A review on smoothing techniques in Markov chains methods

The status of things always changes with the process of time. Markov chains approach considers that as long as the current status is known, the future state of things can be forecasted without understanding the past state. Considering the spatial autocorrelation of spatial things, Markov chains is combined with spatial autocorrelation to develop the spatial Markov chains to study the influence of regional background on regional transition. The industrial structure of regions alters in different periods of time, and its development process and tendency can be approached approximately by using Markov chains methods. Based on the coefficient dataset of industrial structure at the county level in Sichuan province from 2000 to 2007, this paper attempts to apply Markov chains and Spatial Markov chain to investigate the spatial and temporal characteristics of industrial structure level in Sichuan. Firstly, all the coefficient data of industrial structure in Sichuan are classified into 4 different classes (low, middle-low, middle-high and high) and Markov transition probability matrix is estimated to explore whether the convergence of industrial structure level exists in Sichuan. Secondly, conditioning on each region's spatial lag at the beginning of each year, spatial Markov matrices are constructed to investigate the relationship between transition probability of different regions and their neighbors, and maps are accordingly made in order to visualize spatial patterns of class transitions. Thirdly, the evolutionary trends of industrial structure level in the next twenty years, fifty years and one hundred years are forecasted respectively by computing the twentieth, fiftieth and hundredth power of Markov transition probability matrix. Finally, the measures to improve the industrial structure level in Sichuan province are given.

At present, there are many methods to construct a vehicle driving cycle, such as the micro-trip-based method and the Markov chain method. Different methods have different advantages and disadvantages. To compare these methods, this paper uses the micro-trip-based method, the Markov chain method, and the method combining micro-trips and Markov chains to construct the representative driving cycle of a Xi’an urban bus based on the driving data of the Xi’an No.2 bus. Firstly, the driving data is collected and preprocessed. Then, representative driving cycles are constructed based on different methods. Finally, different driving cycles based on different methods are compared. By calculating and comparing characteristic parameters, velocity distributions, acceleration distributions, and vehicle-specific power distributions between different representative driving cycles, this paper shows the advantages and disadvantages of different construction methods.

Soil erosion prediction using Markov and CA-Markov chains methods and remote sensing drought indicators

This paper is a survey of the major techniques and approaches available for the numerical approximation of integrals in statistics. We classify these into five broad categories; namely, asymptotic methods, importance sampling, adaptive importance sampling, multiple quadrature and Markov chain methods. Each method is discussed, giving an outline of the basic supporting theory and particular features of the technique. Conclusions are drawn concerning the relative merits of the methods based on the discussion and their application to three examples. The following broad recommendations are made. Asymptotic methods should only be considered in contexts where the integrand has a dominant peak with approximate ellipsoidal symmetry. Importance sampling (and preferably adaptive importance sampling) based on a multivariate Student should be used instead of asymptotics methods in such a context. Multiple quadrature and, in particular, subregion adaptive integration are the algorithms of choice for lower-dimensional integrals. Due to the difficulties in assessing convergence to stationarity and the error in estimates, Markov chain methods are recommended only when there is no adequate alternative. In certain very high dimensional problems, however, Markov chain methods are the only hope. The importance of the parameterization of the integral is noted for the success of all the methods, and several useful reparameterizations are presented.

BackgroundMedical students must meet curricular expectations and pass national licensing examinations to become physicians. However, no previous studies explicitly modeled stages of medical students acquiring basic science knowledge. In this study, we employed an innovative statistical model to characterize students’ growth using progress testing results over time and predict licensing examination performance.MethodsAll students matriculated from 2016 to 2017 in our medical school with USMLE Step 1 test scores were included in this retrospective cohort study (N = 358). Markov chain method was employed to: 1) identify latent states of acquiring scientific knowledge based on progress tests and 2) estimate students’ transition probabilities between states. The primary outcome of this study, United States Medical Licensing Examination (USMLE) Step 1 performance, were predicted based on students’ estimated probabilities in each latent state identified by Markov chain model.ResultsFour latent states were identified based on students’ progress test results: Novice, Advanced Beginner I, Advanced Beginner II and Competent States. At the end of the first year, students predicted to remain in the Novice state had lower mean Step 1 scores compared to those in the Competent state (209, SD = 14.8 versus 255, SD = 10.8 respectively) and had more first attempt failures (11.5% versus 0%). On regression analysis, it is found that at the end of the first year, if there was 10% higher chance staying in Novice State, Step 1 scores will be predicted 2.0 points lower (95% CI: 0.85–2.81 with P < .01); while 10% higher chance in Competent State, Step 1scores will be predicted 4.3 points higher (95% CI: 2.92–5.19 with P < .01). Similar findings were also found at the end of second year medical school.ConclusionsUsing the Markov chain model to analyze longitudinal progress test performance offers a flexible and effective estimation method to identify students’ transitions across latent stages for acquiring scientific knowledge. The results can help identify students who are at-risk for licensing examination failure and may benefit from targeted academic support.

China imports a large quantity of bauxite each year. Bauxite in fine particles with high moisture has a high risk of liquefaction during the maritime transportation process, which is harmful to the stability and safety of the carrier. To ensure safe shipping, it is necessary to pay attention to the effects of the operation of cargo, the ship’s maneuvering and the ocean environment during the whole transportation process. The simulation of the process risk helps to develop measures to intervene with the cargo behavior to keep the risk to an acceptable level. This study examined the transportation process of a bauxite carrier using the Markov Chain method at different stages of loading, unberthing, departure and sea navigation. Based on the risk transfer matrix of the operational status at different stages of transportation, a cloud simulation model was developed to analyze the transportation process risk of a ship carrying bulk bauxite. Results: the research revealed that the risk evolution rule of the solid bulk cargoes with potential liquefaction during the transportation process, especially bauxite. The risk alteration during the prophase of the transportation process conforms to the rule of the “spoon curve”. Conclusions: a simulation model of the process risk based on the Markov Chain Cloud is suitable for the simulation analysis of the transportation risk of the bulk bauxite carrier. The outcomes of this study may contribute to better safety management to prevent the occurrence of ship capsizing.

Demography is the study of the population consequences of the fates of individuals. Individuals are differentiated on the basis of age or, in general, life cycle stages. The movement of an individual through its life cycle is a random process, and although the eventual destination (death) is certain, the pathways taken to that destination are stochastic and will differ even between identical individuals; this is individual stochasticity. A stage‐classified demographic model contains implicit age‐specific information, which can be analyzed using Markov chain methods. The living stages in the life cycles are transient states in an absorbing Markov chain; death is an absorbing state. This paper presents Markov chain methods for computing the mean and variance of the lifetime number of visits to any transient state, the mean and variance of longevity, the net reproductive rate R 0 , and the cohort generation time. It presents the matrix calculus methods needed to calculate the sensitivity and elasticity of all these indices to any life history parameters. These sensitivities have many uses, including calculation of selection gradients. It is shown that the use of R 0 as a measure of fitness or an invasion exponent gives erroneous results except when R 0 =λ=1. The Markov chain approach is then generalized to variable environments (deterministic environmental sequences, periodic environments, iid random environments, Markovian environments). Variable environments are analyzed using the vec‐permutation method to create a model that classifies individuals jointly by the stage and environmental condition. Throughout, examples are presented using the North Atlantic right whale ( Eubaleana glacialis ) and an endangered prairie plant ( Lomatium bradshawii ) in a stochastic fire environment.

Predicting personalized sequential behavior is a key task for recommender systems. In order to predict user actions such as the next product to purchase, movie to watch, or place to visit, it is essential to take into account both long-term user preferences and sequential patterns (i.e., short-term dynamics). Matrix Factorization and Markov Chain methods have emerged as two separate but powerful paradigms for modeling the two respectively. Combining these ideas has led to unified methods that accommodate long-and short-term dynamics simultaneously by modeling pairwise user-item and item-item interactions. In spite of the success of such methods for tackling dense data, they are challenged by sparsity issues, which are prevalent in real-world datasets. In recent years, similarity-based methods have been proposed for (sequentially-unaware) item recommendation with promising results on sparse datasets. In this paper, we propose to fuse such methods with Markov Chains to make personalized sequential recommendations. We evaluate our method, Fossil, on a variety of large, real-world datasets. We show quantitatively that Fossil outperforms alternative algorithms, especially on sparse datasets, and qualitatively that it captures personalized dynamics and is able to make meaningful recommendations.

The classical procedure of ordering new vehicles in replacement of the existing ones is unsatisfactory as it is based on the average life of a vehicle and is good only after a lapse of several years when 'stable' conditions are reached. In this paper, an alternative procedure is prescribed. It makes use of an autoregrassive equation obeyed by the number of new vehicles. This equation is to obtained by using the method of Markov chains.

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches.

Full-waveform inversion estimates subsurface properties by minimizing the misfit between observed and modelled data. However, conventional deterministic approaches are highly sensitive to noise, dependent on the starting model and prone to converging to local minima of the cost function. Bayesian approaches offer a viable alternative, enhancing solution space exploration and providing uncertainty quantification. This study compares three Bayesian inversion methods: Stochastic-Newton Markov Chain Monte Carlo, Ensemble Smoother with Multiple Data Assimilation and Annealed Stein Variational Gradient Descent. To mitigate ill-conditioning, reduce computational cost, and lower problem dimensionality, we incorporate Discrete Cosine Transform compression of model and data spaces. These methods are evaluated under three scenarios: optimal conditions as a baseline, a less informative prior to assess initialization sensitivity, and a more realistic setting with increased noise, missing traces and wrong assumptions about the source wavelet and noise level. These tests are conducted on a synthetic example based on a portion of the Marmousi model. Results indicate that the ensemble-based approach is the most computationally efficient, is robust to initialization, but strongly underestimates uncertainties. The Markov Chain method, while computationally demanding, is robust to initialization and effectively captures uncertainties. The Variational Inference approach, with intermediate computational cost, achieves good performance in complex scenarios, but it is more sensitive to initialization due to its deterministic nature. This study provides insights into the advantages and limitations of these three Bayesian approaches to acoustic full-waveform inversion and highlights the benefits of the Discrete Cosine Transform compression.

Purpose: Stock market performance and operation have been widely recognized as a viable investment field in financial markets. Therefore, this paper studied the stochastic analysis of the Markov chain and PCA in the closing share price data of Access and Fidelity banks (2016-2022) through the Nigeria Stock Exchange. The share prices were transformed into a 3-step transition probability matrix solution to cover this number of years.Methodology:This research uses the Markov chain method, which defines a stochastic process. Mathematically, a stochastic process can be defined as a collection of random variables ordered in time and determined at a series of time points that may be continuous or discrete.Findings:The criteria for obtaining four share prices formed from the two merged banks' 2x2 matrices were given, and analytical solutions of principal components were considered for future stock price changes.Implication: The solution matrix of the two merged banks showed that they have the best probability of price increasing shortly: 12%, the best probability of reducing in the future by 22%, and the best probability of no-change shortly by 21%, which is a tool for proper decision making in the day-to-day management of the bank; which shows it is profit making organization and are hopeful for future investment plans both short or long term respectively.

Performance analysis of carrier sense multiple access with collision avoidance (CSMA/CA) scheme based on IEEE 802.15.6 standard has been discussed in many literatures. In previous works on IEEE 802.15.6 and another standards, the performance was analyzed by using access probability in one slot duration and the Markov chain model was proposed to calculate the access probability in both saturation and non-saturation models. However, for both saturation and non-saturation models, the access probability or the packet arrival rate was assumed to be fixed and the effect of remained packets that was transmitted unsuccessfully due to busy channel or collision was not considered. In this paper, in order to evaluate the system performance more accurately, the effect of the remained packet is taken into account and a statistical method is proposed to calculate the successful probability of wireless body area networks (WBANs). Moreover, a time-saturation model is defined as a system model in which the system performance is changed following the operating time, and then, the change between three models, i.e., saturation, non-saturation, and time-saturation models, is analyzed. The calculation result indicates that the proposal method can achieve the same performance as the Markov chain method in both saturation and non-saturation models. However, in the time-saturation model, the proposal statistical method is more accurate.

The EWMA Sign control chart is an efficient tool for monitoring shifts in a process regardless the observations' underlying distribution. Recent studies have shown that, for nonparametric control charts, due to the discrete nature of the statistics being used (such as the Sign statistic), it is impossible to accurately compute their Run Length properties using Markov chain or integral equation methods. In this work, a modified nonparametric Phase II EWMA chart based on the Sign statistic is proposed and its exact Run Length properties are discussed. A continuous transformation of the Sign statistic, combined with the classical Markov Chain method, is used for the determination of the chart's in- and out-of-control Run Length properties. Additionally, we show that when ties occur due to measurement rounding-off errors, the EWMA Sign control chart is no longer distribution-free and a Bernoulli trial approach is discussed to handle the occurrence of ties and makes the proposed chart almost distribution-free. Finally, an illustrative example is provided to show the practical implementation of our proposed chart.

An efficient method for computer simulations of liquid and amorphous systems is described. The method is based on replacing the natural trajectory of the system in phase space generated by the Newtonian equations of motion by a Markov chain. Convergence to the Gibbs distribution is proved. The relation to the other simulation methods is discussed. The method is applied to simulation of the structure of amorphous iron. As an example of employing the method to study thermodynamic properties, the quenching of the system is investigated.