Markov Chain Method Research Articles

Partition function approach to non-Gaussian likelihoods: formalism and expansions for weakly non-Gaussian cosmological inference

ABSTRACT Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of non-linearities in the physical model. Their treatment requires Monte Carlo Markov chain (MCMC) or more advanced sampling methods for the determination of confidence contours. As an alternative, we construct canonical partition functions as Laplace transforms of the Bayesian evidence, from which MCMC methods would sample microstates. Cumulants of order n of the posterior distribution follow by direct n-fold differentiation of the logarithmic partition function, recovering the classic Fisher-matrix formalism at second order. We connect this approach for weakly non-Gaussianities to the DALI and Gram−Charlier expansions and demonstrate the validity with a supernova-likelihood on the cosmological parameters Ωm and w. We comment on extensions of the canonical partition function to include kinetic energies in order to bridge to Hamilton Monte Carlo sampling, and on ensemble Markov-chain methods, as they would result from transitioning to macrocanonical partition functions depending on a chemical potential. Lastly we demonstrate the relationship of the partition function approach to the Cramér−Rao boundary and to information entropies.

PERAMALAN JUMLAH PENUMPANG KERETA API DI PULAU JAWA MENGGUNAKAN METODE HOLT WINTERS EXPONENTIAL SMOOTHING DAN FUZZY TIME SERIES MARKOV CHAIN

One of the public transportation choices by the public is the train. The number of train passengers on the island of Java often increases and decreases in certain months. PT.KAI can monitor the number of train passengers by forecasting. Forecasting aims to predict the number of train passengers so that PT.KAI is ready to provide the best service. This study uses monthly data on the number of train passengers on Java Island from January 2015 to February 2020. This study uses multiplicative holt winters exponential smoothing and fuzzy time series markov chain. The multiplicative Holt Winters exponential smoothing method is used on data that contains trend and seasonal elements that experience data fluctuations simultaneously. The fuzzy time series markov chain method is a combination of the fuzzy time series with the markov chain which aims to obtain the greatest probability using the transition probability matrix. Based on the analysis results, it can be concluded that the multiplicative holt winters exponential smoothing method is better at predicting the number of train passengers on Java Island because the value of sMAPE multiplicative holt winters exponential smoothing is smaller, it is 3,0643% and the sMAPE fuzzy time series markov chain value is 5,2955%.

METODE MARKOV CHAIN DALAM PENGENDALIAN PERSEDIAAN UNTUK PERENCANAAN BIAYA PERSEDIAAN BAHAN BAKU PADA TOKO AIRIN BAKERY & CAKE SHOP

Airin Bakery & Cake Shop produces various kinds of cakes and bread. This shop is often faced with problems that occur, namely the supply of raw materials that are insufficient or excess so that the production process does not go well. This study aims to determine the ordering capacity and the right time to order raw materials to minimize the total cost of raw material inventory using the silver meal method. The total inventory cost is Rp. 14,637,947.4 less than the cost set by the company. Inventory control, which is a stochastic process, can also be carried out without regard to safety stock, lead time, and reorder points. The stochastic process of total inventory can be described by a finite number of states. The probability of transitions between these states is described by a markov chain. The markov chain method can predict future raw material inventory costs. After making several states on the amount of raw material inventory, a prediction of the future raw material inventory costs of Rp.31.747.932,98 is obtained

Spatial Dynamics of Land Cover Change in Wae Batu GantungWatershed, Ambon City, Indonesia

The development of built-up land over the last 15 years in Ambon City has affected changes in land cover in the Wae Batugantung watershed. This is due to increasing population growth, and the increasing need for residential land. Changes in land cover in the Wae Batu Gantung watershed have an impact on land degradation, water pollution, flooding, and erosion, which will increase in the future. This study aims to analyze land cover changes in the Wae Batu Gantung watershed in 2012, 2017, 2022, and predict land cover in 2027, and 2031. The Cellular Automata Markov Chain method was used in this study to predict the spatial dynamics of land cover change. The results of the study show that from 2012, 2017, 2022, and predictions for 2027, and 2031 residential land, and open land in the Wae Batutangan watershed continue to expand, in contrast to non-agricultural land cover, and agricultural land which is decreasing

Cellular Automata Markov Chain Application For Prediction Of Land Cover Changes In The Wae Batu Gantung Watershed, Ambon City, Indonesia

The development of built-up land over the last 15 years in Ambon City has affected changes in land cover in the Wae Batugantung watershed. This is due to increasing population growth, and the increasing need for residential land. Changes in land cover in the Wae Batu Gantung watershed have an impact on land degradation, water pollution, flooding, and erosion, which will increase in the future. This study aims to analyze land cover changes in the Wae Batu Gantung watershed in 2012, 2017, 2022, and predict land cover in 2027, and 2031. The Cellular Automata Markov Chain method was used in this study to predict the spatial dynamics of land cover change. The results of the study show that from 2012, 2017, 2022, and predictions for 2027, and 2031 residential land, and open land in the Wae Batutangan watershed continue to expand, in contrast to non-agricultural land cover, and agricultural land which is decreasing. The results of this study are expected to be input into policy making related to spatial utilization in the Wae Batugantung Watershed in the future.

Application of Markov Chain in Predicting Sugar Production at Candi Baru Sugar Factory, Sidoarjo

Granulated sugar is a sugar commonly used daily to manufacture food and beverages. The demand for granulated sugar continues to increase, but the number of sugar factories and the area of ​​sugar cane in Indonesia is decreasing. This causes a gap between the demand for sugar which continues to increase, and the production of granulated sugar continues to decline, resulting in Indonesia being the largest country importer of sugar. The imbalance between the demand and production of granulated sugar At Candi Baru Sugar Factory, Sidoarjo, East Java, resulted in not achieving the target to meet these needs. Therefore, predictions are made to get an overview of production planning to optimize granulated sugar production so that sugar needs can be met. The prediction method used at the Candi Baru sugar factory, Sidoarjo, East Java, for the 2022 milling period is the Markov Chain method with a four-state divisor, namely drastically down, down, up, and up drastically. The application of Markov Chains produces predictions for each state. It is predicted that the production of sugar with the highest percentage for May – December upstate.

Comparison and parallel implementation of alternative moving-window metrics of the connectivity of protected areas across large landscapes

ContextA variety of metrics can be used to measure connectivity of protected areas. Assumptions about animal movement and mortality vary among metrics. There is a need to better understand what to use and why, and how much conclusions depend on the choice of metric.ObjectivesWe compare selected raster-based moving-window metrics for assessing the connectivity of protected areas to natural habitat in the surrounding area, and develop tools to facilitate calculation of these metrics for large landscapes.MethodsWe developed parallel implementations of distance-weighted sum and Spatial Absorbing Markov Chain methods in R packages to improve their useability for large landscapes. We investigated correlations among metrics for Canadian protected areas, varying background mortality, cost of movement, mean displacement, dispersal kernel shape, distance measure used, and the treatment of natural barriers such as water, ice, and steep slopes.ResultsAt smaller spatial scales (2–5 km mean displacement), correlations among metric variants are high, suggesting that any of the metrics we investigated will give similar results and simple metrics will suffice. Differences among metrics are most evident at larger spatial scales (20–40 km mean displacement) in moderately disturbed regions. Assumptions about the impact of natural barriers have a large impact on outcomes.ConclusionIn some circumstances different metrics give similar results, and simple distance-weighted metrics likely suffice. At large spatial scales in moderately disturbed regions there is less agreement among metrics, implying that more detailed information about disperser distribution, behaviour, and mortality risk is required for assessing connectivity.

Pemodelan Kondisi Perkerasan Jalan dengan Metode Probabilistik Rantai Markov

Road pavements are an important part of transportation infrastructure and require regular maintenance. This study aimed to model the condition of road pavement by the probabilistic method of Markov chains. The method used in this study is a literature study and data collection from a survey of road pavement conditions in the field. Data analysis was performed using the Markov chain probabilistic method, which can be used to model changes in pavement conditions over time. The results showed that the Markov chain probabilistic method can be used to model changes in pavement conditions with high accuracy. This method can also be used to make predictions of future pavement conditions and determine the right time to perform maintenance and repairs. The study recommends using the Markov chain probabilistic method as a tool to model pavement conditions and make appropriate maintenance and repair decisions. Thus, it is expected to increase the effectiveness of road pavement management and extend the service life of road pavement.

Wet and Dry Spell Analysis for Crop Planning in Central Plain Zone of Punjab Using Markov Chain Method

A study was conducted during 2017–2018 at department of climate change and agricultural meteorology, PAU, Ludhiana to find out the initial and conditional probability of occurrence of wet and dry spell of rainfall at different locations of Punjab, the analysis was carried out using Markov Chain Method (MCM). The historical data of rainfall for three locations of Punjab viz. Amritsar (1971–2017), Ludhiana (1971–2018) and Patiala (1971–2018) were collected from the Department of Climate Change and Agricultural Meteorology, PAU, Ludhiana and Met Centre, India Meteorological Department, Chandigarh. At Amritsar the chances of occurrence of wet spell were highest during 28th SMW i.e., 72% followed by 68% during 30th and 31st SMW respectively. The conditional probability calculated at Ludhiana showed that the probability of wet spell followed by wet spell was highest (71%) during 28th SMW followed by 66 per cent during 30th and 32nd SMW. At Patiala the probability of wet spell was highest (69%) during 33rd week followed by 63% during 29th SMW. The conditional probability also showed that dry spell followed by dry spell occurred more frequently than wet spell followed by wet spell.

Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

AbstractIn this paper, we investigate classical and Bayes estimates for stress‐strength reliability (SSR) based on two independent progressive first failure censored samples from beta log Weibull distributions with different shape and scale parameters. The maximum likelihood estimation of SSR and its asymptotic confidence interval are obtained. Bayes estimates of SSR are derived under two different loss functions using the Tierney–Kadane's approximation algorithm. In addition, two different bootstrap confidence intervals are provided and the highest posterior density credible interval of SSR is also constructed by applying Monte Carlo Markov chain method. The performances of different point and interval estimates are assessed using the Monte Carlo simulation. Finally, three real data sets are analyzed for illustration purposes.

Predicting DNA kinetics with a truncated continuous-time Markov chain method

Predicting the kinetics of reactions involving nucleic acid strands is a fundamental task in biology and biotechnology. Reaction kinetics can be modeled as an elementary step continuous-time Markov chain, where states correspond to secondary structures and transitions correspond to base pair formation and breakage. Since the number of states in the Markov chain could be large, rates are determined by estimating the mean first passage time from sampled trajectories. As a result, the cost of kinetic predictions becomes prohibitively expensive for rare events with extremely long trajectories. Also problematic are scenarios where multiple predictions are needed for the same reaction, e.g., under different environmental conditions, or when calibrating model parameters, because a new set of trajectories is needed multiple times. We propose a new method, called pathway elaboration, to handle these scenarios. Pathway elaboration builds a truncated continuous-time Markov chain through both biased and unbiased sampling. The resulting Markov chain has moderate state space size, so matrix methods can efficiently compute reaction rates, even for rare events. Also the transition rates of the truncated Markov chain can easily be adapted when model or environmental parameters are perturbed, making model calibration feasible. We illustrate the utility of pathway elaboration on toehold-mediated strand displacement reactions, show that it well-approximates trajectory-based predictions of unbiased elementary step models on a wide range of reaction types for which such predictions are feasible, and demonstrate that it performs better than alternative truncation-based approaches that are applicable for mean first passage time estimation. Finally, in a small study, we use pathway elaboration to optimize the Metropolis kinetic model of Multistrand, an elementary step simulator, showing that the optimized parameters greatly improve reaction rate predictions. Our framework and dataset are available at https://github.com/DNA-and-Natural-Algorithms-Group/PathwayElaboration.

A phase II run sum chart for monitoring process mean and variability

ABSTRACT This article proposes a run sum Max chart for monitoring a process and detecting changes in mean and variability simultaneously. A Markov chain method is applied to evaluate the statistical performance of the chart by using both average run length (ARL) and expected average run length (EARL) criteria. The numerical analysis demonstrates an improved performance of the run sum Max control chart over the usual Max chart. In addition, a numerical comparison with the Max-EWMA control chart as well as with the Max chart supplemented with runs rules, reveals that the run sum Max chart outperforms these charts in the detection of moderate to large shifts in both process parameters. Furthermore, we provide practical guidance for the selection of the appropriate charting procedure, while the use of the proposed run sum Max chart in practice is illustrated via a numerical example.

Damage analysis of concrete-filled square stainless steel columns based on acoustic emission and Markov chain methods

A test of concrete-filled square stainless steel (CFSST) columns with different eccentricities under compression was conducted to evaluate their failure and damage characteristics. Acoustic emission (AE) analysis was used to assess the damage process, and a damage prediction model based on the Markov chain was established. The monitoring results showed that the outward buckling was the dominant damage mode. As the eccentricity increased, the damage location changed from both sides of the column to the compressed side. The AE characteristic energy and b-value accurately described the damage process, which was divided into three stages: initial stability, cracking and buckling, and approaching failure. An analysis of the rise time/peak amplitude ratio (RA) and AE count/duration ratio (AF) indicated that tensile cracking was dominant in the three stages. A prediction model based on Markov chain was proposed to reflect state of CFSST columns, which could provide effective guidance in practical engineering.

An efficient model to estimate the soil profile and stratigraphic uncertainty quantification

Comprehensive geological information is very important and needed in underground construction and underwater infrastructure. However, it is quite difficult to reveal the configuration of different soil features of underground with sparsely measured data. In this study, a new algorithm named General Regression-Markov Chain (GR-MC) was proposed by coupling the general regression neural network and the Markov chain method together to reproduce the characteristics of underground stratification based on rare borehole information. The general regression neural network method was introduced to evaluate the geological variation along the inclined orientation, while the Markov chain method was applied to examine the change in soil types along the depth. The spatial coordinates of the treated construction site were designed as the input variables, while a vector including the probability information of different soil types was set as the output. The proposed GR-MC method is very intuitive and can be efficiently implemented to predict the geological model using only the coordinates as inputs. Moreover, the proposed method can be smoothly extended into a three-dimensional case with low computational resources. Compared to the existing methods, the proposed GR-MC algorithm is computationally efficient and robust. Three cases from real practice were evaluated and the calculated results were consistent with the known borehole information. Besides, the stratigraphic uncertainty was quantified based on information entropy theory. The results can visually reveal the zones of the estimated soil profile with relatively large uncertainty. The practical application is that possible additional borehole locations were identified to reduce the stratigraphic uncertainty of a construction site.

Black hole discs and spheres in galactic nuclei – exploring the landscape of vector resonant relaxation equilibria

ABSTRACT Vector resonant relaxation (VRR) is known to be the fastest gravitational process that shapes the geometry of stellar orbits in nuclear star clusters. This leads to the realignment of the orbital planes on the corresponding VRR time-scale tVRR of a few million years, while the eccentricity e and semimajor axis a of the individual orbits are approximately conserved. The distribution of orbital inclinations reaches an internal equilibrium characterized by two conserved quantities, the total potential energy among stellar orbits, Etot, and the total angular momentum, Ltot. On time-scales longer than tVRR, the eccentricities and semimajor axes change slowly, and the distribution of orbital inclinations are expected to evolve through a series of VRR equilibria. Using a Monte Carlo Markov Chain method, we determine the equilibrium distribution of orbital inclinations in the microcanonical ensemble with fixed Etot and Ltot for isolated nuclear star clusters with a power-law distribution of a, e, and m, where m is the stellar mass. We explore the possible equilibria for nine representative Etot–Ltot pairs that cover the possible parameter space. For all cases, the equilibria show anisotropic mass segregation, where the distribution of more massive objects is more flattened than that for lighter objects. Given that stellar black holes are more massive than the average main-sequence stars, these findings suggest that black holes reside in disc-like structures within nuclear star clusters for a wide range of initial conditions.

Investigating zero-state and steady-state performance of MEWMA-CoDa control chart using variable sampling interval

ABSTRACT Traditional process monitoring control charts (CCs) focused on sampling methods using fixed sampling intervals ( FSI s). The variable sampling intervals ( VSI s) scheme is receiving increasing attention, in which the sampling interval ( SI ) length varies according to the process monitoring statistics. A shorter SI is considered when the process quality indicates the possibility of an out-of-control (OOC) situation; otherwise, a longer SI is preferred. The VSI multivariate exponentially moving average for compositional data ( VSI - MEWMA CoDa ) CC based on a coordinate representation using isometric log-ratio ( ilr ) transformation is proposed in this study. A methodology is proposed to obtain the optimal parameters by considering the zero-state ( ZS ) average time to signal ( ZATS ) and the steady-state (SS) average time to signal ( SATS ). The statistical performance of the proposed CC is evaluated based on a continuous-time Markov chain ( CTMC ) method for both cases, the ZS and the SS using a fixed value of in-control (IC) ATS 0 . Simulation results demonstrate that the VSI - MEWMA CoDa CC has significantly decreased the OOC average time to signal ( ATS ) than the FSI MEWMA CoDa CC. Moreover, it is found that the number of variables (d) has a negative impact on the ATS of the VSI - MEWMA CoDa CC, and the subgroup size (n) has a mildly positive impact on the ATS of the VSI - MEWMA CoDa CC. At the same time, the SATS of the VSI - MEWMA CoDa CC is less than the ZATS of the VSI - MEWMA CoDa CC for all the values of n and d. The proposed VSI - MEWMA CoDa CC under steady-State performs effectively compared to its competitors, such as the FSI - MEWMA CoDa CC, the VSI - T 2 CoDa CC and the FSI - T 2 CoDa CC. An example of an industrial problem from a plant in Europe is also given to study the statistical significance of the VSI - MEWMA CoDa CC.

The Construction of Xi’an Urban Bus Driving Cycle: A Case Study

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.

Regional differences and dynamic evolution of urban land green use efficiency within the Yangtze river economic belt, China

In this study, we calculate the urban land green use efficiency (ULGUE) in the Yangtze River Economic Belt from 2005 to 2019 by using the epsilon-based measure (EBM) model. Further, the spatial-temporal distribution, regional differences and evolution trends of ULGUE in the Yangtze River Economic Belt are investigated in depth by using the Dagum Gini coefficient, Kernel Density estimation and Markov Chain method. The following results are obtained. 1) From the perspective of spatial-temporal evolution, the ULGUE in the Yangtze River Economic Belt show a fluctuating upward trend from 2005 to 2019, and it is manifested as diffusion from downstream to middle and upper reaches. 2) From the perspective of regional differences, there is a relatively obvious imbalance of ULGUE within the Yangtze River Economic Belt, but the differences narrow over time. 3) Considering the distribution dynamic evolution, the box diagram and distribution curve of ULGUE in the Yangtze River Economic Belt have a tendency to move to high values, but there is a more obvious phenomenon of spatial polarization. 4) For the part of time and space transfer, the ULGUE within the Yangtze River Economic Belt show the characteristic of “club convergence”, and the Spatial Markov Chain results show an obvious “spatial spillover” effect.

Life Expectancy in Pre-Frail and Frail States with and without Disability: 18-Years of Follow-Up Data from the HEPESE Study Using the Markov Chain Method.

We estimated the total life expectancy (TLE), frailty-free life expectancy (FFLE), frail life expectancy (FLE), pre-frail life expectancy (PFLE), and FLE with and without disability among 2,000 Mexican Americans aged ≥67 years over an 18-year period. Frailty was defined as the presence of ≥2 criteria (weight loss, weakness, self-reported exhaustion, slowness). We used the Markov chain method to estimate the TLE, FFLE, FLE, PFLE, and FLE with and without disability by age and gender. TLE at age 67 was 17.49 years (women) and 15.54 years (men); FFLE was 6.50 years (women) and 6.45 years (men); PFLE was 6.48 years (women) and 5.42 years (men); FLE was 4.51 years (women) and 3.67 years (men); and FLE with disability was 2.13 years (women) and 1.13 years (men). In conclusion, Mexican American older women had fewer years of non-frail LE, more pre-frail or frail years, and more years with disability than men.

An Enhanced Approach for Load Behavior and Battery Residual Capacity Prediction Using Markov Chain and Monte Carlo Method

The demands for energy storage systems and energy management systems are increasing with the development of modern electric vehicles. The battery management technology is the basis and key to ensure vehicle safety and prolong the battery life of electrified vehicles. One of the technical bottlenecks in battery management technology is the state estimation of the power batteries. Because the behavior of the lithium-ion battery is highly nonlinear, and the internal states and model parameters are susceptible to temperature, noise, and other factors, the battery states are difficult to be observed accurately. In the past decades, many battery state estimation strategies have been developed. However, dynamic systems in the real world, whether linear or nonlinear, usually exhibit behavior that leads to excessive outliers. This article attempts to discuss the coestimation method for state-of-charge and remaining discharge time. First, a temperature-compensated model is presented based on the equivalent-circuit model. Then, the Bayesian estimation method is employed for the coestimation of state-of-charge and remaining discharge time. Moreover, the Markov chain prediction model is presented for the load profiles. Experimental studies showed that the proposed methods have accurate and robust state-of-charge estimates under dynamic driving cycles with mean absolute error less than 2%.