MCMC Analysis for Optimization of Stochastic Models

In any decision making under uncertainties, the goal is mostly to minimize the expected cost. The minimization of cost under uncertainties is usually done by optimization. For simple models, the optimization can easily be done using deterministic methods.However, many models practically contain some complex and varying parameters that can not easily be taken into account using usual deterministic methods of optimization. Thus, it is very important to look for other methods that can be used to get insight into such models. MCMC method is one of the practical methods that can be used for optimization of stochastic models under uncertainty. This method is based on simulation that provides a general methodology which can be applied in nonlinear and non-Gaussian state models. MCMC method is very important for practical applications because it is a uni ed estimation procedure which simultaneously estimates both parameters and state variables. MCMC computes the distribution of the state variables and parameters of the given data measurements. MCMC method is faster in terms of computing time when compared to other optimization methods. This thesis discusses the use of Markov chain Monte Carlo (MCMC) methods for optimization of Stochastic models under uncertainties .The thesis begins with a short discussion about Bayesian Inference, MCMC and Stochastic optimization methods. Then an example is given of how MCMC can be applied for maximizing production at a minimum cost in a chemical reaction process. It is observed that this method performs better in optimizing the given cost function with a very high certainty.

Stochastic variability of output levels in a pulp mill

Quite often, in the construction of a pulp mill involves establishing the size of tanks which will accommodate the material from the various processes in which case estimating the right tank size a priori would be vital. Hence, simulation of the whole production process would be worthwhile. Therefore, there is need to develop mathematical models that would mimic the behavior of the output from the various production units of the pulp mill to work as simulators. Markov chain models, Autoregressive moving average (ARMA) model, Mean reversion models with ensemble interaction together with Markov regime switching models are proposed for that purpose.

Stochastic approximation methods in stochastic optimization

Stochastic approximation methods for stochastic optimization are considered. Reviewed the main methods of stochastic approximation: stochastic quasi-gradient algorithm, Kiefer-Wolfowitz algorithm and adaptive rules for them, simultaneous perturbation stochastic approximation (SPSA) algorithm. Suggested the model and the solution of the retailer's profit optimization problem and considered an application of the SQG-algorithm for the optimization problems with objective functions given in the form of ordinary differential equation.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

The succession dynamics of a macroalgal community after a flood disturbance in a tropical stream from São Paulo State, southeastern Brazil

The succession dynamics of a macroalgal community in a tropical stream (20º58' S and 49º25' W) was investigated after disturbance by a sequence of intensive rains. High precipitation levels caused almost complete loss of the macroalgal community attached to the substratum and provided a strong pressure against its immediate re-establishment. After this disturbance, a weekly sampling program from May 1999 to January 2000 was established to investigate macroalgal recolonization. The community changed greatly throughout the succession process. The number of species varied from one to seven per sampling. Global abundance of macroalgal community did not reveal a consistent temporal pattern of variation. In early succession stages, the morphological form of tufts dominated, followed by unbranched filaments. Latter succession stages showed the almost exclusive occurrence of gelatinous forms, including filaments and colonies. The succession trajectory was mediated by phosphorus availability in which community composition followed a scheme of changes in growth forms. However, we believe that deterministic and stochastic processes occur in lotic ecosystems, but they are dependent on the length of time considered in the succession analyses.

Effect of the establishment of dominance relationships on cortisol and other metabolic parameters in Nile tilapia (Oreochromis niloticus)

The objective of the present study was to investigate the influence of the establishment of dominance relationships and social stress on plasma cortisol and metabolite levels in Nile tilapia (Oreochromis niloticus). During the 30-day experiment, the fish weighing 236 ± 29 g were kept in individual aquaria, except for two pairings lasting 6 h each. Blood samples were taken from the animals before and after pairing. Display, approach, attack, rebuff, chase flight, and coloration were carried out on days 16 and 30. Activities and behaviors characteristic of the establishment of dominance relationships were described. It was possible to classify all experimental fish (N = 30) as dominant or subordinate. No differences were detected between dominant (N = 15) and subordinate (N = 15) fish during isolation or after pairing in cortisol (isolated: 5.76 ± 0.98 vs 5.42 ± 0.63; paired: 10.94 ± 1.62 vs 11.21 ± 2.45 µg/dl), glucose (isolated: 60.02 ± 4.9 vs 67.85 ± 16.16; paired: 110.44 ± 15.72 vs 136.26 ± 22.46 mg/dl), triglyceride (isolated: 167.87 ± 5.06 vs 185.68 ± 7.24; paired: 210.85 ± 13.40 vs 221.82 ± 12.70 mg/dl) or total protein levels (isolated: 7.01 ± 0.42 vs 6.69 ± 0.59; paired: 9.21 ± 0.62 vs 9.51 ± 0.66 g/dl). However, when isolated (N = 30) and paired (N = 30) tilapia were compared, there were significant differences in cortisol and metabolite levels. The similar response presented by dominant and subordinate tilapia indicates that establishment of dominance relationships was a stressor for both groups.

Silicon-containing species in used lube oil re-refining

Nowadays, the re-refining of the used lube oils has gained worldwide a lot of attention due to the necessity for added environmental protection and increasingly stringent environmental legislation. One of the parameters determining the quality of the produced base oils is the composition of feedstock. Estimation of the chemical composition of the used oil collected from several European locations showed that the hydrocarbon structure of the motor oil is changed insignificantly during its operation and the major part of the changes is accounted for with depleted oil additives. In the lube oil re-refining industry silicon, coming mainly from antifoaming agents, is recognized to be a contaminant generating undesired solid deposits in various locations in the re-refining units. In this thesis, a particular attention was paid to the mechanism of solid product formation during the alkali treatment process of silicon-containing used lube oils. The transformations of a model siloxane, tetramethyldisiloxane (TMDS), were studied in a batch reactor at industrially relevant alkali treatment conditions (low temperature, short reaction time) using different alkali agents. The reaction mechanism involving solid alkali metal silanolates was proposed. The experimental data obtained demonstrated that the solids were dominant products at low temperature and short reaction time. The liquid products in the low temperature reactions were represented mainly by linear siloxanes. The prolongation of reaction time resulted in reduction of solids, whereas both temperature and time increase led to dominance of cyclic products in the reaction mixture. Experiments with the varied reaction time demonstrated that the concentration of cyclic trimer being the dominant in the beginning of the reaction diminished with time, whereas the cyclic tetramer tended to increase. Experiments with lower sodium hydroxide concentration showed the same effect. In addition, a decrease of alkali agent concentration in the initial reaction mixture accelerated TMDS transformation reactions resulting in solely liquid cyclic siloxanes yields. Comparison of sodium and potassium hydroxides applied as an alkali agent demonstrated that potassium hydroxide was more efficient, since the activation energy in KOH presence was almost 2-fold lower than that for sodium hydroxide containing reaction mixture. Application of potassium hydroxide for TMDS transformation at 100° C with 3 hours reaction time resulted in 20 % decrease of solid yields compared to NaOH-containing mixture. Moreover, TMDS transformations in the presence of sodium silanolate applied as an alkali agent led to formation of only liquid products without formation of the undesired solids. On the basis of experimental data and the proposed reaction mechanism, a kinetic model was developed, which provided a satisfactory description of the experimental results. Suitability of the selected siloxane as a relevant model of industrial silicon-containing compounds was verified by investigation of the commercially available antifoam agent in base-catalyzed conditions.

Contested dominance modifies the anovulatory consequences of social subordination in female marmosets

Dominance status among female marmosets is reflected in agonistic behavior and ovarian function. Socially dominant females receive submissive behavior from subordinates, while exhibiting normal ovulatory function. Subordinate females, however, receive agonistic behavior from dominants, while exhibiting reduced or absent ovulatory function. Such disparity in female fertility is not absolute, and groups with two breeding females have been described. The data reported here were obtained from 8 female-female pairs of captive female marmosets, each housed with a single unrelated male. Pairs were classified into two groups: "uncontested" dominance (UD) and "contested" dominance (CD), with 4 pairs each. Dominant females in UD pairs showed significantly higher frequencies (4.1) of agonism (piloerection, attack and chasing) than their subordinates (0.36), and agonistic behaviors were overall more frequently displayed by CD than by UD pairs. Subordinates in CD pairs exhibited more agonistic behavior (2.9) than subordinates in UD pairs (0.36), which displayed significantly more submissive (6.97) behaviors than their dominants (0.35). The data suggest that there is more than one kind of dominance relationship between female common marmosets. Assessment of progesterone levels showed that while subordinates in UD pairs appeared to be anovulatory, the degree of ovulatory disruption in subordinates of CD pairs was more varied and less complete. We suggest that such variation in female-female social dominance relationships and the associated variation in the degree and reliability of fertility suppression may explain variations of the reproductive condition of free-living groups of common marmosets.

Early detection of metabolic and energy disorders by thermal time series stochastic complexity analysis

Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile.