Markov Chain Research Articles

Chain novel, or Markov chain? Estimating the authority of U.S. Supreme Court case law

AbstractHow does the authority of case law evolve over time? On the Dworkinian legal formalist view, cases increase in authority as they become more embedded in the “chain” of legal precedent, but on the Holmesian legal realist view, each case's authority is proportional to its ability to predict future legal outcomes. In this article, I show how modeling the citation network of U.S. Supreme Court case law not as a chain novel (à la Dworkin) but instead as a Markov chain (à la Holmes, or so I argue) unlocks an intuitive measure of case authority—called HolmesRank—that outperforms the existing approach in a variety of validation tasks. I then demonstrate how the authority scores produced using this Markov machinery empower the analysis of two important normative questions: (1) the ideological basis of lasting precedential authority and (2) the causal effect of the Supreme Court's citation choices on lower court compliance.

Modeling the delay propagation dynamics in high-speed railway networks with a traffic-driven SIS epidemic model

The propagation of delays is a prevalent issue in high-speed railway (HSR) networks. However, the underlying properties of delay propagation have not been fully explored, hindering the effective management of this problem. In this paper, considering the impact of traffic flow, we model the delay propagation as a traffic-driven susceptible–infected–susceptible (SIS) epidemic spreading process. We introduce a traffic frequency matrix to estimate the traffic rate and further derive the propagation dynamic equations using a continuous-time Markov chain method. We then derive the epidemic threshold of the model, which is proportional to the recovery rate and inversely proportional to the average path length. Finally, through simulation, we study the impacts of various factors including the infection rate, recovery rate, and the degree and number of initial delay stations. Our work provides some insights for the prediction and control of delay propagation in HSR networks.

Multistate Markov chain modeling for child undernutrition transitions in Ethiopia: a longitudinal data analysis, 2002-2016.

The use of the multistate Markov chain model is a valuable tool for studying child undernutrition. This allows us to examine the trends of children's transitions from one state to multiple states of undernutrition. In this study, our objective was to estimate the median duration for a child to first transition from one state of undernutrition to another as well as their first recurrence of undernutrition and also to analyze the typical duration of undernourishment. This involves understanding the central tendency of these transitions and durations in the context of longitudinal data. We used a longitudinal dataset from the Young Lives cohort study (YLCS), which included approximately 1997 Ethiopian children aged 1-15years. These children were selected from five regions and followed through five survey rounds between 2002 and 2016. The surveys provide comprehensive health and nutrition data and are designed to assess childhood poverty. To analyze this dataset, we employed a Markov chain regression model. The dataset constitutes a cohort with repeated measurements, allowing us to track the transitions of individual children across different states of undernutrition over time. The findings of our study indicate that 46% of children experienced concurrent underweight, stunting, and wasting (referred to as USW). The prevalence of underweight and stunted concurrent condition (US) was 18.7% at baseline, higher among males. The incidence density of undernutrition was calculated at 22.5% per year. On average, it took 3.02months for a child in a wasting state to transition back to a normal state for the first time, followed by approximately 3.05months for stunting and 3.89months for underweight. It is noteworthy that the median duration of undernourishment among children in the US (underweight and stunted concurrently) state was 48.8months, whereas those concurrently underweight and wasting experienced a median of 45.4months in this state. Additionally, rural children (HR = 1.75; 95% CI: 1.53-1.97), those with illiterate fathers (HR = 1.50; 95% CI: 1.38-1.62) and mothers (HR = 1.45; 95% CI: 1.02-3.29), and those in households lacking safe drinking water (HR = 1.70; 95% CI: 1.26-2.14) or access to cooking fuel (HR = 1.95; 95% CI: 1.75-2.17) exhibited a higher risk of undernutrition and a slower recovery rate. This study revealed that rural children, especially those with illiterate parents and households lacking safe drinking water but cooking fuels, face an increased risk of undernutrition and slower recovery.

Bayesian Inference for Estimating Heat Sources Through Temperature Assimilation

Abstract This paper utilizes a Bayesian inference framework to address the two-dimensional (2D) steady-state heat conduction problem, focusing on the estimation of unknown distributed heat sources in a thermally conducting medium with uniform conductivity. The goal is to infer the locations, strength, and shape of heaters by assimilating temperature data in Euclidean space, employing a Fourier series to represent each heater's shape. The Markov Chain Monte Carlo (MCMC) method, incorporating the random-walk Metropolis–Hasting (MH) algorithm and parallel tempering, is utilized for posterior distribution exploration in both unbounded and wall-bounded domains. It is found that multiple solutions arise in cases where the number of temperature sensors is less than the number of unknown states. Moreover, smaller heaters introduce greater uncertainty in estimated strength. To address the challenge of estimating the heater's strength and shape simultaneously due to their strong correlation, our method incorporates sharp priors on one to ensure accurate and feasible solutions of the other. The diffusive nature of heat conduction smooths out any deformations in the temperature contours, especially in the presence of multiple heaters positioned near each other, impacting convergence. In wall-bounded domains with Neumann boundary conditions, the inference of heater parameters tends to be more accurate than in unbounded domains.

A defective cure rate quantile regression model for male breast cancer data

In this article, we particularly address the problem of assessing the impact of different prognostic factors, such as clinical stage and age, on the specific survival times of men with breast cancer when cure is a possibility. To this end, we developed a quantile regression model for survival data in the presence of long-term survivors based on the generalized Gompertz distribution in a defective version, which is conveniently reparametrized in terms of the q-th quantile and then linked to covariates via a logarithm link function. This proposal allows us to obtain how each variable affects the survival times in different quantiles. In addition, we are able to study the effects of covariates on the cure rate as well. We consider Markov Chain Monte Carlo methods to develop a Bayesian analysis in the proposed model and we evaluate its performance through Monte Carlo simulation studies. Finally, we illustrate the application of our model in a data set about male breast cancer from Brazil analyzed for the very first time.

Predictions for the abundance and clustering of Hα emitting galaxies

Abstract We predict the surface density and clustering bias of Hα emitting galaxies for the Euclid and Nancy Grace Roman Space Telescope redshift surveys using a new calibration of the GALFORM galaxy formation model. We generate 3000 GALFORM models to train an ensemble of deep learning algorithms to create an emulator. We then use this emulator in a Markov Chain Monte Carlo (MCMC) parameter search of an eleven-dimensional parameter space, to find a best-fitting model to a calibration dataset that includes local luminosity function data, and, for the first time, higher redshift data, namely the number counts of Hα emitters. We discover tensions when exploring fits for the observational data when applying a heuristic weighting scheme in the MCMC framework. We find improved fits to the Hα number counts while maintaining appropriate predictions for the local universe luminosity function. For a flux limited Euclid-like survey to a depth of 2 × 10−16 erg−1 s−1 cm−2 for sources in the redshift range 0.9 < z < 1.8, we estimate 2962-4331 Hα emission-line sources deg−2. For a Nancy Grace Roman survey, with a flux limit of 1 × 10−16 erg−1 s−1 cm−2 and a redshift range 1.0 < z < 2.0, we predict 6786-10322 Hα emission-line sources deg−2.

Spatiotemporal Changes and Influencing Factors of the Coupled Production–Living–Ecological Functions in the Yellow River Basin, China

The imbalance in the “production–living–ecology” function (PLEF) has become a major issue for global cities due to the rapid advancement of urbanization and industrialization worldwide. The realization of PLEF coupling and coordination is crucial for a region’s sustainable development. Existing research has defined the concept of PLEF from the perspective of land function and measured its coupling coordination level using relevant models. However, there is still room for improvement in the indicator system, research methods, and other aspects. This work builds a PLEF coupling coordination evaluation-index system based on the perspective of human habitat using multi-source data in order to examine the spatial differences in PLEF coupling coordination level and the influencing factors in the Yellow River Basin (YRB). Using the modified coupling coordination model, the Moran index, spatial Markov chain model, and geographically weighted random forest model were introduced to analyze its spatial and temporal differentiation and influencing factors. The results found that (a) the level of PLEF coupling coordination in the YRB from 2010 to 2022 has been improving, and the number of severely imbalanced cities has been reduced from 23 to 15, but the level of downstream cities’ coupling coordination is significantly higher than that of upstream cities. The probability of cities maintaining their own level is greater than 50%, and there is basically no cross-level transfer. (b) The Moran index of the PLEF coupling coordination level has risen from 0.137 to 0.229, which shows a significant positive clustering phenomenon and is continually strengthening. The intercity polarization effect is being continually enhanced as seen in the LISA clustering diagram. (c) There is significant heterogeneity between the influencing factors in time and space. In terms of importance level, the series is per capita disposable income (0.416) > nighttime lighting index (0.370) > local general public budget expenditure (0.332) > number of beds per 1000 people (0.191) > NO2 content in the air (0.110). This study systematically investigates the dynamic evolution of the coupled coordination level of PLEF in the YRB and its influencing mechanism, which is of great practical use.

Human-centric lighting asset management for LED bulbs: a context-driven approach on prognostics and maintenance strategy development in public libraries

ABSTRACT Traditional asset management of lighting systems typically focuses on functionality, cost, and lifespan. In contrast, a human-centric approach prioritizes social sustainability and user well-being by ensuring lighting assets “provide the right light at the right time” for diverse activities. Light-emitting diode (LED) bulbs, known for energy efficiency and longevity, have become a preferred choice, yet public libraries often struggle to manage these assets sustainably, remaining in a reactive “fix/replace when it breaks” stage. Current predictive methods, such as artificial intelligence and machine learning, rely on laboratory data that often overlook real-world contexts, leading to performance gaps. This paper presents a context-driven, human-centric methodology for LED prognosis and maintenance strategies in public libraries, employing limited degradation data from LED testing. Advanced analytical techniques, including Markov Chain Monte Carlo (MCMC) and Deviance Information Criterion (DIC), support a shift from function-based to performance-based reliability assessment. By incorporating Mean Time of Exposure (MTOE) and Critical Integrated Levels (CILs), the approach defines optimal maintenance inspection intervals. This research enhances sustainable LED lighting management in public libraries, offering a framework adaptable to broader applications and aligned with human-centric goals..

Exploratory Cost-Utility Analysis of a 37-Gene Panel Versus Usual Care to Guide Therapy for Patients with Intermediate-Risk Myeloid Malignancies.

Genomic risk stratification methods for myeloid malignancies have moved beyond conventional karyotyping and single gene approaches to better define disease behaviour. Next-generation sequencing has been established as the new standard-of-care tool to accurately define prognosis at diagnosis and guide therapy decisions. We aimed to determine the economic value of a 37-gene panel test for informing subsequent care for patients with intermediate-risk myeloid malignancies. We performed an exploratory cost-utility analysis of a 37-gene panel test to inform stem cell transplantation therapy in patients with myeloid malignancies in Queensland, Australia. Clinician surveys provided data on management choice with and without genomics information while both published and individual-level data were used for healthcare costs, quality of life, relapse rates and survival data. We used a decision-analytic cohort model with Markov chains and 5000 simulations to derive the incremental cost per quality-adjusted life year (QALY) gained. Scenario, one-way and probabilistic sensitivity analyses were undertaken to test input variation on the stability of the main findings. Over 10 years, the model predicted mean costs of AU$125,561 for the panel testing strategy and AU$117,045 for usual care, indicating an incremental cost of AU$8516 for panel testing. The corresponding mean QALYs were 4.52 for panel testing and 4.46 for usual care, producing a cost of AU$153,854 per QALY gained. In the Australian system, the likelihood that panel testing would be cost effective was <1 % and would have a more favourable cost-effective profile at a willingness-to-pay of AU$140,000 per QALY gained. Driven by small gains in survival and relapse rates following therapies, genomic panel sequencing for myeloid malignancies in people with intermediate-risk disease is unlikely to be cost effective in Australia.

A queueing system for analysing traffic throughput in mixed traffic with semi- and fully-autonomous vehicles

As autonomous vehicles (AVs) integrate into transportation systems, a transitional period will emerge where semi-autonomous vehicles (semi-AVs), which still require an attentive driver for steering, coexist with fully-autonomous vehicles (fully-AVs). Focusing on this phase, this study proposes a novel framework that incorporates Markov chains into an M / G n / n max / n max state-dependent queueing system to capture the distinct platooning dynamics and their impacts on the long-term travel efficiency of mixed traffic. The developed Markov chain-based traffic queueing system enables the derivation of traffic throughput in mixed semi- and fully-AV traffic, accounting for their diverse platooning and car-following behaviours. Numerical experiments are used to assess the influence of fully- and semi-AVs on throughput and driving experience in the mixed traffic. This study advances the modelling and analysis of traffic flow efficiency during the transitional phase of mixed traffic, offering insights for managing and controlling semi-AV traffic in the near future.

Mapping the Trade Direction of Indian Rice with Markov Chain Analysis

Agriculture is a cornerstone of India’s economy, with rice being a critical crop that ranks second globally, feeding over half of the world’s population and serving as a staple in Southeast Asia. This study explores the direction of India’s rice trade using Markov Chain Analysis, following an examination of the compound annual growth rate (CAGR) in rice exports to various global regions. Results reveal a 2.26 per cent CAGR in rice production, while export values surged by 16.8 per cent annually. Specifically, the CAGR for rice exports to Iraq and Iran reached 58.6 per cent and 46.47 per cent, respectively. In quantity, India’s rice exports grew by 10.82 per cent, with Iraq and Iran at 44 per cent and 34 per cent. The Transitional Probability Matrix for 2001-2022 indicates strong regional retention, with Africa maintaining 78 per cent of trade value and Asia 93.7 per cent, and similar trends in quantity, where Asia retained 92.6 per cent and Africa 89.1 per cent. These findings highlight India’s potential to diversify rice exports and strengthen its global competitive edge, urging a focus on enhancing processing, transportation, and quality standards for wider market appeal.

Stochastic Processes with Expected Stopping Time

Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.

Predicting land cover changes in Xuan Lien Nature Reserve, Thanh Hoa province, Vietnam

The research was carried out in Xuan Lien Nature Reserve, which is a specially protected natural area and one of the five main centers of biodiversity in Vietnam. The work is aimed at analyzing changes and predicting the state of land cover in Xuan Lien Reserve. For these purposes, Landsat-7, Landsat-5 and Landsat-8 images obtained in 2000, 2010 and 2020 were studied. Normalized Difference Vegetation Index (NDVI) method was used to isolate the vegetation cover on the land areas, and Normalized Difference Water Index (NDWI) method was used. The results of the study indicate that the vegetation on the land is transforming in Xuan Lien Reserve. The area of broadleaf forests decreased by 6.2% from 2000 to 2020, and the area of wetlands increased by 4.9% due to the construction of Cua Dat hydroelectric complex in Reserve. The model of Markov chains and cellular automata was used to predict the state of the allocated lands in the study area. The predicted results of the model have been successfully confirmed using the agreement indices. According to the results of the predicted, by 2035 the area of broadleaf forests and wetlands will increase to 86.3% and 7.4%. The change in the structure of the vegetation cover of Reserve's land is explained by the measures taken by the Vietnamese government to regulate the water level in Cua Dat reservoir and expand the forest area.

Neural Methods for Amortized Inference

Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of neural networks, optimization libraries, and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortized, in the sense that, after an initial setup cost, they allow rapid inference through fast feed-forward operations. In this article we review recent progress in the context of point estimation, approximate Bayesian inference, summary-statistic construction, and likelihood approximation. We also cover software and include a simple illustration to showcase the wide array of tools available for amortized inference and the benefits they offer over Markov chain Monte Carlo methods. The article concludes with an overview of relevant topics and an outlook on future research directions.

Investments, credit guarantees, and government subsidies in a regime-switching framework

Abstract This paper examines how credit guarantees and government subsidies impact investment in a regime-switching model. We provide new explicit pricing formulas for a general standard asset. Almost all common corporate securities’ prices can be easily derived by the explicit formulas though project cash flows are driven by both a Brownian motion and a two-state Markov chain. We provide a method about how governments should specify a proper tax subsidy standard for a given tax rate to motivate a firm to invest in a project in the way they wish. If the tax subsidy is sufficiently high (low), an overinvestment (underinvestment) occurs. The higher the tax rate, the more significant the overinvestment (underinvestment). We pin down the subsidy amount required for motivating a firm to invest immediately and fix the optimal capital structure with government subsidies.

Abstract 4125939: Bayesian re-analysis of the STeroids to REduce Systemic inflammation after infant heart Surgery (STRESS) trial

Background: Prophylactic steroids are often used to reduce the systemic inflammatory response to cardiopulmonary bypass in infants undergoing heart surgery. The STRESS trial found that the likelihood of a worse outcome did not differ between infants randomized to methylprednisolone vs placebo in a risk-adjusted primary analysis (adjusted odds ratio [OR], 0.86; 95% CI, 0.71 to 1.05; P=0.14). However, secondary unadjusted analyses showed possible benefits with methylprednisolone. We re-analyzed the STRESS trial using Bayesian analytics to assess probability of benefit with methylprednisolone. Methods: We used a covariate-adjusted proportional odds model using the original STRESS trial model covariates and primary outcome (a ranked composite of death, transplant, major complications and post-op length of stay). We assessed effect thresholds from OR 0.6 to 1.25 (OR &lt;1 conveys benefit, OR &gt;1 conveys harm). We assumed a neutral probability of benefit vs harm with weak prior belief (SD of the normal prior distribution = 0.425). In sensitivity analyses, we evaluated pessimistic (5%-30% prior likelihood of benefit), neutral and optimistic (70%-95% prior likelihood of benefit) prior beliefs, and controlled strength of prior belief as weak (SD = 0.425), moderate (SD = 0.215) and strong (SD = 0.135). We compared posterior distribution of the OR under these priors with the reference results under the vague prior distribution. Analyses consisted of 10 Markov Chain Monte Carlo simulations each consisting of 2000 iterations with a 1000 iteration burn-in to ensure proper posterior convergence. Results: In primary analysis, the posterior probability of benefit from methylprednisolone was 92% and the probability of harm was 8%. The mean absolute benefit was 12%. In sensitivity analyses, the probability of benefit was ≥ 79% for all informative priors except the most pessimistic (Table/Figure). Conclusion: In Bayesian re-analysis of the STRESS trial, probability of benefit with prophylactic methylprednisolone is high and harm is unlikely. Assessing probability of benefit or harm may be more informative than frequentist analytics relying on a p-value threshold. Another advantage is the ability to consider a range of prior evidence.

Partitioning problems via random processes

AbstractThere are a number of well‐known problems and conjectures about partitioning graphs to satisfy local constraints. For example, the majority colouring conjecture of Kreutzer, Oum, Seymour, van der Zypen and Wood states that every directed graph has a 3‐colouring such that for every vertex , at most half of the out‐neighbours of have the same colour as . As another example, the internal partition conjecture, due to DeVos and to Ban and Linial, states that for every , all but finitely many ‐regular graphs have a partition into two non‐empty parts such that for every vertex , at least half of the neighbours of lie in the same part as . We prove several results in this spirit: in particular, two of our results are that the majority colouring conjecture holds for Erdős–Rényi random directed graphs (of any density), and that the internal partition conjecture holds if we permit a tiny number of ‘exceptional vertices’. Our proofs involve a variety of techniques, including several different methods to analyse random recolouring processes. One highlight is a personality‐changing scheme: we ‘forget’ certain information based on the state of a Markov chain, giving us more independence to work with.

Casting a sustainable future: a study on dynamic prediction and influencing factors of economic resilience in fisheries management

Marine fisheries are a critical component of the marine economy. Examining the changes in the economic resilience of marine fisheries allows for identifying potential development risks and supports informed decision-making to optimize growth patterns and mitigate risks. This study applied the CRITIC-based combined weights model to calculate China’s Marine Fisheries Economic Resilience (MFER). It investigated the temporal and spatial evolution of MFER and analyzed the influencing factors using the Geographical Detector and a Two-way fixed-effects model. Furthermore, the future development trends of MFER were predicted using the Markov chain. The results show that the overall MFER in China’s coastal provinces increased steadily from 2001 to 2020. Second, MFER exhibits a clear pattern, with low-value regions improving and high-value areas shifting toward medium- and low-value provinces. Fourth, the trajectory of the MFER center is moving from north to south, with high-value regions expanding in the same direction. Fourth, factors such as EDL, TEC, SPE, and SYS positively impact MFER, while OPE has a negative effect. Finally, the results of the Markov chain indicate that the current development state of MFER is relatively stable, with evidence of club convergence. However, the probability of maintaining the current development level is gradually decreasing. Based on these findings, provide suggestions for the preservation of marine economic security.

Analysis of spatial and temporal characteristics and evolution of green total factor productivity in agriculture in the lower Yellow River basin

The construction of ecological barriers in the Yellow River Basin represents a significant step toward reducing agricultural carbon emissions, achieving carbon neutrality, and reaching carbon peaking in China. The diverse agrarian development objectives of various regions within the basin have resulted in a heterogeneous approach to greening agriculture. Therefore, this paper will evaluate the development of carbon sink agriculture across 34 cities and municipalities in the lower Yellow River basin from 2008 to 2021 based on the EBM-GML model, and analyze the spatial-temporal evolution of agricultural green total factor productivity (AGTFP) in each region through the application of the Moran index, kernel density estimation, and spatial Markov chain analysis. The results demonstrate that agricultural carbon emissions in the Lower Yellow River Basin gradually decreased throughout the study period. Furthermore, overall carbon emission efficiency improved, indicating significant potential for further emission reduction. In addition, Agricultural Green Technology Progress (AGTC) has become a primary driver of AGTFP growth, while Agricultural Green Technology Efficiency (AGEC) has demonstrated a gradual upward trend. Locally, most areas are weakly connected and display an isolated development trend. The results of the kernel density analysis demonstrate a notable degree of mobility in the distributional dynamics of AGTFP growth, characterized by a gradual narrowing of the gap between locations. The transfer of (AGTFP) types in the lower reaches of the Yellow River Basin is stable, with a noticeable “club convergence” phenomenon, while geographical conditions significantly influence the transfer of AGTFP types in this region. Based on long-term trend predictions, the future trajectory of AGTFP in the lower Yellow River Basin appears optimistic and is expected to improve progressively, with the overall distribution tending toward equilibrium.

EpiFusion: Joint inference of the effective reproduction number by integrating phylodynamic and epidemiological modelling with particle filtering.

Accurately estimating the effective reproduction number (Rt) of a circulating pathogen is a fundamental challenge in the study of infectious disease. The fields of epidemiology and pathogen phylodynamics both share this goal, but to date, methodologies and data employed by each remain largely distinct. Here we present EpiFusion: a joint approach that can be used to harness the complementary strengths of each field to improve estimation of outbreak dynamics for large and poorly sampled epidemics, such as arboviral or respiratory virus outbreaks, and validate it for retrospective analysis. We propose a model of Rt that estimates outbreak trajectories conditional upon both phylodynamic (time-scaled trees estimated from genetic sequences) and epidemiological (case incidence) data. We simulate stochastic outbreak trajectories that are weighted according to epidemiological and phylodynamic observation models and fit using particle Markov Chain Monte Carlo. To assess performance, we test EpiFusion on simulated outbreaks in which transmission and/or surveillance rapidly changes and find that using EpiFusion to combine epidemiological and phylodynamic data maintains accuracy and increases certainty in trajectory and Rt estimates, compared to when each data type is used alone. We benchmark EpiFusion's performance against existing methods to estimate Rt and demonstrate advances in speed and accuracy. Importantly, our approach scales efficiently with dataset size. Finally, we apply our model to estimate Rt during the 2014 Ebola outbreak in Sierra Leone. EpiFusion is designed to accommodate future extensions that will improve its utility, such as explicitly modelling population structure, accommodations for phylogenetic uncertainty, and the ability to weight the contributions of genomic or case incidence to the inference.