O uso de modelos ocultos de Markov no estudo do fluxo de rios intermitentes

In this work, we present our understanding about the article of Aksoy [1], which uses Markov chains to model the flow of intermittent rivers. Then, we executed an application of his model in order to generate data for intermittent streamflows, based on a data set of Brazilian streams. After that, we build a hidden Markov model as a proposed new approach to the problem of simulation of such flows. We used the Gamma distribution to simulate the increases and decreases in river flows, along with a two-state Markov chain. The motivation for us to use a hidden Markov model comes from the possibility of obtaining the same information that the Aksoy’s model provides, but using a single tool capable of treating the problem as a whole, and not through multiple independent processes

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Neighborhood and Efficiency in Manufacturing in Brazilian Regions: A Spatial Markov Chain Analysis

This paper analyzes the geography of regional competitiveness in manufacturing in Brazil. The authors estimate stochastic frontiers to calculate regional efficiency of representative firms in 137 regions in the period 2000-2006, in four sectors defined by technological intensity. The efficiency results are analyzed using Markov Spatial Transition Matrices to provide insights into the transition of regions between efficiency levels, considering their local spatial context. The results indicate that geography plays an important role in manufacturing competitiveness. In particular, regions with more competitive neighbors are more likely to improve their relative efficiency (pull effect) over time, and regions with less competitive neighbors are more likely to lose relative efficiency (drag effect). The authors find that the pull effect is stronger than the drag effect.

Algorithms and methodologies for decision support in energy efficiency on buildings

Dissertação apresentada na faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para a obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

Which screening strategy using BMD measurements would be most cost effective for hip fracture prevention in elderly women? A decision analysis based on a Markov model.

INTRODUCTION: Hip fractures are responsible for excessive mortality, decreasing the 5-year survival rate by about 20%. From an economic perspective, they represent a major source of expense, with direct costs in hospitalization, rehabilitation, and institutionalization. The incidence rate sharply increases after the age of 70, but it can be reduced in women aged 70-80 years by therapeutic interventions. Recent analyses suggest that the most efficient strategy is to implement such interventions in women at the age of 70 years. As several guidelines recommend bone mineral density (BMD) screening of postmenopausal women with clinical risk factors, our objective was to assess the cost-effectiveness of two screening strategies applied to elderly women aged 70 years and older. METHODS: A cost-effectiveness analysis was performed using decision-tree analysis and a Markov model. Two alternative strategies, one measuring BMD of all women, and one measuring BMD only of those having at least one risk factor, were compared with the reference strategy "no screening". Cost-effectiveness ratios were measured as cost per year gained without hip fracture. Most probabilities were based on data observed in EPIDOS, SEMOF and OFELY cohorts. RESULTS: In this model, which is mostly based on observed data, the strategy "screen all" was more cost effective than "screen women at risk." For one woman screened at the age of 70 and followed for 10 years, the incremental (additional) cost-effectiveness ratio of these two strategies compared with the reference was 4,235 euros and 8,290 euros, respectively. CONCLUSION: The results of this model, under the assumptions described in the paper, suggest that in women aged 70-80 years, screening all women with dual-energy X-ray absorptiometry (DXA) would be more effective than no screening or screening only women with at least one risk factor. Cost-effectiveness studies based on decision-analysis trees maybe useful tools for helping decision makers, and further models based on different assumptions should be performed to improve the level of evidence on cost-effectiveness ratios of the usual screening strategies for osteoporosis.

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

The cost-effectiveness and public health benefit of nalmefene added to psychosocial support for the reduction of alcohol consumption in alcohol-dependent patients with high/very high drinking risk levels: a Markov model.

OBJECTIVES: To determine whether nalmefene combined with psychosocial support is cost-effective compared with psychosocial support alone for reducing alcohol consumption in alcohol-dependent patients with high/very high drinking risk levels (DRLs) as defined by the WHO, and to evaluate the public health benefit of reducing harmful alcohol-attributable diseases, injuries and deaths. DESIGN: Decision modelling using Markov chains compared costs and effects over 5 years. SETTING: The analysis was from the perspective of the National Health Service (NHS) in England and Wales. PARTICIPANTS: The model considered the licensed population for nalmefene, specifically adults with both alcohol dependence and high/very high DRLs, who do not require immediate detoxification and who continue to have high/very high DRLs after initial assessment. DATA SOURCES: We modelled treatment effect using data from three clinical trials for nalmefene (ESENSE 1 (NCT00811720), ESENSE 2 (NCT00812461) and SENSE (NCT00811941)). Baseline characteristics of the model population, treatment resource utilisation and utilities were from these trials. We estimated the number of alcohol-attributable events occurring at different levels of alcohol consumption based on published epidemiological risk-relation studies. Health-related costs were from UK sources. MAIN OUTCOME MEASURES: We measured incremental cost per quality-adjusted life year (QALY) gained and number of alcohol-attributable harmful events avoided. RESULTS: Nalmefene in combination with psychosocial support had an incremental cost-effectiveness ratio (ICER) of £5204 per QALY gained, and was therefore cost-effective at the £20,000 per QALY gained decision threshold. Sensitivity analyses showed that the conclusion was robust. Nalmefene plus psychosocial support led to the avoidance of 7179 alcohol-attributable diseases/injuries and 309 deaths per 100,000 patients compared to psychosocial support alone over the course of 5 years. CONCLUSIONS: Nalmefene can be seen as a cost-effective treatment for alcohol dependence, with substantial public health benefits. TRIAL REGISTRATION NUMBERS: This cost-effectiveness analysis was developed based on data from three randomised clinical trials: ESENSE 1 (NCT00811720), ESENSE 2 (NCT00812461) and SENSE (NCT00811941).

A behavioral ecology of shermen: hidden stories from trajectory data in the Northern Humboldt Current System

This work proposes an original contribution to the understanding of shermen spatial behavior, based on the behavioral ecology and movement ecology paradigms. Through the analysis of Vessel Monitoring System (VMS) data, we characterized the spatial behavior of Peruvian anchovy shermen at di erent scales: (1) the behavioral modes within shing trips (i.e., searching, shing and cruising); (2) the behavioral patterns among shing trips; (3) the behavioral patterns by shing season conditioned by ecosystem scenarios; and (4) the computation of maps of anchovy presence proxy from the spatial patterns of behavioral mode positions. At the rst scale considered, we compared several Markovian (hidden Markov and semi-Markov models) and discriminative models (random forests, support vector machines and arti cial neural networks) for inferring the behavioral modes associated with VMS tracks. The models were trained under a supervised setting and validated using tracks for which behavioral modes were known (from on-board observers records). Hidden semi-Markov models performed better, and were retained for inferring the behavioral modes on the entire VMS dataset. At the second scale considered, each shing trip was characterized by several features, including the time spent within each behavioral mode. Using a clustering analysis, shing trip patterns were classi ed into groups associated to management zones, eet segments and skippers' personalities. At the third scale considered, we analyzed how ecological conditions shaped shermen behavior. By means of co-inertia analyses, we found signi cant associations between shermen, anchovy and environmental spatial dynamics, and shermen behavioral responses were characterized according to contrasted environmental scenarios. At the fourth scale considered, we investigated whether the spatial behavior of shermen re ected to some extent the spatial distribution of anchovy. Finally, this work provides a wider view of shermen behavior: shermen are not only economic agents, but they are also foragers, constrained by ecosystem variability. To conclude, we discuss how these ndings may be of importance for sheries management, collective behavior analyses and end-to-end models.

Problèmes de premier passage et de commande optimale pour des chaînes de Markov à temps discret.

Nous considérons des processus de diffusion, définis par des équations différentielles stochastiques, et puis nous nous intéressons à des problèmes de premier passage pour les chaînes de Markov en temps discret correspon- dant à ces processus de diffusion. Comme il est connu dans la littérature, ces chaînes convergent en loi vers la solution des équations différentielles stochas- tiques considérées. Notre contribution consiste à trouver des formules expli- cites pour la probabilité de premier passage et la durée de la partie pour ces chaînes de Markov à temps discret. Nous montrons aussi que les résultats ob- tenus convergent selon la métrique euclidienne (i.e topologie euclidienne) vers les quantités correspondantes pour les processus de diffusion. En dernier lieu, nous étudions un problème de commande optimale pour des chaînes de Markov en temps discret. L’objectif est de trouver la valeur qui mi- nimise l’espérance mathématique d’une certaine fonction de coût. Contraire- ment au cas continu, il n’existe pas de formule explicite pour cette valeur op- timale dans le cas discret. Ainsi, nous avons étudié dans cette thèse quelques cas particuliers pour lesquels nous avons trouvé cette valeur optimale.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

A combined Bayesian Markovian approach for behaviour recognition

Numerous techniques exist which can be used for the task of behavioural analysis and recognition. Common amongst these are Bayesian networks and Hidden Markov Models. Although these techniques are extremely powerful and well developed, both have important limitations. By fusing these techniques together to form Bayes-Markov chains, the advantages of both techniques can be preserved, while reducing their limitations. The Bayes-Markov technique forms the basis of a common, flexible framework for supplementing Markov chains with additional features. This results in improved user output, and aids in the rapid development of flexible and efficient behaviour recognition systems.

Variable parameter and double sampling (X)over-bar charts in the presence of correlation: The Markov chain approach

The general assumption under which the (X) over bar chart is designed is that the process mean has a constant in-control value. However, there are situations in which the process mean wanders. When it wanders according to a first-order autoregressive (AR (1)) model, a complex approach involving Markov chains and integral equation methods is used to evaluate the properties of the (X) over bar chart. In this paper, we propose the use of a pure Markov chain approach to study the performance of the (X) over bar chart. The performance of the chat (X) over bar with variable parameters and the (X) over bar with double sampling are compared. (C) 2011 Elsevier B.V. All rights reserved.

Estimação paramétrica e não-paramétrica em modelos de markov ocultos

In this work we study the Hidden Markov Models with finite as well as general state space. In the finite case, the forward and backward algorithms are considered and the probability of a given observed sequence is computed. Next, we use the EM algorithm to estimate the model parameters. In the general case, the kernel estimators are used and to built a sequence of estimators that converge in L1-norm to the density function of the observable process