A Python package for Bayesian estimation using Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) estimation provides a solution to the complex integration problems that are faced in the Bayesian analysis of statistical problems. The implementation of MCMC algorithms is, however, code intensive and time consuming. We have developed a Python package, which is called PyMCMC, that aids in the construction of MCMC samplers and helps to substantially reduce the likelihood of coding error, as well as aid in the minimisation of repetitive code. PyMCMC contains classes for Gibbs, Metropolis Hastings, independent Metropolis Hastings, random walk Metropolis Hastings, orientational bias Monte Carlo and slice samplers as well as specific modules for common models such as a module for Bayesian regression analysis. PyMCMC is straightforward to optimise, taking advantage of the Python libraries Numpy and Scipy, as well as being readily extensible with C or Fortran.

Bounded parameter Markov Decision Processes with average reward criterion

Bounded parameter Markov Decision Processes (BMDPs) address the issue of dealing with uncertainty in the parameters of a Markov Decision Process (MDP). Unlike the case of an MDP, the notion of an optimal policy for a BMDP is not entirely straightforward. We consider two notions of optimality based on optimistic and pessimistic criteria. These have been analyzed for discounted BMDPs. Here we provide results for average reward BMDPs. We establish a fundamental relationship between the discounted and the average reward problems, prove the existence of Blackwell optimal policies and, for both notions of optimality, derive algorithms that converge to the optimal value function.

Exponentiated gradient algorithms for conditional random fields and max-margin Markov Networks

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log(1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

An infinite-horizon robust filter for uncertain hidden Markov Models with conditional relative entropy constraints

We consider a robust filtering problem for uncertain discrete-time, homogeneous, first-order, finite-state hidden Markov models (HMMs). The class of uncertain HMMs considered is described by a conditional relative entropy constraint on measures perturbed from a nominal regular conditional probability distribution given the previous posterior state distribution and the latest measurement. Under this class of perturbations, a robust infinite horizon filtering problem is first formulated as a constrained optimization problem before being transformed via variational results into an unconstrained optimization problem; the latter can be elegantly solved using a risk-sensitive information-state based filtering.

Reconfiguration or innovation in supply chains?

This research explores supply chain competitiveness and dynamic capabilities. It examines a pilot group of Australian supply chain organisations to understand the importance of dynamic capability in building innovation capacity for competitive advantage, and the concept of adopting a strategic approach to supply chain relationship building. A supply chain is after all a group of intra and interorganisational relationships delivering demand to end-users. This exploratory study confirms a positive relationship between the variables indicating both a strategic intent to develop relational capability, and very strong predictive linkages between the importance placed on developing supply chain dynamic capability and achieving supply chain innovation capacity as a competitive advantage.

Wind-energy based path planning for electric unmanned aerial vehicles using Markov Decision Processes

Exploiting wind-energy is one possible way to ex- tend flight duration for Unmanned Arial Vehicles. Wind-energy can also be used to minimise energy consumption for a planned path. In this paper, we consider uncertain time-varying wind fields and plan a path through them. A Gaussian distribution is used to determine uncertainty in the Time-varying wind fields. We use Markov Decision Process to plan a path based upon the uncertainty of Gaussian distribution. Simulation results that compare the direct line of flight between start and target point and our planned path for energy consumption and time of travel are presented. The result is a robust path using the most visited cell while sampling the Gaussian distribution of the wind field in each cell.

Extending persistent monitoring by combining ocean models and Markov decision processes

Ocean processes are complex and have high variability in both time and space. Thus, ocean scientists must collect data over long time periods to obtain a synoptic view of ocean processes and resolve their spatiotemporal variability. One way to perform these persistent observations is to utilise an autonomous vehicle that can remain on deployment for long time periods. However, such vehicles are generally underactuated and slow moving. A challenge for persistent monitoring with these vehicles is dealing with currents while executing a prescribed path or mission. Here we present a path planning method for persistent monitoring that exploits ocean currents to increase navigational accuracy and reduce energy consumption.

Wind-energy based path planning for unmanned aerial vehicles using Markov decision processes

Exploiting wind-energy is one possible way to extend flight duration for Unmanned Arial Vehicles. Wind-energy can also be used to minimise energy consumption for a planned path. In this paper, we consider uncertain time-varying wind fields and plan a path through them. A Gaussian distribution is used to determine uncertainty in the Time-varying wind fields. We use Markov Decision Process to plan a path based upon the uncertainty of Gaussian distribution. Simulation results that compare the direct line of flight between start and target point and our planned path for energy consumption and time of travel are presented. The result is a robust path using the most visited cell while sampling the Gaussian distribution of the wind field in each cell.

Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation

Motor unit number estimation (MUNE) is a method which aims to provide a quantitative indicator of progression of diseases that lead to loss of motor units, such as motor neurone disease. However the development of a reliable, repeatable and fast real-time MUNE method has proved elusive hitherto. Ridall et al. (2007) implement a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to produce a posterior distribution for the number of motor units using a Bayesian hierarchical model that takes into account biological information about motor unit activation. However we find that the approach can be unreliable for some datasets since it can suffer from poor cross-dimensional mixing. Here we focus on improved inference by marginalising over latent variables to create the likelihood. In particular we explore how this can improve the RJMCMC mixing and investigate alternative approaches that utilise the likelihood (e.g. DIC (Spiegelhalter et al., 2002)). For this model the marginalisation is over latent variables which, for a larger number of motor units, is an intractable summation over all combinations of a set of latent binary variables whose joint sample space increases exponentially with the number of motor units. We provide a tractable and accurate approximation for this quantity and also investigate simulation approaches incorporated into RJMCMC using results of Andrieu and Roberts (2009).

Anomalous event detection using a semi-two dimensional hidden Markov model

The rapid increase in the deployment of CCTV systems has led to a greater demand for algorithms that are able to process incoming video feeds. These algorithms are designed to extract information of interest for human operators. During the past several years, there has been a large effort to detect abnormal activities through computer vision techniques. Typically, the problem is formulated as a novelty detection task where the system is trained on normal data and is required to detect events which do not fit the learned `normal' model. Many researchers have tried various sets of features to train different learning models to detect abnormal behaviour in video footage. In this work we propose using a Semi-2D Hidden Markov Model (HMM) to model the normal activities of people. The outliers of the model with insufficient likelihood are identified as abnormal activities. Our Semi-2D HMM is designed to model both the temporal and spatial causalities of the crowd behaviour by assuming the current state of the Hidden Markov Model depends not only on the previous state in the temporal direction, but also on the previous states of the adjacent spatial locations. Two different HMMs are trained to model both the vertical and horizontal spatial causal information. Location features, flow features and optical flow textures are used as the features for the model. The proposed approach is evaluated using the publicly available UCSD datasets and we demonstrate improved performance compared to other state of the art methods.

Safety culture in supply chains : 'Customer is king'

Despite the presence of many regulations governing the operation of heavy vehicles and supply chains in Australia, the truck driving sector continues to have the highest incidence of fatal injuries compared to all other industries. The working environment has been the focus of attention by safety researchers during the past few decades, with particular consideration been given to the concept ‘safety culture’ and how to maintain, modify and advance responses to occupational risk. One important aspect of the heavy industry which sets it apart is the existence of cultural or sub-cultural influences at an industry wide and occupation-specific level rather than organisational level. This paper reports on the findings of stakeholder’s perceptions of the influences of power and control, and culture on industry safety. In-depth structured interviews were conducted during 2011 with Australian industry stakeholders (n=31). The questioning surrounded decision-making processes with regards to identifying risks, self-monitoring and reducing risky activities; as well as how power-affected relationships may influence the operational performance of supply chains and impacts on driver safety. One of the most significant findings from these interviews relates to the notion of power. The perception that the ‘Customer is King’ was widely viewed, with the majority of stakeholders believing that there exists a ‘master slave mentality’ in the industry. There appears to be great frustration in the industry as to the apparent immunity of customers (particularly retail supply chains) to their responsibilities. There was also a strong perception that the customer holds the balance of power by covertly employing remuneration-related incentives and pressures. Smaller trucking companies are perceived as being more vulnerable to the pressure of customer expectations.

Provision of customer knowledge to supply chains

Knowledge about customers is vital for supply chains in order to ensure customer satisfaction. In an ideal supply chain environment, supply chain partners are able to perform planning tasks collaboratively, because they share information. However, customers are not always able or willing to share information with their suppliers. End consumers, on the one hand, do not usually provide a retail company with demand information. On the other hand, industrial customers might consciously hide information. Wherever a supply chain is not provided with demand forecast information, it needs to derive these demand forecasts by other means. Customer Relationship Management provides a set of tools to overcome informational uncertainty. We show how CRM and SCM information can be integrated on the conceptual as well as technical levels in order to provide supply chain managers with relevant information.