The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ

This study examined the independent effect of skewness and kurtosis on the robustness of the linear mixed model (LMM), with the Kenward-Roger (KR) procedure, when group distributions are different, sample sizes are small, and sphericity cannot be assumed. Methods: A Monte Carlo simulation study considering a split-plot design involving three groups and four repeated measures was performed. Results: The results showed that when group distributions are different, the effect of skewness on KR robustness is greater than that of kurtosis for the corresponding values. Furthermore, the pairings of skewness and kurtosis with group size were found to be relevant variables when applying this procedure. Conclusions: With sample sizes of 45 and 60, KR is a suitable option for analyzing data when the distributions are: (a) mesokurtic and not highly or extremely skewed, and (b) symmetric with different degrees of kurtosis. With total sample sizes of 30, it is adequate when group sizes are equal and the distributions are: (a) mesokurtic and slightly or moderately skewed, and sphericity is assumed; and (b) symmetric with a moderate or high/extreme violation of kurtosis. Alternative analyses should be considered when the distributions are highly or extremely skewed and samples sizes are small.

Eye lens monitoring for interventional radiology personnel: dosemeters, calibration and practical aspects of H p (3) monitoring. A 2015 review.

A thorough literature review about the current situation on the implementation of eye lens monitoring has been performed in order to provide recommendations regarding dosemeter types, calibration procedures and practical aspects of eye lens monitoring for interventional radiology personnel. Most relevant data and recommendations from about 100 papers have been analysed and classified in the following topics: challenges of today in eye lens monitoring; conversion coefficients, phantoms and calibration procedures for eye lens dose evaluation; correction factors and dosemeters for eye lens dose measurements; dosemeter position and influence of protective devices. The major findings of the review can be summarised as follows: the recommended operational quantity for the eye lens monitoring is H p (3). At present, several dosemeters are available for eye lens monitoring and calibration procedures are being developed. However, in practice, very often, alternative methods are used to assess the dose to the eye lens. A summary of correction factors found in the literature for the assessment of the eye lens dose is provided. These factors can give an estimation of the eye lens dose when alternative methods, such as the use of a whole body dosemeter, are used. A wide range of values is found, thus indicating the large uncertainty associated with these simplified methods. Reduction factors from most common protective devices obtained experimentally and using Monte Carlo calculations are presented. The paper concludes that the use of a dosemeter placed at collar level outside the lead apron can provide a useful first estimate of the eye lens exposure. However, for workplaces with estimated annual equivalent dose to the eye lens close to the dose limit, specific eye lens monitoring should be performed. Finally, training of the involved medical staff on the risks of ionising radiation for the eye lens and on the correct use of protective systems is strongly recommended.

Balloon-based adjuvant radiotherapy in breast cancer: comparison between 99mTc and HDR 192Ir

Abstract Objective: To perform a comparative dosimetric analysis, based on computer simulations, of temporary balloon implants with 99mTc and balloon brachytherapy with high-dose-rate (HDR) 192Ir, as boosts to radiotherapy. We hypothesized that the two techniques would produce equivalent doses under pre-established conditions of activity and exposure time. Materials and Methods: Simulations of implants with 99mTc-filled and HDR 192Ir-filled balloons were performed with the Siscodes/MCNP5, modeling in voxels a magnetic resonance imaging set related to a young female. Spatial dose rate distributions were determined. In the dosimetric analysis of the protocols, the exposure time and the level of activity required were specified. Results: The 99mTc balloon presented a weighted dose rate in the tumor bed of 0.428 cGy.h-1.mCi-1 and 0.190 cGyh-1.mCi-1 at the balloon surface and at 8-10 mm from the surface, respectively, compared with 0.499 and 0.150 cGyh-1.mCi-1, respectively, for the HDR 192Ir balloon. An exposure time of 24 hours was required for the 99mTc balloon to produce a boost of 10.14 Gy with 1.0 Ci, whereas only 24 minutes with 10.0 Ci segments were required for the HDR 192Ir balloon to produce a boost of 5.14 Gy at the same reference point, or 10.28 Gy in two 24-minutes fractions. Conclusion: Temporary 99mTc balloon implantation is an attractive option for adjuvant radiotherapy in breast cancer, because of its availability, economic viability, and similar dosimetry in comparison with the use of HDR 192Ir balloon implantation, which is the current standard in clinical practice.

Modeling reaction kinetics and mass transfer in ozonation in water solutions

This dissertation is based on four articles dealing with modeling of ozonation. The literature part of this considers some models for hydrodynamics in bubble column simulation. A literature review of methods for obtaining mass transfer coefficients is presented. The methods presented to obtain mass transfer are general models and can be applied to any gas-liquid system. Ozonation reaction models and methods for obtaining stoichiometric coefficients and reaction rate coefficients for ozonation reactions are discussed in the final section of the literature part. In the first article, ozone gas-liquid mass transfer into water in a bubble column was investigated for different pH values. A more general method for estimation of mass transfer and Henry’s coefficient was developed from the Beltrán method. The ozone volumetric mass transfer coefficient and the Henry’s coefficient were determined simultaneously by parameter estimation using a nonlinear optimization method. A minor dependence of the Henry’s law constant on pH was detected at the pH range 4 - 9. In the second article, a new method using the axial dispersion model for estimation of ozone self-decomposition kinetics in a semi-batch bubble column reactor was developed. The reaction rate coefficients for literature equations of ozone decomposition and the gas phase dispersion coefficient were estimated and compared with the literature data. The reaction order in the pH range 7-10 with respect to ozone 1.12 and 0.51 the hydroxyl ion were obtained, which is in good agreement with literature. The model parameters were determined by parameter estimation using a nonlinear optimization method. Sensitivity analysis was conducted using object function method to obtain information about the reliability and identifiability of the estimated parameters. In the third article, the reaction rate coefficients and the stoichiometric coefficients in the reaction of ozone with the model component p-nitrophenol were estimated at low pH of water using nonlinear optimization. A novel method for estimation of multireaction model parameters in ozonation was developed. In this method the concentration of unknown intermediate compounds is presented as a residual COD (chemical oxygen demand) calculated from the measured COD and the theoretical COD for the known species. The decomposition rate of p-nitrophenol on the pathway producing hydroquinone was found to be about two times faster than the p-nitrophenol decomposition rate on the pathway producing 4- nitrocatechol. In the fourth article, the reaction kinetics of p-nitrophenol ozonation was studied in a bubble column at pH 2. Using the new reaction kinetic model presented in the previous article, the reaction kinetic parameters, rate coefficients, and stoichiometric coefficients as well as the mass transfer coefficient were estimated with nonlinear estimation. The decomposition rate of pnitrophenol was found to be equal both on the pathway producing hydroquinone and on the path way producing 4-nitrocathecol. Comparison of the rate coefficients with the case at initial pH 5 indicates that the p-nitrophenol degradation producing 4- nitrocathecol is more selective towards molecular ozone than the reaction producing hydroquinone. The identifiability and reliability of the estimated parameters were analyzed with the Marcov chain Monte Carlo (MCMC) method. @All rights reserved. No part of the publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the author.

Hankintaprosessin suorituskyvyn arviointi ja kehittäminen

Tämän työn tarkoituksena oli tarkastella kohdeorganisaation hankintaprosessin suorituskykyä. Tutkimuksen päämääränä oli tuottaa yritykselle sellaista tietoa ja arviointikriteerejä, joiden avulla yritys voi kehittää valmiuksiaan oman suorituskyvyn tehokkaampaan arviointiin tulevaisuudessa. Tutkielma tehtiin Skanska Oy:n osto-osastolle Helsinkiin. Tutkimuksen kohteeksi valittiin kausisopimusten hankintaprosessi epäsuorissa hankinnoissa, kotimaisilla markkinoilla. Keskitetyn kausisopimusten hankintaprosessin tarkoituksena on tuottaa yritykselle kilpailukykyisiä sopimuksia sekä saavuttaa prosessin parempi hallinta ja läpinäkyvyys. Tietoa tutkimuksen kohteena olevasta prosessista kerättiin haastatteluilla ja keskustelutuokioilla sekä yrityksen dokumenteista. Aineiston keräämisen kautta pyrittiin saamaan syvempi kuva prosessin toiminnasta, sen ongelmakohdista sekä niiden syistä ja seurauksista. Toisen tarkastelunäkökulman prosessin arvioinnille tarjosi läpimenoajan mittaaminen. Saatua aineistoa luokiteltiin vika- ja vaikutusanalyysiin pohjautuvalla mallilla sekä Monte Carlo – simulaatiomenetelmään perustuvalla ohjelmalla. Työn tuloksena esitetään tutkimuksen kohteena olevalle prosessille sopivia kehitystoimenpiteitä sekä suositeltavia prosessin mittaamisalueita.

Indirect likelihood inference (revised)

Standard indirect Inference (II) estimators take a given finite-dimensional statistic, Z_{n} , and then estimate the parameters by matching the sample statistic with the model-implied population moment. We here propose a novel estimation method that utilizes all available information contained in the distribution of Z_{n} , not just its first moment. This is done by computing the likelihood of Z_{n}, and then estimating the parameters by either maximizing the likelihood or computing the posterior mean for a given prior of the parameters. These are referred to as the maximum indirect likelihood (MIL) and Bayesian Indirect Likelihood (BIL) estimators, respectively. We show that the IL estimators are first-order equivalent to the corresponding moment-based II estimator that employs the optimal weighting matrix. However, due to higher-order features of Z_{n} , the IL estimators are higher order efficient relative to the standard II estimator. The likelihood of Z_{n} will in general be unknown and so simulated versions of IL estimators are developed. Monte Carlo results for a structural auction model and a DSGE model show that the proposed estimators indeed have attractive finite sample properties.

PRACTICAL STOCHASTIC MODEL FOR CHEMICAL KINETICS

The Practical Stochastic Model is a simple and robust method to describe coupled chemical reactions. The connection between this stochastic method and a deterministic method was initially established to understand how the parameters and variables that describe the concentration in both methods were related. It was necessary to define two main concepts to make this connection: the filling of compartments or dilutions and the rate of reaction enhancement. The parameters, variables, and the time of the stochastic methods were scaled with the size of the compartment and were compared with a deterministic method. The deterministic approach was employed as an initial reference to achieve a consistent stochastic result. Finally, an independent robust stochastic method was obtained. This method could be compared with the Stochastic Simulation Algorithm developed by Gillespie, 1977. The Practical Stochastic Model produced absolute values that were essential to describe non-linear chemical reactions with a simple structure, and allowed for a correct description of the chemical kinetics.

Loviisan ydinvoimalaitoksen todennäköisyyspohjaisen riskianalyysin tason 2 epävarmuustarkastelut

Diplomityössä tarkastellaan Loviisan ydinvoimalaitoksen todennäköisyyspohjaisen riskianalyysin tason 2 epävarmuuksia. Tason 2 riskitutkimuksissa tutkitaan ydinvoimalaitosonnettomuuksia, joiden seurauksena osa reaktorin radioaktiivisista aineista vapautuu ympäristöön. Näiden tutkimuksien päätulos on suuren päästön vuotuinen taajuus ja se on pääosin todelliseen laitoshistoriaan perustuva tilastollinen odotusarvo. Tämän odotusarvon uskottavuutta voidaan parantaa huomioimalla merkittävimmät laskentaan liittyvät epävarmuudet. Epävarmuuksia laskentaan aiheutuu muiden muassa vakavan reaktorionnettomuuden ilmiöistä, turvallisuusjärjestelmien laitteista, inhimillisistä toiminnoista sekä luotettavuusmallin määrittelemättömistä osista. Diplomityössä kuvataan, kuinka epävarmuustarkastelut integroidaan osaksi Loviisan ydinvoimalaitoksen todennäköisyyspohjaisia riskianalyysejä. Tämä toteutetaan diplomityössä kehitetyillä apuohjelmilla PRALA:lla ja PRATU:lla, joiden avulla voidaan lisätä laitoshistorian perusteella muodostetut epävarmuusparametrit osaksi riskianalyysien luotettavuusdataa. Lisäksi diplomityössä on laskettu laskentaesimerkkinä Loviisan ydinvoimalaitoksen suuren päästön vuotuisen taajuuden vaihtelua kuvaava luottamusväli. Tämä laskentaesimerkki pohjautuu pääosin konservatiivisiin epävarmuusarvioihin, ei todellisiin tilastollisiin epävarmuuksiin. Laskentaesimerkin tulosten perusteella Loviisan suuren päästön taajuudella on laaja vaihteluväli; virhekertoimeksi saatiin 8,4 nykyisillä epävarmuusparametreilla. Suuren päästön taajuuden luottamusväliä voidaan kuitenkin tulevaisuudessa supistaa, kun hyödynnetään todelliseen laitoshistoriaan perustuvia epävarmuusparametreja.

Estimativa da relação hipsométrica em clones de Eucalyptus sp. com o modelo de curtis ajustado por métodos bayesianos empíricos

Neste trabalho foi considerado o modelo de Curtis para a relação hipsométrica em clones de Eucalyptus sp. com os parâmetros sujeitos a restrições. Para fazer a inferência dos parâmetros do modelo com restrições, utilizou-se uma abordagem bayesiana com densidade a priori construída empiricamente. As estimativas bayesianas são calculadas com a técnica de simulação de Monte Carlo em Cadeia de Markov (MCMC). O método proposto foi aplicado a diferentes conjuntos de dados reais, dos quais foram selecionados cinco para exemplificar os resultados. Estes foram comparados com os resultados obtidos pelo método de mínimos quadrados, destacando-se a superioridade da abordagem bayesiana proposta.

Vaikutusalakirjastojen muodostaminen Serpent-ARES-laskentaketjussa

Tässä diplomityössä on esitetty työn yhteydessä toteutetun Serpent-ARES-laskentaketjun muodostamiseksi tarvittavat toimenpiteet. ARES-reaktorisydän-simulaattorissa tarvittavien homogenisoitujen ryhmävakiokirjastojen muodostaminen Serpentiä käyttäen tekee laskentaketjusta muiden käytössä olevien reaktorisydämen laskentaketjujen mahdollisista virhelähteistä riippumattoman. Monte Carlo-laskentamenetelmään perustuvaa reaktorifysiikan laskentaohjelmaa käyttämällä ryhmävakiokirjastot muodostetaan uudella menetelmällä ja näin saadaan viranomaiskäyttöön voimayhtiöiden käyttämistä menetelmistä riippumaton laskentaketju reaktorien turvallisuusmarginaalien laskentaan. Työn yhteydessä muodostetun laskentaketjun ja tehtyjen vaikutusalakirjastojen muodostamisrutiinien sekä parametrisovitteiden toimivuus on todettu laskemalla Olkiluoto 3 - reaktorin alkulatauksen säätösauvojen tehokkuuksia ja sammutusmarginaaleja eri olosuhteissa. Menetelmä on todettu toimivaksi parametrien pätevyysalueella ja saadut laskentatulokset ovat oikeaa suuruusluokkaa. Parametrimallin tarkkuutta ja pätevyysaluetta on syytä vielä kehittää, ennen kuin laskentaketjua voidaan käyttää varmentamaan muilla menetelmillä laskettujen tulosten oikeellisuutta.

Value at Risk in Foreign Exchange Risk Management

This thesis examines the suitability of VaR in foreign exchange rate risk management from the perspective of a European investor. The suitability of four different VaR models is evaluated in respect to have insight if VaR is a valuable tool in managing foreign exchange rate risk. The models evaluated are historical method, historical bootstrap method, variance-covariance method and Monte Carlo simulation. The data evaluated are divided into emerging and developed market currencies to have more intriguing analysis. The foreign exchange rate data in this thesis is from 31st January 2000 to 30th April 2014. The results show that the previously mentioned VaR models performance in foreign exchange risk management is not to be considered as a single tool in foreign exchange rate risk management. The variance-covariance method and Monte Carlo simulation performs poorest in both currency portfolios. Both historical methods performed better but should also be considered as an additional tool along with other more sophisticated analysis tools. A comparative study of VaR estimates and forward prices is also included in the thesis. The study reveals that regardless of the expensive hedging cost of emerging market currencies the risk captured by VaR is more expensive and thus FX forward hedging is recommended

Reconstructive dosimetry for cutaneous radiation syndrome

According to the International Atomic Energy Agency (IAEA), a relatively significant number of radiological accidents have occurred in recent years mainly because of the practices referred to as potentially high-risk activities, such as radiotherapy, large irradiators and industrial radiography, especially in gammagraphy assays. In some instances, severe injuries have occurred in exposed persons due to high radiation doses. In industrial radiography, 80 cases involving a total of 120 radiation workers, 110 members of the public including 12 deaths have been recorded up to 2014. Radiological accidents in industrial practices in Brazil have mainly resulted in development of cutaneous radiation syndrome (CRS) in hands and fingers. Brazilian data include 5 serious cases related to industrial gammagraphy, affecting 7 radiation workers and 19 members of the public; however, none of them were fatal. Some methods of reconstructive dosimetry have been used to estimate the radiation dose to assist in prescribing medical treatment. The type and development of cutaneous manifestations in the exposed areas of a person is the first achievable gross dose estimation. This review article presents the state-of-the-art reconstructive dosimetry methods enabling estimation of local radiation doses and provides guidelines for medical handling of the exposed individuals. The review also presents the Chilean and Brazilian radiological accident cases to highlight the importance of reconstructive dosimetry.

Performance measurement model for projects from a strategic management perspective

This research studied the project performance measurement from the perspective of strategic management. The objective was to find a generic model for project performance measurement that emphasizes strategy and decision making. Research followed the guidelines of a constructive research methodology. As a result, the study suggests a model that measures projects with multiple meters during and after projects. Measurement after the project is suggested to be linked to the strategic performance measures of a company. The measurement should be conducted with centralized project portfolio management e.g. using the project management office in the organization. Metrics, after the project, measure the project’s actual benefit realization. During the project, the metrics are universal and they measure the accomplished objectives relation to costs, schedule and internal resource usage. Outcomes of these measures should be forecasted by using qualitative or stochastic methods. Solid theoretical background for the model was found from the literature that covers the subjects of performance measurement, projects and uncertainty. The study states that the model can be implemented in companies. This statement is supported by empirical evidence from a single case study. The gathering of empiric evidence about the actual usefulness of the model in companies is left to be done by the evaluative research in the future.

Public-private partnership investments in dry ports – Russian logistics markets and risks

The investments have always been considered as an essential backbone and so-called ‘locomotive’ for the competitive economies. However, in various countries, the state has been put under tight budget constraints for the investments in capital intensive projects. In response to this situation, the cooperation between public and private sector has grown based on public-private mechanism. The promotion of favorable arrangement for collaboration between public and private sectors for the provision of policies, services, and infrastructure in Russia can help to address the problems of dry ports development that neither municipalities nor the private sector can solve alone. Especially, the stimulation of public-private collaboration is significant under the exposure to externalities that affect the magnitude of the risks during all phases of project realization. In these circumstances, the risk in the projects also is becoming increasingly a part of joint research and risk management practice, which is viewed as a key approach, aiming to take active actions on existing global and specific factors of uncertainties. Meanwhile, a relatively little progress has been made on the inclusion of the resilience aspects into the planning process of a dry ports construction that would instruct the capacity planner, on how to mitigate the occurrence of disruptions that may lead to million dollars of losses due to the deviation of the future cash flows from the expected financial flows on the project. The current experience shows that the existing methodological base is developed fragmentary within separate steps of supply chain risk management (SCRM) processes: risk identification, risk evaluation, risk mitigation, risk monitoring and control phases. The lack of the systematic approach hinders the solution of the problem of risk management processes of dry port implementation. Therefore, management of various risks during the investments phases of dry port projects still presents a considerable challenge from the practical and theoretical points of view. In this regard, the given research became a logical continuation of fundamental research, existing in the financial models and theories (e.g., capital asset pricing model and real option theory), as well as provided a complementation for the portfolio theory. The goal of the current study is in the design of methods and models for the facilitation of dry port implementation through the mechanism of public-private partnership on the national market that implies the necessity to mitigate, first and foremost, the shortage of the investments and consequences of risks. The problem of the research was formulated on the ground of the identified contradictions. They rose as a continuation of the trade-off between the opportunities that the investors can gain from the development of terminal business in Russia (i.e. dry port implementation) and risks. As a rule, the higher the investment risk, the greater should be their expected return. However, investors have a different tolerance for the risks. That is why it would be advisable to find an optimum investment. In the given study, the optimum relates to the search for the efficient portfolio, which can provide satisfaction to the investor, depending on its degree of risk aversion. There are many theories and methods in finance, concerning investment choices. Nevertheless, the appropriateness and effectiveness of particular methods should be considered with the allowance of the specifics of the investment projects. For example, the investments in dry ports imply not only the lump sum of financial inflows, but also the long-term payback periods. As a result, capital intensity and longevity of their construction determine the necessity from investors to ensure the return on investment (profitability), along with the rapid return on investment (liquidity), without precluding the fact that the stochastic nature of the project environment is hardly described by the formula-based approach. The current theoretical base for the economic appraisals of the dry port projects more often perceives net present value (NPV) as a technique superior to other decision-making criteria. For example, the portfolio theory, which considers different risk preference of an investor and structures of utility, defines net present value as a better criterion of project appraisal than discounted payback period (DPP). Meanwhile, in business practice, the DPP is more popular. Knowing that the NPV is based on the assumptions of certainty of project life, it cannot be an accurate appraisal approach alone to determine whether or not the project should be accepted for the approval in the environment that is not without of uncertainties. In order to reflect the period or the project’s useful life that is exposed to risks due to changes in political, operational, and financial factors, the second capital budgeting criterion – discounted payback period is profoundly important, particularly for the Russian environment. Those statements represent contradictions that exist in the theory and practice of the applied science. Therefore, it would be desirable to relax the assumptions of portfolio theory and regard DPP as not fewer relevant appraisal approach for the assessment of the investment and risk measure. At the same time, the rationality of the use of both project performance criteria depends on the methods and models, with the help of which these appraisal approaches are calculated in feasibility studies. The deterministic methods cannot ensure the required precision of the results, while the stochastic models guarantee the sufficient level of the accuracy and reliability of the obtained results, providing that the risks are properly identified, evaluated, and mitigated. Otherwise, the project performance indicators may not be confirmed during the phase of project realization. For instance, the economic and political instability can result in the undoing of hard-earned gains, leading to the need for the attraction of the additional finances for the project. The sources of the alternative investments, as well as supportive mitigation strategies, can be studied during the initial phases of project development. During this period, the effectiveness of the investments undertakings can also be improved by the inclusion of the various investors, e.g. Russian Railways’ enterprises and other private companies in the dry port projects. However, the evaluation of the effectiveness of the participation of different investors in the project lack the methods and models that would permit doing the particular feasibility study, foreseeing the quantitative characteristics of risks and their mitigation strategies, which can meet the tolerance of the investors to the risks. For this reason, the research proposes a combination of Monte Carlo method, discounted cash flow technique, the theory of real options, and portfolio theory via a system dynamics simulation approach. The use of this methodology allows for comprehensive risk management process of dry port development to cover all aspects of risk identification, risk evaluation, risk mitigation, risk monitoring, and control phases. A designed system dynamics model can be recommended for the decision-makers on the dry port projects that are financed via a public-private partnership. It permits investors to make a decision appraisal based on random variables of net present value and discounted payback period, depending on different risks factors, e.g. revenue risks, land acquisition risks, traffic volume risks, construction hazards, and political risks. In this case, the statistical mean is used for the explication of the expected value of the DPP and NPV; the standard deviation is proposed as a characteristic of risks, while the elasticity coefficient is applied for rating of risks. Additionally, the risk of failure of project investments and guaranteed recoupment of capital investment can be considered with the help of the model. On the whole, the application of these modern methods of simulation creates preconditions for the controlling of the process of dry port development, i.e. making managerial changes and identifying the most stable parameters that contribute to the optimal alternative scenarios of the project realization in the uncertain environment. System dynamics model allows analyzing the interactions in the most complex mechanism of risk management process of the dry ports development and making proposals for the improvement of the effectiveness of the investments via an estimation of different risk management strategies. For the comparison and ranking of these alternatives in their order of preference to the investor, the proposed indicators of the efficiency of the investments, concerning the NPV, DPP, and coefficient of variation, can be used. Thus, rational investors, who averse to taking increased risks unless they are compensated by the commensurate increase in the expected utility of a risky prospect of dry port development, can be guided by the deduced marginal utility of investments. It is computed on the ground of the results from the system dynamics model. In conclusion, the outlined theoretical and practical implications for the management of risks, which are the key characteristics of public-private partnerships, can help analysts and planning managers in budget decision-making, substantially alleviating the effect from various risks and avoiding unnecessary cost overruns in dry port projects.

Parameter estimation for Chaotic or Stochastic Dynamics

Since its discovery, chaos has been a very interesting and challenging topic of research. Many great minds spent their entire lives trying to give some rules to it. Nowadays, thanks to the research of last century and the advent of computers, it is possible to predict chaotic phenomena of nature for a certain limited amount of time. The aim of this study is to present a recently discovered method for the parameter estimation of the chaotic dynamical system models via the correlation integral likelihood, and give some hints for a more optimized use of it, together with a possible application to the industry. The main part of our study concerned two chaotic attractors whose general behaviour is diff erent, in order to capture eventual di fferences in the results. In the various simulations that we performed, the initial conditions have been changed in a quite exhaustive way. The results obtained show that, under certain conditions, this method works very well in all the case. In particular, it came out that the most important aspect is to be very careful while creating the training set and the empirical likelihood, since a lack of information in this part of the procedure leads to low quality results.