Markov Chain Monte Carlo Process Research Articles

Development and performance assessment of a new opensource Bayesian inference R platform for building energy model calibration

Many factors contribute to the inherent uncertainty of energy consumption modeling in buildings. It is essential to perform a calibration and sensitivity analysis in order to manage these uncertainties. Despite the availability of several calibration methods, they are often deterministic and lack quantified uncertainties. Moreover, the selection of parameters in building energy modeling for calibration depends on the user’s experience. Therefore, a more rigorous selection process is required. This study developed a new automated Bayesian Inference calibration platform running as an R package. A sensitivity analysis module and a Bayesian inference module determine the calibration parameters and uncertainties, respectively. The Meta-model module is developed to replace the building energy model for the Markov Chain Monte Carlo process to save computing time. The proposed platform is successfully demonstrated on a synthetic high-rise office building and a real high-rise residential building in a hot and arid climate. The relationship between the number of calibration parameters, calibration performance, and the accuracy of the Meta-model is further discussed. The developed calibration platform in this study proved to have clear advantages over the existing platforms, with the ability to reasonably estimate building energy performance in a short computing time.

Seemingly unrelated time series model for forecasting the peak and short-term electricity demand: Evidence from the Kalman filtered Monte Carlo method

In this extant paper, a multivariate time series model using the seemingly unrelated times series equation (SUTSE) framework is proposed to forecast the peak and short-term electricity demand using time series data from February 2, 2014, to August 2, 2018. Further the Markov Chain Monte Carlo (MCMC) method, Gibbs Sampler, together with the Kalman Filter were applied to the SUTSE model to simulate the variances to predict the next day's peak and electricity demand. Relying on the study results, the running ergodic mean showed the convergence of the MCMC process. Before forecasting the peak and short-term electricity demand, a week's prediction from the 28th to the 2nd of August of 2018 was analyzed and it found that there is a possible decrease in the daily energy over time. Further, the forecast for the next day (August 3, 2018) was about 2187 MW and 44090 MWh for the peak and electricity demands respectively. Finally, the robustness of the SUTSE model was assessed in comparison to the SUTSE model without MCMC. Evidently, SUTSE with the MCMC method had recorded an accuracy of about 96% and 95.8% for Peak demand and daily energy respectively.

Optimizing facility maintenance planning under uncertainty

Maintenance of civil infrastructure is necessary to ensure assets perform as intended over their service life. As these elements age and degrade, appropriate repair planning helps ensure continued operation. Unfortunately, optimal repair planning can be complex due to uncertainty regarding component conditions. This uncertainty also makes budgeting difficult. This paper presents a novel methodology for optimizing maintenance planning of facility components under uncertainty. The proposed methodology integrates a Markov chain Monte Carlo process to capture the uncertainty inherent in equipment degradation, and a mixed integer programming model to generate an optimal repair plan and an associated minimized budget. This approach identifies an optimal set of facility components that need to be repaired to minimize the total facility repair cost required to meet or exceed a user-defined goal for facility health. The proposed method has distinct advantages over many non-linear approaches in literature as it can guarantee an optimal solution with significantly lower computational time. This computational advantage enables the technique to scale to more significant problems, such as determining repair plans across a portfolio of facilities. The method outperforms basic decision heuristics used to define repair plans and existing non-linear optimization methods in terms of consistently meeting a facility health metric at a minimal cost. Data obtained from the U.S. Army Corps of Engineers is used within a case study to demonstrate the feasibility of the proposed approach as it applies to building infrastructure maintenance.

Guided Sampling for Multistructure Data via Neighborhood Consensus and Residual Sorting

Robust model fitting is a critical technique for artificial intelligence. The performance of most robust model fitting techniques heavily depends on the use of sampling algorithms. In this paper, we propose an efficient guided sampling algorithm for multi-structure data by using the neighborhood consensus and the residual sorting. Specifically, a Neighborhood Consensus based Strategy (NCS) is first proposed to select the first datum (i.e., seed datum) of a minimal subset, and then a Residual Sorting based Strategy (RSS) samples the rest data of the minimal subset based on the seed datum. This strategy effectively combines the benefits of neighborhood consensus and residual sorting, where neighborhood consensus can judge whether a selected data point is an inlier, and residual sorting encourages this strategy to select data points from the same structure of the first selected data point. Moreover, to achieve better fitting performance, the Markov Chain Monte Carlo process is used to combine NCS with the random selection strategy to select the seed datum, and an appropriate size is set to the initial block of randomly sampled hypotheses for RSS. Experimental results on three vision tasks (e.g., two-view motion segmentation and 3D motion segmentation) demonstrate that the proposed algorithm achieves superior performance to several state-of-the-art sampling algorithms.

Quantitative analysis of species distribution of the Mississippian Zaphrentites delanouei group from the Vale of Glamorgan, UK

The evolutionary process of anagenesis is thought to control distributions of members of the Zaphrentites delanouei species group, the Tournaisian‐Viséan solitary rugose corals, within the Carboniferous Limestone. We present alternative interpretations specific to the Friars Point Limestone Formation, which point to composite evolutionary processes closer to anacladogenesis. We use a Markov Chain Monte Carlo process to organize fossils into matrices representing states of concurrence, where concurrence is the number of species coexisting in each bed. We analyse their distributions according to transitions between states. Data testing by matrix multiplication shows whether stochastic equilibrium or convergence is reached, to determine probabilities of species coexistence. Taking the probabilities from the Markov Chain Monte Carlo process to represent the first generation of a branching process, we proceed to calculate the second to fourth generations. Finally, we model these values in a Galton–Watson process to determine the likelihood of ultimate extinction, and whether the species belong to the same population without immigration or emigration. Results show that the species distribution is both anagenetic (0.725) and cladogenetic (0.275). Therefore, we define the evolutionary process as anacladogenetic with the potential for up to eight species in addition to the six defined in the literature. This represents some evidence for a population unaffected by immigration or emigration, with a high likelihood of ultimate extinction for most localities. We deduce that second or third‐generation concurrences are a requisite for survival, even with anacladogenesis. As an environmental corollary, the amplification of extinction rates was exacerbated within a regressive marine system, and our techniques will allow further exploration of evolutionary mechanisms and energy within coral ecosystems.

The Temperature and Emission Measure Distribution in the Quiet and Active Solar Corona: A Bayesian Approach

The reconstruction of the differential emission measure (DEM) from observations of spectral line intensities provides information on the temperature distribution of the emission measure in the region observed. The inversion process is known to be highly unstable, and it has been necessary to provide additional constraints, such as requiring that the DEM should be smooth. However, this is a nonphysical constraint. The goal of this analysis is to make an empirical determination of the ability of a set of emission-line intensities to constrain the reconstruction. Here, a simple model is used, by means of a Markov Chain Monte Carlo process, to arrive at solutions that reproduce the observed intensities in a region of the quiet Sun and a solar active region. These solutions are compared by means of the reduced chi-squared. The conclusion from this analysis is that the observations are only capable of constraining a model consisting of four temperature–emission measure pairs plus a determination of the standard deviation of the model from the observed line intensities. A more complex model with five temperature–emission measure pairs does not improve the fit and leads to parameters that are irrelevant. A more general conclusion is that the information content of a set of observed emission lines is limited with respect to the determination of the emission measure distribution.

Quantum Markov chain Monte Carlo with digital dissipative dynamics on quantum computers

Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo process that allows sampling of the Gibbs distribution of a multivariate model. To demonstrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.

Constructing the resistivity-to-sediment-type transform for the interpretation of airborne electromagnetic data

A novel Markov chain Monte Carlo (MCMC)-based methodology was developed for the transformation of resistivity, derived from airborne electromagnetic (AEM) data, into sediment type. This methodology was developed and tested using AEM data and well sediment type and resistivity logs from Butte and Glenn Counties in the California Central Valley. Our methodology accounts for the spatially varying sensitivity of the AEM method by constructing different transforms separated based on the sensitivity of the AEM method. The large spatial separation that typically exists between the AEM data and the wells with sediment type logs was avoided by planning the acquisition of AEM data so as to fly as close as possible to the well locations. We had 55 locations with sediment type logs and AEM data separated by 100 m, determined to be the maximum acceptable separation distance. Differences in vertical resolution between the AEM method and the sediment type logs were addressed by modeling the physics of the AEM measurement, allowing for a comparison of field and AEM data generated during the MCMC process. The influence of saturation state was captured by creating one set of transforms for the region above the top of the saturated zone and another for below. Using the set of transforms developed at the 55 locations, an inverse distance weighting scheme that included a well quality ranking was used to construct a set of 12 (six sensitivity bins, and two saturation states) resistivity-to-sediment-type transforms at every AEM data location. These represent a set of transforms that accommodate the variation in AEM sensitivity and are independent of the inversion used to retrieve the resistivity model. Thus, these transforms avoid two of the significant limitations common to resistivity-to-sediment-type transforms used to interpret AEM data.

A New Framework for Plug-In Electric Vehicle Charging Models Supported by Solar Photovoltaic Energy Resources Un nouveau cadre pour les modèles de recharge du véhicule électrique rechargeable supporté par des ressources d’énergie solaire photovoltaïque

This article proposes a new framework for modeling plug-in electric vehicle (PEV) charging demand supported by solar photovoltaic (PV) energy resources in a distribution system. The proposed work focuses on modeling the stochastic nature of both PEV loads and PV generation while considering the effect of the temporal-spatial characteristics of the driver's behavior, as well as solar irradiation and temperature. A trip chain, based on the Markov Chain Monte Carlo process, is developed to properly model PEV daily driving activities and the PV uncertainty. Charging facilities are assumed available at home, work, and fast-charging stations, having charging levels of 3.7, 6.6, and 50 kW, respectively. The proposed framework is examined, considering the National Household Travel Survey global data, as well as the city of Buffalo and New York state. The impact of varying the penetration levels of PEV and PV resources is also investigated. This work strengthens the proposed models in the literature by integrating the temporal-spatial characteristics of PEV charging demand into PV stochastic models.

MCMC Guided CNN Training and Segmentation for Pancreas Extraction

Efficient organ segmentation is the precondition of various quantitative analysis. Segmenting the pancreas from abdominal CT images is a challenging task because of its high anatomical variability in shape, size and location. What’s more, the pancreas only occupies a small portion in abdomen, and the organ border is very fuzzy. All these factors make the segmentation methods of other organs less suitable for pancreas. In this work, we propose a Markov Chain Monte Carlo (MCMC) guided convolutional neural network (CNN) approach, in order to handle such difficulties in morphological and photometric variabilities. Specifically, the proposed method mainly consists of three steps: First, registration is carried out to mitigate the body weight and location variability. Then, an MCMC scheme is designed to guide the adaptive selection of 3D patches, which are fed to the CNN for training. At the same time, the pancreas distribution is also learned for subsequent segmentation. Eventually, the same MCMC process guides the segmentation process with patch-wise predictions fused using a Bayesian voting scheme. This method is evaluated on the NIH pancreatic dataset including 82 abdominal contrast-enhanced CT volumes. We have achieved a competitive result of 78.13% Dice Similarity Coefficient value and 82.65% Recall value in testing data.

Optimizing the Huff ‘n’ Puff Gas Injection Performance in Shale Reservoirs Considering the Uncertainty: A Duvernay Shale Example

SummaryRecent studies have indicated that huff ‘n’ puff (HNP) gas injection has the potential to recover an additional 30 to 70% oil from multifractured horizontal wells in shale reservoirs. Nonetheless, this technique is very sensitive to production constraints and is impacted by uncertainty related to measurement quality (particularly frequency and resolution) and lack of constraining data. In this paper, a Bayesian workflow is provided to optimize the HNP process under uncertainty using a Duvernay shale well as an example.Compositional simulations are conducted that incorporate a tuned pressure/volume/temperature (PVT) model and a set of measured cyclic injection/compaction pressure-sensitive permeability data. Markov-Chain Monte Carlo (MCMC) is used to estimate the posterior distributions of the model uncertain variables by matching the primary production data. The MCMC process is accelerated by using an accurate proxy model (kriging) that is updated using a highly adaptive sampling algorithm. Gaussian processes are then used to optimize the HNP control variables by maximizing the lower confidence interval (μ-σ) of cumulative oil production (after 10 years) across a fixed ensemble of uncertain variables sampled from posterior distributions.The uncertain variable space includes several parameters representing reservoir and fracture properties. The posterior distributions for some parameters, such as primary fracture permeability and effective half-length, are narrower, whereas wider distributions are obtained for other parameters. The results indicate that the impact of uncertain variables on HNP performance is nonlinear. Some uncertain variables (such as molecular diffusion) that do not show strong sensitivity during the primary production strongly impact gas injection HNP performance. The results of optimization under uncertainty confirm that the lower confidence interval of cumulative oil production can be maximized by an injection time of approximately 1.5 months, a production time of approximately 2.5 months, and very short soaking times. In addition, a maximum injection rate and a flowing bottomhole pressure around the bubblepoint are required to ensure maximum incremental recovery. Analysis of the objective function surface highlights some other sets of production constraints with competitive results. Finally, the optimal set of production constraints, in combination with an ensemble of uncertain variables, results in a median HNP cumulative oil production that is 30% greater than that for primary production.The application of a Bayesian framework for optimizing the HNP performance in a real shale reservoir is introduced for the first time. This work provides practical guidelines for the efficient application of advanced techniques for optimization under uncertainty, resulting in better decision making.

Replica Exchange MCMC Hardware With Automatic Temperature Selection and Parallel Trial

A replica exchange Markov Chain Monte Carlo (MCMC) engine is developed with automatic temperature adjustment for solving combinatorial optimization problems by minimizing the energy of the Ising model. The automatic temperature adjustment scheme ensures that the MCMC process is optimized at every stage of the execution. This approach is performed by dynamically adjusting temperatures of all replicas, based on the properties of any given problem, in addition to the capability of automatically inserting new replicas or removing any existing replicas to achieve the best possible resource efficiency and execution time. The proposed algorithm is integrated with parallel evaluation of energy increment and update scheme. The engine is implemented on the FPGA platform with a capacity of running up to 42 replicas in pipeline, each running 1024 fully-connected Ising spins in parallel. The performance of the hardware is examined with three different classes of problems, Vertex Cover, Maximum-Cut, and Travelling Salesman using the engine in three modes, simulated annealing, with replica exchange while the adjustments are turned on or off. Up to 16x speedup is observed by turning on the replica exchange capability in addition to the advantage of eliminating the challenging process of finding an optimal annealing schedule for simulated annealing process.

Facilitating Bayesian analysis of combustion kinetic models with artificial neural network

Bayesian analysis provides a framework for the inverse uncertainty quantification (UQ) of combustion kinetic models. As the workhorse of the Bayesian approach, the Markov chain Monte Carlo (MCMC) methods, however, incur a substantial computational cost. In this work, a surrogate model is employed to improve the traditional MCMC algorithm. Specifically, the test errors of three typical surrogate models are compared, namely Polynomial Chaos Expansion (PCE), High Dimensional Model Representation (HDMR) and Artificial Neural Network (ANN); and ANN is shown to be a relatively more efficient surrogate model for the approximation of combustion reaction systems under extensive conditions. An inverse UQ method, which is the combination of the ANN and traditional MCMC method, and as such termed ANN–MCMC, is adopted. The calculation is performed on the methanol oxidation system and a series of ignition delay data are employed to optimize the rate coefficients of the kinetic model. The estimated posterior distributions of the rate coefficients and the model predictions using the ANN–MCMC are compared with the traditional MCMC methods, with the results showing that the ANN–MCMC can significantly reduce the computational cost needed for the MCMC algorithm, especially on the estimation of the posterior distributions of the input parameters. The rejection rate of the samples in a Markov chain is very high, especially for the calculation of the posterior distribution of less sensitive parameters, thus a large number of samples are needed to reach a desired accuracy for traditional MCMC process. While no samples are rejected when training the ANN surrogate model. Therefore, fewer original samples are needed to get a converged ANN surrogate, which can then generate a large number of low-cost ANN samples for a better accuracy of the MCMC process. The errors for the estimated posterior distributions using ANN–MCMC depend on the accuracy of converged ANN surrogates and more accurate results are obtained with improved settings of ANN. The ANN–MCMC is especially suitable to the computational systems when the computational ability is limited.

Decoding via Sampling

We propose a novel decoding algorithm called “sampling decoding”, which is constructed using a Markov Chain Monte Carlo (MCMC) method and implements Maximum a Posteriori Probability decoding in an approximate manner. It is also shown that sampling decoding can be easily extended to universal coding or to be applicable for Markov sources. In simulation experiments comparing the proposed algorithm with the sum-product decoding algorithm, sampling decoding is shown to perform better as sample size increases, although decoding time becomes proportionally longer. The mixing time, which measures how large a sample size is needed for the MCMC process to converge to the limiting distribution, is evaluated for a simple coding matrix construction.

Geodetic Evidence That Mercury Has A Solid Inner Core

Geodetic analysis of radio tracking measurements of the MESSENGER spacecraft while in orbit about Mercury has yielded new estimates for the planet's gravity field, tidal Love number, and pole coordinates. The derived right ascension (α = 281.0082° ± 0.0009°; all uncertainties are 3 standard deviations) and declination (δ =61.4164° ± 0.0003°) of the spin pole place Mercury in the Cassini state. Confirmation of the equilibrium state with an estimated mean (whole-planet) obliquity ϵ of 1.968 ± 0.027 arcmin enables the confident determination of the planet's normalized polar moment of inertia (0.333 ± 0.005), which indicates a high degree of internal differentiation. Internal structure models generated by a Markov-Chain Monte Carlo process and consistent with the geodetic constraints possess a solid inner core with a radius (r ic ) between 0.3 and 0.7 that of the outer core (r oc ).

Growth curves in meat-type and laying quail: a Bayesian perspective

The aim of this study was to assess the goodness of fit for nonlinear models, using the best model to describe body growth curves, comparing the parameters obtained for gender and one meat-type (Coturnix coturnix coturnix) and two laying (Coturnix coturnix japonica) quail strains, as well as nesting via MCMC (Markov chain Monte Carlo processes) methods under a Bayesian approach. A total of 1,350 one-day-old mixed quail were used: 400 of meat-type, 450 of yellow laying, and 500 of red laying strains distributed in a completely randomized design with three treatments (each treatment corresponded to one strain) and five replications. The experimental period consisted of 1 to 42 days of age. At 21 days of age, quail sexing was performed by means of sexual dimorphism, being individually identified at one day of age with numbered rings, allowing determining growth curves by gender. Birds were reared in a conventional system, fed ad libitum with diets formulated to meet nutritional requirements. Body weight was determined weekly and assessed using nonlinear models: Logistic, Brody, Von Bertalanffy, and Gompertz, whose parameters were estimated under a Bayesian approach via MCMC algorithm by means of BRugs package from the software R. DIC (Deviance Information Criterion) criterion was used to select the best nonlinear model, i.e. the lower the DIC value is, the better the model goodness of fit to the data. Gompertz model was better adjusted to the data regardless the gender or strain. Meat-type quail had the highest asymptotic weights and the highest age at which growth rate was maximum, followed by red and yellow strains. All nestings presented significant differences (p < 0.05) between gender for contrasted parameters. Meat-type, yellow, and red females presented values significantly (p < 0.05) higher for asymptotic weight (370, 203, and 215 g, respectively) when compared to males (274, 131, and 143 g, respectively), which were earlier in body growth. Gompertz model was better adjusted to body weight data of quail regardless the gender or strain and the Bayesian approach allowed obtaining accurate estimations. Meat-type strain presented the highest body asymptotic weight, followed by red and yellow laying strains. Females presented higher asymptotic weight than that found for males of their respective strains but were later in growth.

Growth curves in meat-type and laying quail: a Bayesian perspective

The aim of this study was to assess the goodness of fit for nonlinear models, using the best model to describe body growth curves, comparing the parameters obtained for gender and one meat-type (Coturnix coturnix coturnix) and two laying (Coturnix coturnix japonica) quail strains, as well as nesting via MCMC (Markov chain Monte Carlo processes) methods under a Bayesian approach. A total of 1,350 one-day-old mixed quail were used: 400 of meat-type, 450 of yellow laying, and 500 of red laying strains distributed in a completely randomized design with three treatments (each treatment corresponded to one strain) and five replications. The experimental period consisted of 1 to 42 days of age. At 21 days of age, quail sexing was performed by means of sexual dimorphism, being individually identified at one day of age with numbered rings, allowing determining growth curves by gender. Birds were reared in a conventional system, fed ad libitum with diets formulated to meet nutritional requirements. Body weight was determined weekly and assessed using nonlinear models: Logistic, Brody, Von Bertalanffy, and Gompertz, whose parameters were estimated under a Bayesian approach via MCMC algorithm by means of BRugs package from the software R. DIC (Deviance Information Criterion) criterion was used to select the best nonlinear model, i.e. the lower the DIC value is, the better the model goodness of fit to the data. Gompertz model was better adjusted to the data regardless the gender or strain. Meat-type quail had the highest asymptotic weights and the highest age at which growth rate was maximum, followed by red and yellow strains. All nestings presented significant differences (p < 0.05) between gender for contrasted parameters. Meat-type, yellow, and red females presented values significantly (p < 0.05) higher for asymptotic weight (370, 203, and 215 g, respectively) when compared to males (274, 131, and 143 g, respectively), which were earlier in body growth. Gompertz model was better adjusted to body weight data of quail regardless the gender or strain and the Bayesian approach allowed obtaining accurate estimations. Meat-type strain presented the highest body asymptotic weight, followed by red and yellow laying strains. Females presented higher asymptotic weight than that found for males of their respective strains but were later in growth.

A unified hypothesis generation framework for multi-structure model fitting

Generating promising hypotheses plays a critical role in the success of multi-structure model fitting methods. However, conventional multi-structure hypothesis generation strategies do not exploit the information derived from the results of model selection to guide the subsequent hypothesis generation process. This leads to the problem that these hypothesis generation strategies are often computationally expensive for generating promising hypotheses, especially for heavily contaminated multi-structure data. To address this problem, we first propose a guided sampling strategy to accelerate promising hypothesis generation process by using information derived from the results of model selection on the fly. Then we present a Unified Hypothesis Generation (UHG) framework, which effectively combines the conventional multi-structure hypothesis generation strategy with the proposed guided sampling strategy by using a Markov Chain Monte Carlo process based on a cooling schedule. Experimental results on public databases demonstrate that the proposed UHG achieves significant superiority over several state-of-the-art sampling methods in terms of accuracy and efficiency, especially on multi-structure data.

Efficient guided hypothesis generation for multi-structure epipolar geometry estimation

We propose an Efficient Guided Hypothesis Generation (EGHG) method for multi-structure epipolar geometry estimation. Based on the Markov Chain Monte Carlo process, EGHG combines two guided sampling strategies: a global sampling strategy and a local sampling strategy. The global sampling strategy, guided by using both spatial sampling probabilities and keypoint matching scores, rapidly obtains promising solutions. The spatial sampling probabilities are computed by using a normalized exponential loss function. The local sampling strategy, guided by using both Joint Feature Distributions (JFDs) and keypoint matching scores, efficiently achieves accurate solutions. In the local sampling strategy, EGHG updates a set of current best hypothesis candidates on the fly, and then computes JFDs between the input data and these candidates. Experimental results on public real image pairs show that EGHG significantly outperforms several state-of-the-art sampling methods on multi-structure data.

Modelling of turbulent wind flow using the embedded Markov chain method

Small wind turbines are usually installed to provide off-grid power and as such can be situated close to the load in a less-than-ideal wind resource. These wind regimes are often governed by low mean speeds and high wind turbulence. This can result in energy production less than that specified by the manufacturer's power curve. Wind turbulence is detrimental to the fatigue life of key components and overall turbine reliability and therefore must be considered in the design stage of small wind turbines. Consequently it is important to accurately simulate wind speed data at highly turbulent sites to quantify loading on turbine components. Here we simulate wind speed data using the Markov chain Monte Carlo process and incorporate long term effects using an embedded Markov chain. First, second and third order Markov chain predictions were found to be in good agreement with measured wind data acquired at 1 Hz. The embedded Markov chain was able to predict site turbulent intensity with a reasonable degree of accuracy. The site exhibited distinctive peaks in wind speed possibly caused by diurnal heating and cooling of the earth's surface. The embedded Markov chain method was able to simulate these peaks albeit with a time offset.