Linear programming for large-scale Markov decision problems

We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest goal of competing with a low-dimensional family of policies. We use the dual linear programming formulation of the MDP average cost problem, in which the variable is a stationary distribution over state-action pairs, and we consider a neighborhood of a low-dimensional subset of the set of stationary distributions (defined in terms of state-action features) as the comparison class. We propose a technique based on stochastic convex optimization and give bounds that show that the performance of our algorithm approaches the best achievable by any policy in the comparison class. Most importantly, this result depends on the size of the comparison class, but not on the size of the state space. Preliminary experiments show the effectiveness of the proposed algorithm in a queuing application.

Ergodic control of partially observed Markov chains

The ergodic or long-run average cost control problem for a partially observed finite-state Markov chain is studied via the associated fully observed separated control problem for the nonlinear filter. Dynamic programming equations for the latter are derived, leading to existence and characterization of optimal stationary policies.

Asymptotic behaviour of point processes with Markov-dependent intervals

This splitting techniques for MARKOV chains developed by NUMMELIN (1978a) and ATHREYA and NEY (1978b) are used to derive an imbedded renewal process in WOLD's point process with MARKOV-correlated intervals. This leads to a simple proof of renewal theorems for such processes. In particular, a key renewal theorem is proved, from which analogues to both BLACKWELL's and BREIMAN's forms of the renewal theorem can be deduced.

Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.

A hidden Markov model approach for determining vessel activity from vessel monitoring system data.

Many fisheries worldwide have adopted vessel monitoring systems (VMS) for compliance purposes. An added benefit of these systems is that they collect a large amount of data on vessel locations at very fine spatial and temporal scales. This data can provide a wealth of information for stock assessment, research, and management. However, since most VMS implementations record vessel location at set time intervals with no regard to vessel activity, some methodology is required to determine which data records correspond to fishing activity. This paper describes a probabilistic approach, based on hidden Markov models (HMMs), to determine vessel activity. A HMM provides a natural framework for the problem and, by definition, models the intrinsic temporal correlation of the data. The paper describes the general approach that was developed and presents an example of this approach applied to the Queensland trawl fishery off the coast of eastern Australia. Finally, a simulation experiment is presented that compares the misallocation rates of the HMM approach with other approaches.

The cost-effectiveness of the MobileMums intervention to increase physical activity among mothers with young children: A Markov model informed by a randomised controlled trial

Objectives: To determine the cost-effectiveness of the MobileMums intervention. MobileMums is a 12-week programme which assists mothers with young children to be more physically active, primarily through the use of personalised SMS text-messages. Design: A cost-effectiveness analysis using a Markov model to estimate and compare the costs and consequences of MobileMums and usual care. Setting: This study considers the cost-effectiveness of MobileMums in Queensland, Australia. Participants: A hypothetical cohort of over 36 000 women with a child under 1 year old is considered. These women are expected to be eligible and willing to participate in the intervention in Queensland, Australia. Data sources: The model was informed by the effectiveness results from a 9-month two-arm community-based randomised controlled trial undertaken in 2011 and registered retrospectively with the Australian Clinical Trials Registry (ACTRN12611000481976). Baseline characteristics for the model cohort, treatment effects and resource utilisation were all informed by this trial. Main outcome measures: The incremental cost per quality-adjusted life year (QALY) of MobileMums compared with usual care. Results: The intervention is estimated to lead to an increase of 131 QALYs for an additional cost to the health system of 1.1 million Australian dollars (AUD). The expected incremental cost-effectiveness ratio for MobileMums is 8608 AUD per QALY gained. MobileMums has a 98% probability of being cost-effective at a cost-effectiveness threshold of 64 000 AUD. Varying modelling assumptions has little effect on this result. Conclusions: At a cost-effectiveness threshold of 64 000 AUD, MobileMums would likely be a cost-effective use of healthcare resources in Queensland, Australia. Trial registration number: Australian Clinical Trials Registry; ACTRN12611000481976.

Bayesian Inference for Retrospective Population Genetics Models Using Markov Chain Monte Carlo Methods

Genetics, the science of heredity and variation in living organisms, has a central role in medicine, in breeding crops and livestock, and in studying fundamental topics of biological sciences such as evolution and cell functioning. Currently the field of genetics is under a rapid development because of the recent advances in technologies by which molecular data can be obtained from living organisms. In order that most information from such data can be extracted, the analyses need to be carried out using statistical models that are tailored to take account of the particular genetic processes. In this thesis we formulate and analyze Bayesian models for genetic marker data of contemporary individuals. The major focus is on the modeling of the unobserved recent ancestry of the sampled individuals (say, for tens of generations or so), which is carried out by using explicit probabilistic reconstructions of the pedigree structures accompanied by the gene flows at the marker loci. For such a recent history, the recombination process is the major genetic force that shapes the genomes of the individuals, and it is included in the model by assuming that the recombination fractions between the adjacent markers are known. The posterior distribution of the unobserved history of the individuals is studied conditionally on the observed marker data by using a Markov chain Monte Carlo algorithm (MCMC). The example analyses consider estimation of the population structure, relatedness structure (both at the level of whole genomes as well as at each marker separately), and haplotype configurations. For situations where the pedigree structure is partially known, an algorithm to create an initial state for the MCMC algorithm is given. Furthermore, the thesis includes an extension of the model for the recent genetic history to situations where also a quantitative phenotype has been measured from the contemporary individuals. In that case the goal is to identify positions on the genome that affect the observed phenotypic values. This task is carried out within the Bayesian framework, where the number and the relative effects of the quantitative trait loci are treated as random variables whose posterior distribution is studied conditionally on the observed genetic and phenotypic data. In addition, the thesis contains an extension of a widely-used haplotyping method, the PHASE algorithm, to settings where genetic material from several individuals has been pooled together, and the allele frequencies of each pool are determined in a single genotyping.

Optimal maintenance and replacement via a semi-Markov decision model

Optimal bang-coast maintenance policies for a machine, subject to failure, are considered. The approach utilizes a semi-Markov model for the system. A simplified model for modifying the probability of machine failure with maintenance is employed. A numerical example is presented to illustrate the procedure and results.

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.

Control aspects in proportionality Markov manpower systems

In this paper, the control aspects of a hierarchical organization under the influence of "proportionality" policies are analyzed. Proportionality policies are those that restrict the recruitment to every level of the hierarchy (except the bottom most level or base level) to be in strict proportion to the promotions into that level. Both long term and short term control analysis have been discussed. In long term control the specific roles of the parameters of the system with regard to control of the shape and size of the system have been analyzed and yield suitable control strategies. In short term control, the attainability of a target or goal structure within a specific time from a given initial structure has been analyzed and yields the required recruitment strategies. The theoretical analyses have been illustrated with computational examples and also with real world data.

Control aspects in proportionality Markov manpower systems

In this paper, the control aspects of a hierarchical organization under the influence of "proportionality" policies are analyzed. Proportionality policies are those that restrict the recruitment to every level of the hierarchy (except the bottom most level or base level) to be in strict proportion to the promotions into that level. Both long term and short term control analysis have been discussed. In long term control the specific roles of the parameters of the system with regard to control of the shape and size of the system have been analyzed and yield suitable control strategies. In short term control, the attainability of a target or goal structure within a specific time from a given initial structure has been analyzed and yields the required recruitment strategies. The theoretical analyses have been illustrated with computational examples and also with real world data. The control of such proportionality systems is then compared with that of the general systems (which do not follow such policies) with some significant conclusions. The control relations of such proportionality systems are found to be simpler and more practically feasible than those of general Markov systems, which do not have such restrictions. Such proportionality systems thus not only retain and match the flexibility of general Markov systems but also have the added advantage of simpler and more practically feasible controls. The proportionality policies hence act as an alternative and more practicably feasible means of control. (C) 2004 Elsevier Inc. All rights reserved.

A reinforcement learning based algorithm for finite horizon Markov decision processes

We develop a simulation based algorithm for finite horizon Markov decision processes with finite state and finite action space. Illustrative numerical experiments with the proposed algorithm are shown for problems in flow control of communication networks and capacity switching in semiconductor fabrication.

Markov Chain Model for Cracking Behavior of Reinforced Concrete Beams

In this paper, nonhomogeneous Markov chains are proposed for modeling the cracking behavior of reinforced concrete beams subjected to monotonically increasing loads. The model facilitates prediction of the maximum crackwidth at a given load given the crackwidth at a lower load level, and thus leads to a better understanding of the cracking phenomenon. To illustrate the methodology developed, the results of three reinforced concrete beams tested in the laboratory are analyzed and presented.