11

10011563

Probabilistic Approach of Dealing with Uncertainties in Distributed Constraint Optimization Problems and Situation Awareness for Multi-agent Systems

In this paper, we describe how Bayesian inferential reasoning will contributes in obtaining a well-satisfied prediction for Distributed Constraint Optimization Problems (DCOPs) with uncertainties. We also demonstrate how DCOPs could be merged to multi-agent knowledge understand and prediction (i.e. Situation Awareness). The DCOPs functions were merged with Bayesian Belief Network (BBN) in the form of situation, awareness, and utility nodes. We describe how the uncertainties can be represented to the BBN and make an effective prediction using the expectation-maximization algorithm or conjugate gradient descent algorithm. The idea of variable prediction using Bayesian inference may reduce the number of variables in agents’ sampling domain and also allow missing variables estimations. Experiment results proved that the BBN perform compelling predictions with samples containing uncertainties than the perfect samples. That is, Bayesian inference can help in handling uncertainties and dynamism of DCOPs, which is the current issue in the DCOPs community. We show how Bayesian inference could be formalized with Distributed Situation Awareness (DSA) using uncertain and missing agents’ data. The whole framework was tested on multi-UAV mission for forest fire searching. Future work focuses on augmenting existing architecture to deal with dynamic DCOPs algorithms and multi-agent information merging.

10

10005884

Human Action Recognition Using Variational Bayesian HMM with Dirichlet Process Mixture of Gaussian Wishart Emission Model

In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

9

10003521

Development of an Automatic Calibration Framework for Hydrologic Modelling Using Approximate Bayesian Computation

Hydrologic models are increasingly used as tools to
predict stormwater quantity and quality from urban catchments.
However, due to a range of practical issues, most models produce
gross errors in simulating complex hydraulic and hydrologic systems.
Difficulty in finding a robust approach for model calibration is one of
the main issues. Though automatic calibration techniques are
available, they are rarely used in common commercial hydraulic and
hydrologic modelling software e.g. MIKE URBAN. This is partly
due to the need for a large number of parameters and large datasets in
the calibration process. To overcome this practical issue, a
framework for automatic calibration of a hydrologic model was
developed in R platform and presented in this paper. The model was
developed based on the time-area conceptualization. Four calibration
parameters, including initial loss, reduction factor, time of
concentration and time-lag were considered as the primary set of
parameters. Using these parameters, automatic calibration was
performed using Approximate Bayesian Computation (ABC). ABC is
a simulation-based technique for performing Bayesian inference
when the likelihood is intractable or computationally expensive to
compute. To test the performance and usefulness, the technique was
used to simulate three small catchments in Gold Coast. For
comparison, simulation outcomes from the same three catchments
using commercial modelling software, MIKE URBAN were used.
The graphical comparison shows strong agreement of MIKE URBAN
result within the upper and lower 95% credible intervals of posterior
predictions as obtained via ABC. Statistical validation for posterior
predictions of runoff result using coefficient of determination (CD),
root mean square error (RMSE) and maximum error (ME) was found
reasonable for three study catchments. The main benefit of using
ABC over MIKE URBAN is that ABC provides a posterior
distribution for runoff flow prediction, and therefore associated
uncertainty in predictions can be obtained. In contrast, MIKE
URBAN just provides a point estimate. Based on the results of the
analysis, it appears as though ABC the developed framework
performs well for automatic calibration.

8

10001030

FEM Models of Glued Laminated Timber Beams Enhanced by Bayesian Updating of Elastic Moduli

Two finite element (FEM) models are presented in this paper to address the random nature of the response of glued timber structures made of wood segments with variable elastic moduli evaluated from 3600 indentation measurements. This total database served to create the same number of ensembles as was the number of segments in the tested beam. Statistics of these ensembles were then assigned to given segments of beams and the Latin Hypercube Sampling (LHS) method was called to perform 100 simulations resulting into the ensemble of 100 deflections subjected to statistical evaluation. Here, a detailed geometrical arrangement of individual segments in the laminated beam was considered in the construction of two-dimensional FEM model subjected to in fourpoint bending to comply with the laboratory tests. Since laboratory measurements of local elastic moduli may in general suffer from a significant experimental error, it appears advantageous to exploit the full scale measurements of timber beams, i.e. deflections, to improve their prior distributions with the help of the Bayesian statistical method. This, however, requires an efficient computational model when simulating the laboratory tests numerically. To this end, a simplified model based on Mindlin’s beam theory was established. The improved posterior distributions show that the most significant change of the Young’s modulus distribution takes place in laminae in the most strained zones, i.e. in the top and bottom layers within the beam center region. Posterior distributions of moduli of elasticity were subsequently utilized in the 2D FEM model and compared with the original simulations.

7

9998715

Generalized Mean-field Theory of Phase Unwrapping via Multiple Interferograms

On the basis of Bayesian inference using the maximizer of the posterior marginal estimate, we carry out phase unwrapping using multiple interferograms via generalized mean-field theory. Numerical calculations for a typical wave-front in remote sensing using the synthetic aperture radar interferometry, phase diagram in hyper-parameter space clarifies that the present method succeeds in phase unwrapping perfectly under the constraint of surface- consistency condition, if the interferograms are not corrupted by any noises. Also, we find that prior is useful for extending a phase in which phase unwrapping under the constraint of the surface-consistency condition. These results are quantitatively confirmed by the Monte Carlo simulation.

6

9598

Bayesian Inference for Phase Unwrapping Using Conjugate Gradient Method in One and Two Dimensions

We investigated statistical performance of Bayesian inference using maximum entropy and MAP estimation for several models which approximated wave-fronts in remote sensing using SAR interferometry. Using Monte Carlo simulation for a set of wave-fronts generated by assumed true prior, we found that the method of maximum entropy realized the optimal performance around the Bayes-optimal conditions by using model of the true prior and the likelihood representing optical measurement due to the interferometer. Also, we found that the MAP estimation regarded as a deterministic limit of maximum entropy almost achieved the same performance as the Bayes-optimal solution for the set of wave-fronts. Then, we clarified that the MAP estimation perfectly carried out phase unwrapping without using prior information, and also that the MAP estimation realized accurate phase unwrapping using conjugate gradient (CG) method, if we assumed the model of the true prior appropriately.

5

7645

Maximizer of the Posterior Marginal Estimate of Phase Unwrapping Based On Statistical Mechanics of the Q-Ising Model

We constructed a method of phase unwrapping for a typical wave-front by utilizing the maximizer of the posterior marginal (MPM) estimate corresponding to equilibrium statistical mechanics of the three-state Ising model on a square lattice on the basis of an analogy between statistical mechanics and Bayesian inference. We investigated the static properties of an MPM estimate from a phase diagram using Monte Carlo simulation for a typical wave-front with synthetic aperture radar (SAR) interferometry. The simulations clarified that the surface-consistency conditions were useful for extending the phase where the MPM estimate was successful in phase unwrapping with a high degree of accuracy and that introducing prior information into the MPM estimate also made it possible to extend the phase under the constraint of the surface-consistency conditions with a high degree of accuracy. We also found that the MPM estimate could be used to reconstruct the original wave-fronts more smoothly, if we appropriately tuned hyper-parameters corresponding to temperature to utilize fluctuations around the MAP solution. Also, from the viewpoint of statistical mechanics of the Q-Ising model, we found that the MPM estimate was regarded as a method for searching the ground state by utilizing thermal fluctuations under the constraint of the surface-consistency condition.

4

7551

Production Throughput Modeling under Five Uncertain Variables Using Bayesian Inference

Throughput is an important measure of performance of production system. Analyzing and modeling of production throughput is complex in today-s dynamic production systems due to uncertainties of production system. The main reasons are that uncertainties are materialized when the production line faces changes in setup time, machinery break down, lead time of manufacturing, and scraps. Besides, demand changes are fluctuating from time to time for each product type. These uncertainties affect the production performance. This paper proposes Bayesian inference for throughput modeling under five production uncertainties. Bayesian model utilized prior distributions related to previous information about the uncertainties where likelihood distributions are associated to the observed data. Gibbs sampling algorithm as the robust procedure of Monte Carlo Markov chain was employed for sampling unknown parameters and estimating the posterior mean of uncertainties. The Bayesian model was validated with respect to convergence and efficiency of its outputs. The results presented that the proposed Bayesian models were capable to predict the production throughput with accuracy of 98.3%.

3

11109

Maximizer of the Posterior Marginal Estimate for Noise Reduction of JPEG-compressed Image

We constructed a method of noise reduction for
JPEG-compressed image based on Bayesian inference using the
maximizer of the posterior marginal (MPM) estimate. In this method,
we tried the MPM estimate using two kinds of likelihood, both of
which enhance grayscale images converted into the JPEG-compressed
image through the lossy JPEG image compression. One is the
deterministic model of the likelihood and the other is the probabilistic
one expressed by the Gaussian distribution. Then, using the Monte
Carlo simulation for grayscale images, such as the 256-grayscale
standard image “Lena" with 256 × 256 pixels, we examined the
performance of the MPM estimate based on the performance measure
using the mean square error. We clarified that the MPM estimate via
the Gaussian probabilistic model of the likelihood is effective for
reducing noises, such as the blocking artifacts and the mosquito noise,
if we set parameters appropriately. On the other hand, we found that
the MPM estimate via the deterministic model of the likelihood is not
effective for noise reduction due to the low acceptance ratio of the
Metropolis algorithm.

2

8104

Estimation of Bayesian Sample Size for Binomial Proportions Using Areas P-tolerance with Lowest Posterior Loss

This paper uses p-tolerance with the lowest posterior
loss, quadratic loss function, average length criteria, average
coverage criteria, and worst outcome criterion for computing of
sample size to estimate proportion in Binomial probability function
with Beta prior distribution. The proposed methodology is examined,
and its effectiveness is shown.

1

3809

A Bayesian Hierarchical 13COBT to Correct Estimates Associated with a Delayed Gastric Emptying

The use of a Bayesian Hierarchical Model (BHM) to interpret breath measurements obtained during a 13C Octanoic Breath Test (13COBT) is demonstrated. The statistical analysis was implemented using WinBUGS, a commercially available computer package for Bayesian inference. A hierarchical setting was adopted where poorly defined parameters associated with a delayed Gastric Emptying (GE) were able to "borrow" strength from global distributions. This is proved to be a sufficient tool to correct model's failures and data inconsistencies apparent in conventional analyses employing a Non-linear least squares technique (NLS). Direct comparison of two parameters describing gastric emptying ng ( tlag -lag phase, t1/ 2 -half emptying time) revealed a strong correlation between the two methods. Despite our large dataset ( n = 164 ), Bayesian modeling was fast and provided a successful fitting for all subjects. On the contrary, NLS failed to return acceptable estimates in cases where GE was delayed.