First-order Markov Model Research Articles

Information bounds for Gaussian copula parameter in stationary semiparametric Markov models

Let {Vt}t=1n be any univariate stationary first-order semiparametric Markov process generated from an unknown invariant marginal distribution and a bivariate Gaussian copula with unknown correlation coefficient α0∈(−1,1). We prove that 1−α02 is the semiparametric efficient variance bound for estimating the correlation parameter α0 in any Gaussian copula generated first-order stationary Markov models. Surprisingly, this variance bound is strictly larger than 1−α022 (when α0≠0), which is the semiparametric efficient variance bound derived by Klaassen and Wellner (1997) for estimating the correlation parameter using any i.i.d. data {(Xi,Yi)}i=1n generated from a bivariate Gaussian copula with two unknown marginal distributions.

Forecasting the Power Generation Mix in Italy Based on Grey Markov Models

This study considers an application of the first-order Grey Markov Model to foresee the values of Italian power generation in relation to the available energy sources. The model is used to fit data from the Italian energy system from 2000 to 2022. The integration of Markovian error introduces a random element to the model, which is able now to capture inherent uncertainties and misalignments between the Grey Model predictions and the real data. This application provides valuable insights for strategic planning in the energy sector and future developments. The results show good accuracy of the predictions, which could provide powerful information for the effective implementation of energy policies concerning the evolution of energy demand in the country. Results show an improvement in the performance of more than 50% in terms of Root Mean Squared Error (RMSE) when the Markov chain is integrated in the analysis. Despite advancements, Italy’s 2032 energy mix will still significantly rely on fossil fuels, emphasizing the need for sustained efforts beyond 2032 to enhance sustainability.

The entropy rate of Linear Additive Markov Processes.

This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive but simple model able to generate sequences with a given autocorrelation structure. Our research establishes that the theoretical entropy rate of a LAMP model is equivalent to the theoretical entropy rate of the underlying first-order Markov Chain. The LAMP model captures complex relationships and long-range dependencies in data with similar expressibility to a higher-order Markov process. While a higher-order Markov process has a polynomial parameter space, a LAMP model is characterised only by a probability distribution and the transition matrix of an underlying first-order Markov Chain. This surprising result can be explained by the information balance between the additional structure imposed by the next state distribution of the LAMP model, and the additional randomness of each new transition. Understanding the entropy of the LAMP model provides a tool to model complex dependencies in data while retaining useful theoretical results. To emphasise the practical applications, we use the LAMP model to estimate the entropy rate of the LastFM, BrightKite, Wikispeedia and Reuters-21578 datasets. We compare estimates calculated using frequency probability estimates, a first-order Markov model and the LAMP model, also considering two approaches to ensure the transition matrix is irreducible. In most cases the LAMP entropy rates are lower than those of the alternatives, suggesting that LAMP model is better at accommodating structural dependencies in the processes, achieving a more accurate estimate of the true entropy.

Development of pedestrian collision avoidance strategy based on the fusion of Markov and social force models

Abstract. In urban traffic, accurate prediction of pedestrian trajectory and advanced collision avoidance strategy can effectively reduce the collision risk between intelligent vehicles and pedestrians. In order to improve the prediction accuracy of pedestrian trajectory and the safety of collision avoidance, a longitudinal and lateral intelligent collision avoidance strategy based on pedestrian trajectory prediction is proposed. Firstly, the process of a pedestrian crossing the road is considered as a combination of free motion described by first-order Markov model and the constrained motion presented by improved social force model. The predicted pedestrian trajectory is obtained by weighted fusion of the trajectories of the two models with a multiple linear regression algorithm. Secondly, according to the predicted pedestrian trajectory and time to collision (TTC) the longitudinal and lateral collision avoidance strategy is designed. The improved artificial potential field method is used to plan the lateral collision avoidance path in real time based on the predicted pedestrian position, and a fuzzy controller is constructed to obtain the desired deceleration of the vehicle. Finally, the pedestrian motion fusion model and the longitudinal and lateral collision avoidance strategy are verified by Prescan and Simulink co-simulation. The results show that the average displacement error (ADE) and final displacement error (FDE) of pedestrian trajectory based on pedestrian motion fusion model are smaller compared with a Markov model and improved social force model, and the proposed pedestrian collision avoidance strategy can effectively achieve longitudinal and lateral collision avoidance.

Relationship Between Pain and Delirium in Critically Ill Adults.

Although opioids are frequently used to treat pain, and are an important risk for ICU delirium, the association between ICU pain itself and delirium remains unclear. We sought to evaluate the relationship between ICU pain and delirium. Prospective cohort study. A 32-bed academic medical-surgical ICU. Critically ill adults (n = 4,064) admitted greater than or equal to 24 hours without a condition hampering delirium assessment. None. Daily mental status was classified as arousable without delirium, delirium, or unarousable. Pain was assessed six times daily in arousable patients using a 0-10 Numeric Rating Scale (NRS) or the Critical Care Pain Observation Tool (CPOT); daily peak pain score was categorized as no (NRS = 0/CPOT = 0), mild (NRS = 1-3/CPOT = 1-2), moderate (NRS = 4-6/CPOT = 3-4), or severe (NRS = 7-10/CPOT = 5-8) pain. To address missingness, a Multiple Imputation by Chained Equations approach that used available daily pain severity and 19 pain predictors was used to generate 25 complete datasets. Using a first-order Markov model with a multinomial logistic regression analysis, that controlled for 11 baseline/daily delirium risk factors and considered the competing risks of unarousability and ICU discharge/death, the association between peak daily pain and next-day delirium in each complete dataset was evaluated. Among 14,013 ICU days (contributed by 4,064 adults), delirium occurred on 2,749 (19.6%). After pain severity imputation on 1,818 ICU days, mild, moderate, and severe pain were detected on 2,712 (34.1%), 1,682 (21.1%), and 894 (11.2%) of the no-delirium days, respectively, and 992 (36.1%), 513 (18.6%), and 27 (10.1%) of delirium days (p = 0.01). The presence of any pain (mild, moderate, or severe) was not associated with a transition from awake without delirium to delirium (aOR 0.96; 95% CI, 0.76-1.21). This association was similar when days with only mild, moderate, or severe pain were considered. All results were stable after controlling for daily opioid dose. After controlling for multiple delirium risk factors, including daily opioid use, pain may not be a risk factor for delirium in the ICU. Future prospective research is required.

Multiple Markov Chains for Categorial Drought Prediction on the U.S. Drought Monitor at Weekly Scale

Abstract Predicting drought severity is essential for drought management and early warning systems. Although numerous physical model-based and data-driven methods have been put forward for drought prediction, their abilities are largely constrained by data requirements and modeling complexity. There remains a challenging task to efficiently predict categorial drought, especially for the U.S. Drought Monitor (USDM). Aiming at this issue, multiple Markov chains for USDM-based categorial drought prediction are successfully proposed and evaluated in this paper. In particular, this study concentrated on how the Markov order, step size, and training set length affected prediction accuracy (PA). According to experiments from 2000 to 2021, it was found that the 1-step and first-order Markov models had the best accuracy in predicting droughts up to 4 weeks ahead. The PA steadily dropped with increasing step size, and the average accuracy at monthly scale was 88%. In terms of seasonal variability, summer (July–August) had the lowest PA while winter had the highest (January–February). In comparison with the western region, the PA in the eastern United States is 25% higher. Moreover, the length of the training set had an obvious impact on the PA of the model. The PA in 1-step prediction was 87% and 78% under 20- and 5-yr training sets, respectively. The results of the study showed that Markov models predicted categorical drought with high accuracy in the short term and showed different performances on time and space scales. Proper use of Markov models would help disaster managers and policy makers to put mitigation policies and measures into practice.

Improving Prediction of Tobacco Use Over Time: Findings from Waves 1-4 of the Population Assessment of Tobacco and Health Study.

First-order Markov models assume future tobacco use behavior is dependent on current tobacco use and are often used to characterize patterns of tobacco use over time. Higher-order Markov models that assume future behavior is dependent on current and prior tobacco use may better estimate patterns of tobacco use. This study compared Markov models of different orders to examine whether incorporating information about tobacco use history improves model estimation of tobacco use and estimated tobacco use transition probabilities. We used data from four waves of the Population Assessment of Tobacco and Health Study. In each Wave, a participant was categorized into one of the following tobacco use states: never smoker, former smoker, menthol cigarette smoker, non-menthol cigarette smoker, or e-cigarette/dual user. We compared first-, second-, and third-order Markov models using multinomial logistic regression and estimated transition probabilities between tobacco use states. The third-order model was the best fit for the data. The percentage of former smokers, menthol cigarette smokers, non-menthol cigarette smokers, and e-cigarette/dual users in Wave 3 that remained in the same tobacco use state in Wave 4 ranged from 63.4% to 97.2%, 29.2% to 89.8%, 34.8% to 89.7%, and 20.5% to 80.0%, respectively, dependent on tobacco use history. Individuals who were current tobacco users, but former smokers in the prior two years, were most likely to quit. Transition probabilities between tobacco use states varied widely depending on tobacco use history. Higher-order Markov models improve estimation of tobacco use over time and can inform understanding of trajectories of tobacco use behavior. Findings from this study suggest that transition probabilities between tobacco use states vary widely depending on tobacco use history. Tobacco product users (cigarette or e-cigarette/dual users) who were in the same tobacco use state in the prior two years were least likely to quit. Individuals who were current tobacco users, but former smokers in the prior two years, were most likely to quit. Quitting smoking for at least two years is an important milestone in the process of cessation.

Flexible structure learning under uncertainty.

Experience is known to facilitate our ability to interpret sequences of events and make predictions about the future by extracting temporal regularities in our environments. Here, we ask whether uncertainty in dynamic environments affects our ability to learn predictive structures. We exposed participants to sequences of symbols determined by first-order Markov models and asked them to indicate which symbol they expected to follow each sequence. We introduced uncertainty in this prediction task by manipulating the: (a) probability of symbol co-occurrence, (b) stimulus presentation rate. Further, we manipulated feedback, as it is known to play a key role in resolving uncertainty. Our results demonstrate that increasing the similarity in the probabilities of symbol co-occurrence impaired performance on the prediction task. In contrast, increasing uncertainty in stimulus presentation rate by introducing temporal jitter resulted in participants adopting a strategy closer to probability maximization than matching and improving in the prediction tasks. Next, we show that feedback plays a key role in learning predictive statistics. Trial-by-trial feedback yielded stronger improvement than block feedback or no feedback; that is, participants adopted a strategy closer to probability maximization and showed stronger improvement when trained with trial-by-trial feedback. Further, correlating individual strategy with learning performance showed better performance in structure learning for observers who adopted a strategy closer to maximization. Our results indicate that executive cognitive functions (i.e., selective attention) may account for this individual variability in strategy and structure learning ability. Taken together, our results provide evidence for flexible structure learning; individuals adapt their decision strategy closer to probability maximization, reducing uncertainty in temporal sequences and improving their ability to learn predictive statistics in variable environments.

Role of monomer sequence in the crystallization and rheology of PBAT

Poly(butylene adipate-ran-terephthalate) (PBAT) is a typical biodegradable aliphatic−aromatic polyester. It has been widely used as compost bags, packaging films, and agricultural mulching films because of its complete biodegradability, good processability and mechanical properties, and low water vapor permeability. In this work, we showed that a small difference in the monomer ratio of the BT (butylene terephthalate) and BA (butylene adipate) units of PBAT would lead to significant differences in the continuous sequential block distributions as determined by the high-resolution NMR tests and the first-order Markovian model. As a result, macroscopic properties, such as crystallization behaviors, phase separation behaviors, and rheology, are greatly affected. A PBAT sample with a higher BA content and, consequently, a longer continuous BA block sequence has a lower crystallization temperature, a weaker concentration fluctuation at elevated temperatures, and a stronger strain hardening in melt elongation.

CLUSTERING OF SEQUENTIAL CAD MODELLING DATA

AbstractAutomating modelling activities in computer-aided design (CAD) systems is no exception within design automation, one of the current research endeavours aiming to use and transform design-related data in design decision-making processes and the generation and evaluation facilitation of new design solutions. The paper explores the differences between CAD models based on their feature-based CAD modelling sequences that lead to the final models' design. The dataset collected and structured for the study contains more than 1400 CAD models clustered on two levels by using an unsupervised K-means clustering algorithm. The algorithm is performed on the number (total and unique) and the first-order Markov model transition matrices of the CAD modelling operations and their sequential order, respectively. Therefore, three and ten groups (clusters) of CAD models are obtained regarding the level of clustering. The results show that most of the obtained groups are specified by the dominant transition between particular modelling operations. In addition, the study also provides insight into the potential of using feature-based CAD modelling operations' sequences as a first step toward automating the user interaction with the CAD system.

A high-order hidden Markov model for dynamic decision analysis of multi-homing ride-sourcing drivers

Ride-sourcing drivers enjoy flexibility in scheduling work hours and choosing platforms, which generates multi-homing behavior on multiple platforms. It is challenging to observe the labor supply of multi-homing ride-sourcing drivers due to data limitations, which motivates our research on modeling drivers' dynamic decisions on labor supply in the competitive ride-sourcing market with multiple platforms. We propose a dynamic discrete choice framework by modeling drivers' high-frequency decision sequences on platform switching as high-order hidden Markov processes and considering time-varying factors. The high-order hidden Markov framework relaxes the first-order Markovian assumption and builds interdependencies of unobserved states across multiple time periods. The estimation of the proposed model takes advantage of city-scale multiple platforms datasets in Hangzhou, China, including more than 16 million records of the order payment information and more than 46 thousand records of active ride-sourcing drivers' information. The case study results indicate that the high-order hidden Markov model (HO-HMM) has superior explanatory power in fitting multiple platforms datasets than the multinomial logit model and the first-order hidden Markov model. HO-HMM performs an advantage in modeling the extended historical dependency of drivers' decisions and individual driver behavior modeling with high interpretability. The results uncover the variations of drivers' attitudes in different hidden (unobservable) states and towards different platforms. In general, ride-sourcing drivers respond actively and positively to income and working time. The findings support the platforms' decision-making on pricing, reward, and personalized management of ride-sourcing drivers, and provide beneficial suggestions for improving income in the competitive ride-sourcing market.

Novel Approaches for Resource Management Across Edge Servers

Edge computing aims at reducing computation and storage across the cloud and provides service with reduced latency. Edge devices can be mobile devices, routers, cameras, printers or any Internet of Things (IoT) devices that generate vast amounts of data. The processing of these data is done by virtual machines (VMs) present in the edge servers that are located within close proximity of the edge devices. This work proposes two models which predict resource contention at the edge servers, namely, a Dynamic Markov model for Resource Contention Prediction in Edge Cloud (DMRCP) and a Hybrid Cascade of Regression and Markov model for Resource Contention Prediction (CRMRCP). In DMRCP, a history matrix is updated based on the CPU utilization of a Virtual Machine (VM). This history matrix is used to update a transition probability matrix. This matrix is used to predict the future state of the VM. In the CRMRCP approach, the past CPU utilization values of the virtual machines in the edge servers are used for predicting a set of future CPU utilization values using linear regression, polynomial regression, lasso regression and ridge regression. Then, the predicted future CPU utilization values are used by the dynamic and the second-order Markov models to classify the state of the edge servers as overloaded, underloaded or normally loaded. In both the approaches, the VMs that may cause resource contention are predicted and are migrated to other edge servers such that the destination edge server does not get overloaded after the migration. The DMRCP method is compared with the first-order and the second-order Markov models and the number of VM migrations is analysed to evaluate the performance. The number of VM migrations in the CRMRCP method is compared with that in the second-order Markov model. The overall results prove that the number of VM migrations for the DMRCP is 52.9% less compared to the first-order Markov model and 21.1% less when compared to the second-order Markov model. The number of VM migrations in CRMRCP is reduced by 81.8% when ridge regression cascaded with the second-order Markov model is used.

Bayesian Analysis of First-Order Markov Models for Autocorrelated Binary Responses.

In many clinical trials, patient outcomes are often binary-valued which are measured asynchronously over time across various dose levels. To account for autocorrelation among such longitudinally observed outcomes, a first-order Markov model for binary data is developed. Moreover, to account for the asynchronously observed time points, nonhomogeneous models for the transition probabilities are proposed. The transition probabilities are modeled using B-spline basis functions after suitable transformations. Additionally, if the underlying dose-response curve is assumed to be non-decreasing, our model allows for the estimation of any underlying non-decreasing curve based on suitably constructed prior distributions. We also extended our model to the mixed effect model to incorporate individual-specific random effects. Numerical comparisons with traditional models are provided based on simulated data sets, and also practical applications are illustrated using real data sets.

Probabilistic Prediction of Collisions between Cyclists and Vehicles Based on Uncertainty of Cyclists’ Movements

The uncertainty of cyclists’ movements has a significant impact on predicting the risk of collisions between cyclists and vehicles. The purpose of this study was to provide a method for assessing collision risk using probability, taking into account the uncertainty of cyclists’ movements. A cyclist model was first developed using a first-order Markov model. Then, based on Monte Carlo sampling, the distribution characteristics of the minimum distance and the time-to-collision (TTC) between the vehicle and the cyclist were extracted. By fitting these features, the probability density functions of the collision distance and TTC were estimated to derive the collision probabilities. The effectiveness of the collision probability prediction model was benchmarked against a deterministic crash risk prediction model (autonomous emergency braking [AEB] system) applied to three real-world cases previously reconstructed in an in-depth crash database. The results show that the collision probability prediction model can effectively predict the risk of collisions between cyclists and vehicles with better accuracy than AEB systems using a fixed trigger threshold. This study is a valuable reference for the development of advanced vehicle collision avoidance systems to protect cyclists and other vulnerable road users.

Memory Channel Models of a Hybrid PLC-VLC Link for a Smart Underground Mine

In this article, discrete memory channel models of a low-cost, visible light communication (VLC) and a hybrid amplify-and-forward (AF) powerline communication (PLC) and VLC channel are derived using data obtained from an underground mining testbed. The testbed is set up close to the mining face, where blasting occurs. Then, the noise distributions as a result of the connection of a blasting equipment and the mains switchboard supply on the powerline channel are modeled. The baseband signals are communicated over software-defined radios, using multicarrier modulation in the VLC and hybrid AF PLC-VLC channels. Aided by a Fritchman 3-state semi-hidden Markov model (SHMM) for channel state classification, the channels are modeled using a first-order (FO) Markov process, which considers only one previous state in the channel. In addition, the block diagonal (BD) Markov model, which groups similar successive states of the channel, is implemented in order to reduce the training complexity. The models for the error distribution are then derived for both VLC and hybrid PLC-VLC channels. Results show that the probability of error obtained from the trained models closely matches the probability of error obtained from the channel measurements, validating the suitability of the SHMM for modeling VLC and hybrid PLC-VLC channels. In addition, the modified BD Markov model, which groups the channel states shows better performance with reduced complexity when compared with the FO Markov model.

When History and Heterogeneity Matter: A Tutorial on the Impact of Markov Model Specifications in the Context of Colorectal Cancer Screening.

Markov models are used in health research to simulate health care utilization and disease states over time. Health phenomena, however, are complex, and the memoryless assumption of Markov models may not appropriately represent reality. This tutorial provides guidance on the use of Markov models of different orders and stratification levels in health decision-analytic modeling. Colorectal cancer (CRC) screening is used as a case example to examine the impact of using different Markov modeling approaches on CRC outcomes. This study used insurance claims data from commercially insured individuals in Oregon to estimate transition probabilities between CRC screening states (no screen, colonoscopy, fecal immunochemical test or fecal occult blood test). First-order, first-order stratified by sex and geography, and third-order Markov models were compared. Screening trajectories produced from the different Markov models were incorporated into a microsimulation model that simulated the natural history of CRC disease progression. Simulation outcomes (e.g., future screening choices, CRC incidence, deaths due to CRC) were compared across models. Simulated CRC screening trajectories and resulting CRC outcomes varied depending on the Markov modeling approach used. For example, when using the first-order, first-order stratified, and third-order Markov models, 30%, 31%, and 44% of individuals used colonoscopy as their only screening modality, respectively. Screening trajectories based on the third-order Markov model predicted that a higher percentage of individuals were up-to-date with CRC screening as compared with the other Markov models. The study was limited to insurance claims data spanning 5 y. It was not possible to validate which Markov model better predicts long-term screening behavior and outcomes. Findings demonstrate the impact that different order and stratification assumptions can have in decision-analytic models. This tutorial uses colorectal cancer screening as a case example to provide guidance on the use of Markov models of different orders and stratification levels in health decision-analytic models.Colorectal cancer screening trajectories and projected health outcomes were sensitive to the use of alternate Markov model specifications.Although data limitations precluded the assessment of model accuracy beyond a 5-y period, within the 5-y period, the third-order Markov model was slightly more accurate in predicting the fifth colorectal cancer screening action than the first-order Markov model.Findings from this tutorial demonstrate the importance of examining the memoryless assumption of the first-order Markov model when simulating health care utilization over time.

Bivariate copula-based CUSUM charts for monitoring conditional nonlinear processes with first-order autocorrelation

This paper considers the bivariate copula-based first-order Markov models to describe nonlinear dependence in autocorrelated data. Then the cumulative sum (CUSUM) charts based on log-likelihood ratio are developed to monitor the mean shifts. The performance of the proposed CUSUM charts is studied in both linear and nonlinear time series under weak, moderate and strong dependence by numerical simulations. Comparisons with the AR(1) model-based CUSUM and EWMA charts are present under the same range of scenarios. Simulation results show that the Clayton copula-based CUSUM charts are more effective to almost all the mean shifts and further have an obvious advantage in strong dependence. An example from chemical production is given to illustrate the implementation of the proposed control scheme.

Eighteen-month Course and Outcome of Adolescent Restrictive Eating Disorders: Persistence, Crossover, and Recovery

ABSTRACT Objective In adults, low-weight restrictive eating disorders, including anorexia nervosa (AN), are marked by chronicity and diagnostic crossover from restricting to binge-eating/purging. Less is known about the naturalistic course of these eating disorders in adolescents, particularly atypical AN (atyp-AN) and avoidant/restrictive food intake disorder (ARFID). To inform nosology of low-weight restrictive eating disorders in adolescents, we examined outcomes including persistence, crossover, and recovery in an 18-month observational study. Method We assessed 82 women (ages 10–23 years) with low-weight eating disorders including AN (n = 40; 29 restricting, 11 binge-eating/purging), atyp-AN (n = 26; 19 restricting, seven binge-eating/purging), and ARFID (n = 16) at baseline, nine months (9 M; 75% retention), and 18 months (18 M; 73% retention) via semi-structured interviews. First-order Markov modeling was used to determine diagnostic persistence, crossover, and recovery occurring at 9 M or 18 M. Results Among all diagnoses, the likelihood of remaining stable within a given diagnosis was greater than that of transitioning, with the greatest probability among ARFID (0.84) and AN-R (0.62). Persistence of BP and atypical presentations at follow-up periods was less stable (AN-BP probability 0.40; atyp-AN-R probability 0.48; atyp-AN-BP probability, 0.50). Crossover from binge-eating/purging to restricting occurred 72% of the time; crossover from restricting to binge-eating/purging occurred 23% of the time. The likelihood of stable recovery (e.g., recovery at both 9 M and 18 M) was between 0.00 and 0.36. Conclusion Across groups, intake diagnosis persisted in about two-thirds, and recovery was infrequent, underscoring the urgent need for innovative treatment approaches to these illnesses. Frequent crossover between AN and atyp-AN supports continuity between typical and atypical presentations, whereas no crossover to ARFID supports its distinction.

Improved Block Oriented Unit Memory Convolutional Codes

This paper is concerned with a special class of unit memory convolutional codes (UMCCs), called block oriented UMCCs (BOUMCCs). Distinguished from conventional UMCCs, which usually have small constraint lengths, the BOUMCCs have relatively large constraint lengths. We conduct the performance analysis by assuming a first-order Markov model, which indicates that the performance of the BOUMCCs depends critically on both the error propagation and the sub-frame error rate of the first layer. The error propagation can be alleviated by the use of partial superposition, which is specified by a superposition matrix with a fraction of columns being nulled. Given a superposition fraction, we propose a tree growing and pruning algorithm (TGPA) with a tunable sliding window, which provides a convenient way to trade off the decoding delay and the performance. We also present a structured construction and show by simulation that there is no performance degradation compared with random construction. Numerical results also show that, by taking the TBCCs as basic codes, the performance of BOUMCCs with TGPA is comparable to that of other short codes but with a more flexible construction or a lower complexity.

Prediction for Various Drought Classes Using Spatiotemporal Categorical Sequences

Drought frequently spreads across large spatial and time scales and is more complicated than other natural disasters that can damage economic and other natural resources worldwide. However, improved drought monitoring and forecasting techniques can help to minimize the vulnerability of society to drought and its consequent influences. This emphasizes the need for improved drought monitoring tools and assessment techniques that provide information more precisely about drought occurrences. Therefore, this study developed a new method, Model-Based Clustering for Spatio-Temporal Categorical Sequences (MBCSTCS), that uses state selection procedures through finite mixture modeling and model-based clustering. The MBCSTCS uses the functional structure of first-order Markov model components for modeling each data group. In MBCSTCS, the suitable order K of the components is selected by Bayesian information criterion (BIC). In MBCSTCS, the estimated mixing proportions and the posterior probabilities are used to compute probability distribution associated with the future steps of transitions. Furthermore, MBCSTCS predicts drought occurrences in future time using spatiotemporal categorical sequences of various drought classes. The MBCSTCS is applied to the six meteorological stations in the northern area of Pakistan. Moreover, it is found that MBCSTCS provides expeditious information for the long-term spatiotemporal categorical sequences. These findings may be helpful to make plans for early warning systems, water resource management, and drought mitigation policies to decrease the severe effects of drought.