom-from-disease testing, specifying a sample size to balance higher statistical power with larger sample sizes against increased research and ethics costs, with the recognition that tests can generate false positive and negative results: i.e., tests exhibit imperfect sensitivity and specificity. In this paper, we revisit the mathematics behind exact calculations of sample size in terms of the binomial and hypergeometric distributions, and present a new algorithm – implemented and available to use in R as a Shiny application with a graphical user interface – to determine sample size for practical situations. Often, sample size calculations are based upon simulations or approximations, but we show here that exact calculations are feasible. In addition, we relax the liberal assumption – which provides conservative sample-size estimates – that sensitivity and specificity are known exactly, and instead assume both are Beta distributed with known hyperparameters. The application presented here was originally designed as a learning tool for students and is now made available for wider use.

Antidepressant therapeutic strategies and health care utilization in patients with depression.

Individuals with depression who do not respond to initial antidepressant may switch to a different antidepressant, add a second antidepressant, or add an atypical antipsychotic. Previous studies comparing these strategies' efficacy and safety reported conflicting results, and the impact of these strategies on subsequent health care utilization is unknown. To compare health care utilization between individuals with depression who switched antidepressants, added a second antidepressant (ie, combination), or added an atypical antipsychotic (ie, augmentation) following their initial antidepressant. This retrospective cohort study used a 25% random sample of the IQVIA PharMetrics Plus for Academics health plan claims database. The study cohort included individuals aged 10-64 years who newly initiated an antidepressant at any point from January 2016 to December 2020. New use was defined as no evidence of an antidepressant in the 180 days preceding the antidepressant dispensing. Individuals had to have a depression diagnosis and a treatment change in the 180 days following the initial antidepressant. The index date was the date of the first observed antidepressant change, which was defined as a switch, combination, or augmentation. Health care utilization, measured as the number of outpatient visits, any all-cause hospitalization, and any emergency department (ED) visit, was assessed in the 180 days after the index date. Negative binomial regression models evaluated the rate ratio of the number of outpatient visits. Logistic regression models estimated the odds ratio of a hospitalization, and modified Poisson regression estimated the relative risk of an ED visit. Models were adjusted for demographics, clinical characteristics, and previous health care utilization. Among 3,847 individuals with depression who had the first treatment change following the initial antidepressant, we identified 2,418 (62.9%) who switched, 1,268 (33.0%) who combined, and 161 (4.2%) who augmented their antidepressant. The augmentation group had a significantly higher rate of outpatient visits than the combination group (adjusted rate ratio = 1.14, 95% CI = 1.04-1.25). There was no statistically significant difference in hospitalizations or ED visits between the switch and augmentation vs combination groups. Augmentation comprised 4% of our antidepressant cohort but had higher outpatient health care utilization than those who combined treatment.

Local calibration of JPCP transverse cracking and IRI models using maximum likelihood estimation

The calibration of transfer functions is essential for accurate pavement performance predictions in the Pavement-ME design. Several studies have used the least square approach to calibrate these transfer functions. Least square is a widely used simplistic approach based on certain assumptions. Literature shows that these least square approach assumptions may not apply to the non-normal distributions. This study introduces a new methodology for calibrating the transverse cracking and international roughness index (IRI) models in rigid pavements using maximum likelihood estimation (MLE). Synthetic data for transverse cracking, with and without variability, are generated to illustrate the applicability of MLE using different known probability distributions (exponential, gamma, log-normal, and negative binomial). The approach uses measured data from the Michigan Department of Transportation's (MDOT) pavement management system (PMS) database for 70 jointed plain concrete pavement (JPCP) sections to calibrate and validate transfer functions. The MLE approach is combined with resampling techniques to improve the robustness of calibration coefficients. The results show that the MLE transverse cracking model using the gamma distribution consistently outperforms the least square for synthetic and observed data. For observed data, MLE estimates of parameters produced lower SSE and bias than least squares (e.g., for the transverse cracking model, the SSE values are 3.98 vs 4.02, and the bias values are 0.00 and -0.41). Although negative binomial distribution is the most suitable fit for the IRI model for MLE, the least square results are slightly better than MLE. The bias values are -0.312 and 0.000 for the MLE and least square methods. Overall, the findings indicate that MLE is a robust method for calibration, especially for non-normally distributed data such as transverse cracking.

Reliable individual differences in researcher performance capacity estimates: evaluating productivity as explanatory variable

AbstractAre latent variables of researcher performance capacity merely elaborate proxies of productivity? To investigate this research question, we propose extensions of recently used item-response theory models for the estimation of researcher performance capacity. We argue that productivity should be considered as a potential explanatory variable of reliable individual differences between researchers. Thus, we extend the Conway-Maxwell Poisson counts model and a negative binomial counts model by incorporating productivity as a person-covariate. We estimated six different models: a model without productivity as item and person-covariate, a model with raw productivity as person-covariate, a model with log-productivity as person covariate, a model that treats log-productivity as a known offset, a model with item-specific influences of productivity, and a model with item-specific influences of productivity as well as academic age as person-covariate. We found that the model with item-specific influences of productivity fitted two samples of social science researchers best. In the first dataset, reliable individual differences decreased substantially from excellent reliability when productivity is not modeled at all to inacceptable levels of reliability when productivity is controlled as a person-covariate, while in the second dataset reliability decreased only negligibly. This all emphasizes the critical role of productivity in researcher performance capacity estimation.

Delay-dependent observer based control for uncertain fuzzy-chaotic systems with deception attacks and faulty actuators

In this study, the robust fault-tolerant control problem for T-S fuzzy chaotic systems is studied with the use of a proportional integral observer. Particularly, to accurately consider the real-world scenario, the chaotic system model incorporates the parameter uncertainties, input delay and external disruptions. Furthermore, a fuzzy-based observer is put forward based on analyzed system output with the intent of estimating the states of undertaken chaotic systems. Herein, the system output is susceptible to randomly occurring deception attacks and adheres to the Bernoulli distribution. Precisely, the consideration of deception attacks in the output channel allows for more secure state estimation in a networked setting. Subsequently, we develop a proportional integral observer-based fault-tolerant control that allows for the attainment of goals despite faults and delays in the input channel. Moreover, by setting up the Lyapunov-Krasovskii functional and blending it with Wirtinger's integral inequalities, we put together adequate conditions that ensure the asymptotic stability of the closed-loop systems by establishing conditions in the form of linear matrix inequalities. In the follow-up, based on the established matrix inequalities, the exact procedure for computing the gain matrices is outlined. As a last step, we put forward numerical simulation outcomes that exhibit the viability of the theoretical findings.

Network screening and analysis of pedestrian and bicyclist crashes on Florida arterials using a corridor-level approach

In this paper, a corridor-level approach is used to network screen and analyze pedestrian and bicyclist crashes. This approach uses less data than site-level analyses while also considering the relationship between intersections and roadway segments. 548 roadway corridors covering over 1000 centerline miles (1609 km) were identified on urban and suburban arterial roads in seven Florida counties based on context classification and lane count. From 2017 to 2021, these corridors experienced 3773 pedestrian crashes and 2599 bicyclist crashes, with about 88 % of these crashes resulting in fatalities or injuries. Three negative binomial regression models were developed to predict pedestrian crashes only, bicyclist crashes only, and both pedestrian and bicyclist crashes together (combined crashes model). Significant predictors from the models included traffic volume, speed limit, area type, intersection-related variables, and modality-related variables. Using the combined crashes model, a 0.75-mile (1.21-km) corridor was identified as the corridor with highest potential for crash frequency reduction. Examination of this corridor suggested that bicycle lanes, improved lighting, and midblock crossings could be effective countermeasures to reduce pedestrian and bicyclist crashes. Based on several performance metrics, the developed approach provided an accurate and statistically reliable way to model crashes in corridors. This corridor-level approach can help agencies expedite network screening and identify locations where many pedestrian and bicyclist crashes are likely to occur so they can take proactive actions to prevent these crashes and help keep these vulnerable road users safe.

Association of fall risk-increasing drugs with falls in generally healthy older adults: a 3-year prospective observational study of the DO-HEALTH trial

BackgroundThe association between fall risk-increasing drugs (FRIDs, medications known to be associated with falls) and the number of falls among generally healthy and active community-dwelling older adults is understudied. Prior studies have focused on individual medication classes or have predominantly relied on retrospective assessments of falls. The aim of this study was to investigate the association between FRID use at baseline and the prospective incidence rates of total, injurious and recurrent falls in community-dwelling older adults.MethodsThis is a 3-year observational analysis of DO-HEALTH, a randomized controlled trial, among community-dwelling adults aged ≥ 70 years without major diseases at baseline. The main exposures were use of at least one FRID and multiple FRIDs (≥ 2 FRIDs) at baseline. The number of total falls (including high- and low-trauma falls, as well as injurious falls) over 3 years of follow-up was defined as the primary outcome, and the number of injurious and the number of recurrent total falls (≥ 2 falls), as the two separate secondary outcomes. To examine these associations, separate negative binomial regression models controlled for the fixed effects of treatment allocation in the DO-HEALTH trial, study site, fall in the last year, age, sex, BMI, and walking aid were used. Additionally, an offset of the logarithm of each participant’s time in the study was included in the models.ResultsA total of 2157 participants were included, with a baseline median age of 74.0 years, 61.7% of whom were women, and 41.9% having experienced a prior fall in the year preceding enrolment. At baseline, 908 (42.1%) participants used at least one FRID, and 351 (16.3%) reported multiple FRIDs use. Prospectively, over 3 years of follow-up, 3333 falls were reported by 1311 (60.8%) out of the 2157 participants. Baseline use of at least one FRID was significantly associated with increased incidence rates of total falls (incidence rate ratio (IRR) [95% Confidence Interval (CI)] = 1.13 [1.01–1.27]), injurious falls (IRR = 1.15 [1.02–1.29]), and recurrent falls (IRR = 1.12 [1.01–1.23]) over 3 years. These associations were most pronounced among users of multiple FRIDs, with increased incidence rates of total falls (IRR = 1.22 [1.05–1.42]), injurious falls (IRR = 1.33 [1.14–1.54]) and recurrent falls (IRR = 1.14 [1.02–1.29]).ConclusionOur results suggest that FRID use is associated with increased prospective incidence rates of total, injurious, and recurrent falls even among generally healthy older adults.Trial registrationDO-HEALTH is registered as NCT01745263 on clinicaltrials.gov, with a registration date of 2012-12-06.

Preoperative dysphagia and adverse postoperative outcomes in middle aged and older adults

BackgroundDysphagia is a swallowing impairment with adverse health consequences. The impact of preoperative dysphagia on postoperative outcomes is not known. This study will examine the association between preoperative dysphagia and postoperative outcomes. MethodsThis is a retrospective, observational study of patients ≥50 years of age undergoing surgery not directly involving the swallowing mechanism (i.e., oral cavity, larynx, pharynx, or esophagus). The National COVID Cohort Collaborative (N3C) database from January 1st, 2020 to August 31st, 2023 was used. The N3C database comprises electronic health record (EHR) data from more than 75 US health systems and harmonizes these data in a centralized resource. The main predictor was dysphagia with or without malnutrition in the 3 months prior to surgery. Logistic regression models assessed the association between our main predictor and outcomes of mortality, readmission, and medical/surgical complications adjusted for covariates. A negative binomial regression model was used for length of stay (LOS). Results380,869 adults ≥50 years old were included, mean age 66.0 (SD = 9.2), 52.6 % male. 7.9 % had dysphagia and/or malnutrition 3 months preoperatively including 3.0 % preoperative dysphagia alone, 3.8 % preoperative malnutrition alone, and 1.1 % both. Adjusted models demonstrated higher odds of mortality (1-year mortality odds ratio (OR) 1.37, 95 % confidence interval (CI) 1.29 to 1.44), readmission (90-day readmission OR 1.19, 95 % CI 1.14 to 1.24), and medical/surgical complications (OR 1.35, 95 % CI 1.28 to 1.42) among patients with 3 months preoperative dysphagia with or without malnutrition compared to patients with neither condition. ConclusionPatients with 3 months preoperative dysphagia with and without malnutrition had poor postoperative outcomes. These findings highlight the rationale for integrating dysphagia screening and intervention into routine preoperative protocols to mitigate the risk of adverse postoperative outcomes.

The formative time delay and electron avalanche number distributions for multielectron initiation of streamer breakdown

Electron avalanche statistics were mainly studied with a single electron initiation and there was no mathematical transition reported to the formative time delay distribution. This paper deals with the transition from the electron avalanche number distribution to the formative time delay distribution for multielectron initiation and streamer breakdown mechanism. The goal of the research is a detailed analysis of the formative time delay of electrical breakdown for different applications, such as spark counters, resistive plate chambers, gas-discharge switches, and high voltage systems with gas as an insulator. The electron avalanche number distribution for multielectron initiation is described by negative binomial distribution (NBD). Regarding the newly derived formative time delay distribution, when the number of initiating electrons k is small, the formative time delay distributions are asymmetric with the pronounced right tail. With increasing k, the formative time distributions shift to the shorter formative times and become narrower and higher, more symmetric and Gauss-like. As statistical tests show, for k≳20 the hypothesis that the formative time delay distributions are Gaussians cannot be rejected. As illustrations, the formative time delay distributions in neon and air at low reduced electric field are shown and briefly discussed. The distributions for methylal, ether and methane are presented in order to compare the estimated distribution parameters with available experimental data and to model the measured distributions.

A Note on Confidence Intervals for a Binomial p: Andersson–Nerman vs. Wilson

ABSTRACTNumerous approximate confidence intervals in closed form have been suggested over the years for the parameter in the binomial distribution. One of the oldest and still most advocated is the Wilson (score) interval, which in this article will be compared with the less well‐known Andersson–Nerman (henceforth AN) interval. These intervals are quite closely related, but it will be shown analytically and illustrated by examples that the coverage probability of the AN interval always equals or exceeds that of the Wilson interval, while also having uniformly larger expected length. Asymptotic expressions for the coverage probability and expected length of the AN interval are provided, using Edgeworth and Taylor expansions, respectively. The well‐behaved Wilson and AN pivots are furthermore contrasted with the problematic Wald pivot. The latter gives rise to the Wald interval, which is probably one of the best known and most used procedures altogether in the history of statistical inference. Unfortunately, this interval performs poorly, but even to this day it is to be found in many current textbooks. Therefore, it is still of relevance to search for attractive alternatives based on sound statistical principles.

MRI-Based Circumferential Strain in Boys with Early Duchenne Muscular Dystrophy Cardiomyopathy

Background: In boys with Duchenne muscular dystrophy (DMD), cardiomyopathy has become the primary cause of death. Although both positive late gadolinium enhancement (LGE) and reduced left ventricular ejection fraction (LVEF) are late findings in a DMD cohort, LV end-systolic circumferential strain at middle wall (Ecc) serves as a biomarker for detecting early impairment in cardiac function associated with DMD. However, Ecc derived from cine Displacement Encoding with Stimulated Echoes (DENSE) has not been quantified in boys with DMD. We aim to: (1) use cine DENSE to quantify regional Ecc in LGE negative (-) boys with DMD and healthy controls; and (2) compare Ecc with LVEF in terms of differentiating DMD boys with LGE (-) from healthy boys. Methods: 10 LGE (-) boys with DMD and 12 healthy boys were enrolled prospectively in an IRB-approved study for CMR at 3T. Navigator-gated cine DENSE was used to obtain short-axis mid-ventricular data and estimate global and regional Ecc. Group-wise differences were tested via a Wilcoxon rank-sum test. Within-group differences were tested via a Skillings-Mack test followed by pairwise Wilcoxon signed-rank tests. A binomial logistic regression model was adopted to differentiate between DMD boys with LGE (-) and healthy boys. Results: When compared to healthy boys, LGE (-) boys with DMD demonstrated significantly impaired septal Ecc [−0.13 (0.01) vs. −0.16 (0.03), p = 0.019]. In comparison to the Ecc in other segments, both groups of boys exhibited significantly reduced septal Ecc and significantly elevated lateral Ecc. Septal Ecc outperformed LVEF in distinguishing DMD boys with LGE (-) from healthy boys. Conclusions: Reduced septal Ecc may serve as an early indicator of cardiac involvement in LGE (-) DMD boys prior to reduced LVEF and a positive LGE finding.

Balancing work and earnings: The long-term impact on mental health

Earnings and work hours (e.g., weekly work hours) are key determinants of one's mental health. While higher earnings are linked to better mental health due to reduced financial stress, they may come at the cost of longer work hours harmful for mental health. Therefore, balancing work hours with earnings is crucial for mental health. Using the 2015, 2017, and 2019 waves of the Panel Study of Income Dynamics (N = 6,776), this study explores how one's earnings and work hours combine to influence mental health using growth mixture modeling and a negative binomial regression model, with generalized propensity score weighting for causal inference. The findings reveal that working 40 h a week with earnings two to three times the US federal poverty threshold benefits mental health. However, earning more by working 60 h a week does not provide additional mental health benefits. Additionally, individuals with a history of low earnings face a high risk of psychological distress, even as their earnings improve over time. This risk is similar to that experienced by those consistently earning low incomes. Our findings highlight the importance of clarifying work-earning balance for one's mental health as well as identifying people with mental health needs from a longitudinal perspective.

Climate and Ecosystem Factors Mediate Soil Freeze-Thaw Cycles at the Continental Scale.

Freeze-thaw cycles (FTC) alter soil function through changes to physical organization of the soil matrix and biogeochemical processes. Understanding how dynamic climate and soil properties influence FTC may enable better prediction of ecosystem response to changing climate patterns. In this study, we quantified FTC occurrence and frequency across 40 National Ecological Observatory Network (NEON) sites. We used site mean annual precipitation (MAP) and mean annual temperature (MAT) to define warm and wet, warm and dry, and cold and dry climate groupings. Site and soil properties, including MAT, MAP, maximum-minimum temperature difference, aridity index, precipitation as snow (PAS), and organic mat thickness, were used to characterize climate groups and investigate relationships between site properties and FTC occurrence and frequency. Ecosystem-specific drivers of FTC provided insight into potential changes to FTC dynamics with climate warming. Warm and dry sites had the most FTC, driven by rapid diurnal FTC close to the soil surface in winter. Cold and dry sites were characterized by fewer, but longer-duration FTC, which mainly occurred in spring and increased in number with higher organic mat thickness (Spearman's ⍴=0.97, p<0.01). The influence of PAS and MAT on the occurrence of FTC depended on climate group (binomial model interaction p (χ2)<0.05), highlighting the role of a persistent snowpack in buffering soil temperature fluctuations. Integrating ecosystem type and season-specific FTC patterns identified here into predictive models may increase predictive accuracy for dynamic system response to climate change.

Probabilistic Cellular Automata Simulation of Microstructure Evolution: The Role of Model Parameters on Precision and Uncertainty

Abstract Probabilistic cellular automata (PCA) is a widely used and cost-efficient method for simulating microstructural evolution. In this method, probabilistic state change rules determine the evolution of cell states at each time step. However, its stochastic nature introduces inherent uncertainty, leading to non-repeatable results. Most microstructural simulation studies assess the accuracy of simulations by comparing predicted results with experimental observations, neglecting uncertainties in mathematical models and algorithms. In this study, the precision and stochastic behavior of microstructure evolution in the PCA simulations were investigated. The probabilities of transformations of cell states at each time step were formulated, and discrete probability distribution functions (dPDF) were introduced to analyze the frequency distribution of simulation outcomes. The performance and consistency of these dPDFs were assessed by comparing statistical analyses of PCA simulation results with dPDF predictions, revealing that the variance of simulation results is less than that of the binomial distribution function. Additionally, the effects of modeling parameters, such as model size, cellular resolution, and probability distribution of state changes in two- and three-dimensional PCA modeling, on the precision and reliability of simulation results were studied. In PCA models, simulation uncertainty inversely relates to the square root of model size. Furthermore, in 2D simulations, uncertainty is inversely proportional to the square root of the cellular resolution, while in 3D simulations, it is inversely proportional to the cellular resolution itself. These findings provide a simple and computationally efficient method for evaluating PCA simulation uncertainty and determining optimal simulation parameters, including model size, cellular resolution, and dimensionality.

A comprehensive uncertainty framework for historical flood frequency analysis: a 500-year-long case study

Abstract. The value of historical data for flood frequency analysis has been acknowledged and studied for a long time. A specific statistical framework must be used to comply with the censored nature of historical data, for which only floods large enough to induce written records or to trigger flood marks are usually recorded. It is assumed that all floods which exceeded a given perception threshold were recorded as written testimonies or flood marks. Conversely, all years without a flood record in the historical period are assumed to have had a maximum discharge below the perception threshold. This paper proposes a binomial model that explicitly recognizes the uncertain nature of both the perception threshold and the starting date of the historical period. This model is applied to a case study for the Rhône River at Beaucaire, France, where a long (1816–2020) systematic series of annual maximum discharges is available along with a collection of 13 historical floods from documentary evidence over 3 centuries (1500–1815). Results indicate that the inclusion of historical floods reduces the uncertainty of 100- or 1000-year flood quantiles, even when only the number of perception threshold exceedances is known. However, ignoring the uncertainty around the perception threshold leads to a noticeable underestimation of flood quantile uncertainty. A qualitatively similar conclusion is found when ignoring the uncertainty around the historical period length. However, its impact on flood quantile uncertainty appears to be much smaller than that of the perception threshold.