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Parameter Dependencies in an Accumulation-to-Threshold Model of Simple Perceptual DecisionsNikitin, Vyacheslav Y. January 2015 (has links)
No description available.
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Étude de la performance d’un algorithme Metropolis-Hastings avec ajustement directionnelMireuta, Matei 08 1900 (has links)
Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont des outils très populaires
pour l’échantillonnage de lois de probabilité complexes et/ou en grandes dimensions.
Étant donné leur facilité d’application, ces méthodes sont largement répandues
dans plusieurs communautés scientifiques et bien certainement en statistique, particulièrement
en analyse bayésienne. Depuis l’apparition de la première méthode MCMC en
1953, le nombre de ces algorithmes a considérablement augmenté et ce sujet continue
d’être une aire de recherche active.
Un nouvel algorithme MCMC avec ajustement directionnel a été récemment développé
par Bédard et al. (IJSS, 9 :2008) et certaines de ses propriétés restent partiellement
méconnues. L’objectif de ce mémoire est de tenter d’établir l’impact d’un paramètre clé
de cette méthode sur la performance globale de l’approche. Un second objectif est de
comparer cet algorithme à d’autres méthodes MCMC plus versatiles afin de juger de sa
performance de façon relative. / Markov Chain Monte Carlo algorithms (MCMC) have become popular tools for sampling
from complex and/or high dimensional probability distributions. Given their relative
ease of implementation, these methods are frequently used in various scientific
areas, particularly in Statistics and Bayesian analysis. The volume of such methods has
risen considerably since the first MCMC algorithm described in 1953 and this area of
research remains extremely active.
A new MCMC algorithm using a directional adjustment has recently been described
by Bédard et al. (IJSS, 9:2008) and some of its properties remain unknown. The objective
of this thesis is to attempt determining the impact of a key parameter on the global
performance of the algorithm. Moreover, another aim is to compare this new method to
existing MCMC algorithms in order to evaluate its performance in a relative fashion.
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New simulation schemes for the Heston modelBégin, Jean-François 06 1900 (has links)
Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier.
Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée.
Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations.
Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)).
Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme.
Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma. / Financial stocks are often modeled by stochastic differential equations (SDEs). These equations could describe the behavior of the underlying asset as well as some of the model's parameters. For example, the Heston (1993) model, which is a stochastic volatility model, describes the behavior of the stock and the variance of the latter.
The Heston model is very interesting since it has semi-closed formulas for some derivatives, and it is quite realistic. However, many simulation schemes for this model have problems when the Feller (1951) condition is violated.
In this thesis, we introduce new simulation schemes to simulate price paths using the Heston model. These new algorithms are based on Broadie and Kaya's (2006) method. In order to increase the speed of the exact scheme of Broadie and Kaya, we use, among other things, Markov chains Monte Carlo (MCMC) algorithms and some well-chosen approximations.
In our first algorithm, we modify the second step of the Broadie and Kaya's method in order to get faster schemes. Instead of using the second-order Newton method coupled with the inversion approach, we use a Metropolis-Hastings algorithm.
The second algorithm is a small improvement of our latter scheme. Instead of using the real integrated variance over time p.d.f., we use Smith's (2007) approximation. This helps us decrease the dimension of our problem (from three to two).
Our last algorithm is not based on MCMC methods. However, we still try to speed up the second step of Broadie and Kaya. In order to achieve this, we use a moment-matched gamma random variable. According to Stewart et al. (2007), it is possible to approximate a complex gamma convolution (somewhat near the representation given by Glasserman and Kim (2008) when T-t is close to zero) by a gamma distribution.
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New simulation schemes for the Heston modelBégin, Jean-François 06 1900 (has links)
Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier.
Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée.
Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations.
Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)).
Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme.
Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma. / Financial stocks are often modeled by stochastic differential equations (SDEs). These equations could describe the behavior of the underlying asset as well as some of the model's parameters. For example, the Heston (1993) model, which is a stochastic volatility model, describes the behavior of the stock and the variance of the latter.
The Heston model is very interesting since it has semi-closed formulas for some derivatives, and it is quite realistic. However, many simulation schemes for this model have problems when the Feller (1951) condition is violated.
In this thesis, we introduce new simulation schemes to simulate price paths using the Heston model. These new algorithms are based on Broadie and Kaya's (2006) method. In order to increase the speed of the exact scheme of Broadie and Kaya, we use, among other things, Markov chains Monte Carlo (MCMC) algorithms and some well-chosen approximations.
In our first algorithm, we modify the second step of the Broadie and Kaya's method in order to get faster schemes. Instead of using the second-order Newton method coupled with the inversion approach, we use a Metropolis-Hastings algorithm.
The second algorithm is a small improvement of our latter scheme. Instead of using the real integrated variance over time p.d.f., we use Smith's (2007) approximation. This helps us decrease the dimension of our problem (from three to two).
Our last algorithm is not based on MCMC methods. However, we still try to speed up the second step of Broadie and Kaya. In order to achieve this, we use a moment-matched gamma random variable. According to Stewart et al. (2007), it is possible to approximate a complex gamma convolution (somewhat near the representation given by Glasserman and Kim (2008) when T-t is close to zero) by a gamma distribution.
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Étude de la performance d’un algorithme Metropolis-Hastings avec ajustement directionnelMireuta, Matei 08 1900 (has links)
Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont des outils très populaires
pour l’échantillonnage de lois de probabilité complexes et/ou en grandes dimensions.
Étant donné leur facilité d’application, ces méthodes sont largement répandues
dans plusieurs communautés scientifiques et bien certainement en statistique, particulièrement
en analyse bayésienne. Depuis l’apparition de la première méthode MCMC en
1953, le nombre de ces algorithmes a considérablement augmenté et ce sujet continue
d’être une aire de recherche active.
Un nouvel algorithme MCMC avec ajustement directionnel a été récemment développé
par Bédard et al. (IJSS, 9 :2008) et certaines de ses propriétés restent partiellement
méconnues. L’objectif de ce mémoire est de tenter d’établir l’impact d’un paramètre clé
de cette méthode sur la performance globale de l’approche. Un second objectif est de
comparer cet algorithme à d’autres méthodes MCMC plus versatiles afin de juger de sa
performance de façon relative. / Markov Chain Monte Carlo algorithms (MCMC) have become popular tools for sampling
from complex and/or high dimensional probability distributions. Given their relative
ease of implementation, these methods are frequently used in various scientific
areas, particularly in Statistics and Bayesian analysis. The volume of such methods has
risen considerably since the first MCMC algorithm described in 1953 and this area of
research remains extremely active.
A new MCMC algorithm using a directional adjustment has recently been described
by Bédard et al. (IJSS, 9:2008) and some of its properties remain unknown. The objective
of this thesis is to attempt determining the impact of a key parameter on the global
performance of the algorithm. Moreover, another aim is to compare this new method to
existing MCMC algorithms in order to evaluate its performance in a relative fashion.
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Recyclage des candidats dans l'algorithme Metropolis à essais multiplesGroiez, Assia 03 1900 (has links)
Les méthodes de Monte Carlo par chaînes de Markov (MCCM) sont des méthodes
servant à échantillonner à partir de distributions de probabilité. Ces techniques
se basent sur le parcours de chaînes de Markov ayant pour lois stationnaires
les distributions à échantillonner. Étant donné leur facilité d’application, elles
constituent une des approches les plus utilisées dans la communauté statistique,
et tout particulièrement en analyse bayésienne. Ce sont des outils très populaires
pour l’échantillonnage de lois de probabilité complexes et/ou en grandes dimensions.
Depuis l’apparition de la première méthode MCCM en 1953 (la méthode de
Metropolis, voir [10]), l’intérêt pour ces méthodes, ainsi que l’éventail d’algorithmes
disponibles ne cessent de s’accroître d’une année à l’autre.
Bien que l’algorithme Metropolis-Hastings (voir [8]) puisse être considéré
comme l’un des algorithmes de Monte Carlo par chaînes de Markov les plus généraux,
il est aussi l’un des plus simples à comprendre et à expliquer, ce qui en fait
un algorithme idéal pour débuter. Il a été sujet de développement par plusieurs
chercheurs. L’algorithme Metropolis à essais multiples (MTM), introduit dans la
littérature statistique par [9], est considéré comme un développement intéressant
dans ce domaine, mais malheureusement son implémentation est très coûteuse
(en termes de temps).
Récemment, un nouvel algorithme a été développé par [1]. Il s’agit de l’algorithme
Metropolis à essais multiples revisité (MTM revisité), qui définit la méthode
MTM standard mentionnée précédemment dans le cadre de l’algorithme
Metropolis-Hastings sur un espace étendu.
L’objectif de ce travail est, en premier lieu, de présenter les méthodes MCCM,
et par la suite d’étudier et d’analyser les algorithmes Metropolis-Hastings ainsi
que le MTM standard afin de permettre aux lecteurs une meilleure compréhension
de l’implémentation de ces méthodes. Un deuxième objectif est d’étudier les
perspectives ainsi que les inconvénients de l’algorithme MTM revisité afin de voir
s’il répond aux attentes de la communauté statistique. Enfin, nous tentons de combattre le problème de sédentarité de l’algorithme MTM revisité, ce qui donne
lieu à un tout nouvel algorithme. Ce nouvel algorithme performe bien lorsque le
nombre de candidats générés à chaque itérations est petit, mais sa performance
se dégrade à mesure que ce nombre de candidats croît. / Markov Chain Monte Carlo (MCMC) algorithms are methods that are used
for sampling from probability distributions. These tools are based on the path
of a Markov chain whose stationary distribution is the distribution to be sampled.
Given their relative ease of application, they are one of the most popular
approaches in the statistical community, especially in Bayesian analysis. These
methods are very popular for sampling from complex and/or high dimensional
probability distributions.
Since the appearance of the first MCMC method in 1953 (the Metropolis algorithm,
see [10]), the interest for these methods, as well as the range of algorithms
available, continue to increase from one year to another.
Although the Metropolis-Hastings algorithm (see [8]) can be considered as
one of the most general Markov chain Monte Carlo algorithms, it is also one of
the easiest to understand and explain, making it an ideal algorithm for beginners.
As such, it has been studied by several researchers. The multiple-try Metropolis
(MTM) algorithm , proposed by [9], is considered as one interesting development
in this field, but unfortunately its implementation is quite expensive (in terms of
time).
Recently, a new algorithm was developed by [1]. This method is named the revisited
multiple-try Metropolis algorithm (MTM revisited), which is obtained by
expressing the MTM method as a Metropolis-Hastings algorithm on an extended
space.
The objective of this work is to first present MCMC methods, and subsequently
study and analyze the Metropolis-Hastings and standard MTM algorithms
to allow readers a better perspective on the implementation of these methods.
A second objective is to explore the opportunities and disadvantages of
the revisited MTM algorithm to see if it meets the expectations of the statistical
community. We finally attempt to fight the sedentarity of the revisited MTM algorithm,
which leads to a new algorithm. The latter performs efficiently when the
number of generated candidates in a given iteration is small, but the performance of this new algorithm then deteriorates as the number of candidates in a given
iteration increases.
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Equações simultâneas no contexto clássico e bayesiano: uma abordagem à produção de sojaVASCONCELOS, Josimar Mendes de 08 August 2011 (has links)
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Previous issue date: 2011-08-08 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The last years has increased the quantity of researchers and search scientific in the plantation, production and value of the soybeans in the Brazil, in grain. In front of this, the present dissertation looks for to analyze the data and estimate models that explain, of satisfactory form, the variability observed of the quantity produced and value of the production of soya in grain in the Brazil, in the field of the study. For the development of these analyses is used the classical and Bayesian inference, in the context of simultaneous equations by the tools of indirect square minimum in two practices. In the classical inference uses the estimator of square minima in two practices. In the Bayesian inference worked the method of Mountain Carlo via Chain of Markov with the algorithms of Gibbs and Metropolis-Hastings by means of the technician of simultaneous equations. In the study, consider the variable area harvested, quantity produced, value of the production and gross inner product, in which it adjusted the model with the variable answer quantity produced and afterwards the another variable answer value of the production for finally do the corrections and obtain the final result, in the classical and Bayesian method. Through of the detours normalized, statistics of the proof-t, criteria of information Akaike and Schwarz normalized stands out the good application of the method of Mountain Carlo via Chain of Markov by the algorithm of Gibbs, also is an efficient method in the modelado and of easy implementation in the statistical softwares R & WinBUGS, as they already exist smart libraries to compile the method. Therefore, it suggests work the method of Mountain Carlo via chain of Markov through the method of Gibbs to estimate the production of soya in grain. / Nos últimos anos tem aumentado a quantidade de pesquisadores e pesquisas científicas na plantação, produção e valor de soja no Brasil, em grão. Diante disso, a presente dissertação busca analisar os dados e ajustar modelos que expliquem, de forma satisfatória, a variabilidade observada da quantidade produzida e valor da produção de soja em grão no Brasil, no campo do estudo. Para o desenvolvimento dessas análises é utilizada a inferência clássica e bayesiana, no contexto de equações simultâneas através da ferramenta de mínimos quadrados em dois estágios. Na inferência clássica utiliza-se o estimador de mínimos quadrados em dois estágios. Na inferência bayesiana trabalhou-se o método de Monte Carlo via Cadeia de Markov com os algoritmos de Gibbs e Metropolis-Hastings por meio da técnica de equações simultâneas. No estudo, consideram-se as variáveis área colhida, quantidade produzida, valor da produção e produto interno bruto, no qual ajustou-se o modelo com a variável resposta quantidade produzida e depois a variável resposta valor da produção para finalmente fazer as correções e obter o resultado final, no método clássico e bayesiano. Através, dos desvios padrão, estatística do teste-t, critérios de informação Akaike e Schwarz normalizados destaca-se a boa aplicação do método de Monte Carlo via Cadeia de Markov pelo algoritmo de Gibbs, também é um método eficiente na modelagem e de fácil implementação nos softwares estatísticos R & WinBUGS, pois já existem bibliotecas prontas para compilar o método. Portanto, sugere-se trabalhar o método de Monte Carlo via cadeia de Markov através do método de Gibbs para estimar a produção de soja em grão, no Brasil.
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[en] PROBABILISTIC PORE PRESSURE PREDICTION IN RESERVOIR ROCKS THROUGH COMPRESSIONAL AND SHEAR VELOCITIES / [pt] PREVISÃO PROBABILÍSTICA DE PRESSÃO DE POROS EM ROCHAS RESERVATÓRIO ATRAVÉS DE VELOCIDADES COMPRESSIONAIS E CISALHANTESBRUNO BROESIGKE HOLZBERG 24 March 2006 (has links)
[pt] Esta tese propõe uma metodologia de estimativa de
pressão
de poros em rochasreservatório
através dos atributos sísmicos velocidade compressional
V(p) e velocidade
cisalhante V(s). Na metodologia, os atributos são
encarados como observações realizadas
sobre um sistema físico, cujo comportamento depende de
um
determinado número de
grandezas não observáveis, dentre as quais a pressão de
poros é apenas uma delas. Para
estimar a pressão de poros, adota-se uma abordagem
Bayesiana de inversão. Através de
uma função de verossimilhança, estabelecida através de
um
modelo de física de rochas
calibrável para a região, e do teorema de Bayes, combina-
se as informações pré-existentes
sobre os parâmetros de rocha, fluido e estado de tensões
com os atributos sísmicos
observados, inferindo probabilisticamente a pressão de
poros. Devido a não linearidade
do problema e ao interesse de se realizar uma rigorosa
análise de incertezas, um algoritmo
baseado em simulações de Monte Carlo (um caso especial
do
algoritmo de Metropolis-
Hastings) é utilizado para realizar a inversão. Exemplos
de aplicação da metodologia
proposta são simulados em reservatórios criados
sinteticamente. Através dos exemplos,
demonstra-se que o sucesso da previsão de pressão de
poros
depende da combinação de
diferentes fatores, como o grau de conhecimento prévio
sobre os parâmetros de rocha e
fluido, a sensibilidade da rocha perante a variação de
pressões diferenciais e a qualidade
dos atributos sísmicos. Visto que os métodos existentes
para previsão de pressão de poros
utilizam somente o atributo V(p) , a contribuição do
atributo V(s) na previsão é avaliada. Em
um cenário de rochas pouco consolidadas (ou em areias),
demonstra-se que o atributo V(s)
pode contribuir significativamente na previsão, mesmo
apresentando grandes incertezas
associadas. Já para um cenário de rochas consolidadas,
demonstra-se que as incertezas
associadas às pressões previstas são maiores, e que a
contribuição do atributo V(s) na
previsão não é tão significativa quanto nos casos de
rochas pouco consolidadas. / [en] This work proposes a method for pore pressure prediction
in reservoir rocks
through compressional- and shear-velocity data (seismic
attributes). In the method, the
attributes are considered observations of a physic system,
which behavior depends on a
several not-observable parameters, where the pore pressure
is only one of these
parameters. To estimate the pore pressure, a Bayesian
inversion approach is adopted.
Through the use of a likelihood function, settled through
a calibrated rock physics model,
and through the Bayes theorem, the a priori information
about the not-observable
parameters (fluid and rock parameters and stress state) is
combined with the seismic
attributes, inferring probabilistically the pore pressure.
Due the non-linearity of the
problem, and due the uncertainties analysis demanding, an
algorithm based on Monte
Carlo simulations (a special case of the Metropolis-
Hastings algorithm) is used to solve the
inverse problem. The application of the proposed method is
simulated through some
synthetic examples. It is shown that a successfully pore
pressure prediction in reservoir
rocks depends on a set of factors, as how sensitive are
the rock velocities to pore pressure
changes, the a priori information about rock and fluid
parameters and the uncertainties
associates to the seismic attributes. Since the current
methods for pore pressure prediction
use exclusively the attribute compressional velocity V(p),
the contribution of the attribute
shear velocity V(s) on prediction is evaluated. In a
poorly consolidated rock scenario (or in
sands), the V(s) data, even with great uncertainties
associated, can significantly contribute to
a better pore pressure prediction. In a consolidated rock
scenario, the uncertainties
associated to pore pressure estimates are higher, and the
s V data does not contribute to
pore pressure prediction as it contributes in a poorly
consolidated rock scenario.
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Recyclage des candidats dans l'algorithme Metropolis à essais multiplesGroiez, Assia 03 1900 (has links)
No description available.
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Reaction Time Modeling in Bayesian Cognitive Models of Sequential Decision-Making Using Markov Chain Monte Carlo SamplingJung, Maarten Lars 25 February 2021 (has links)
In this thesis, a new approach for generating reaction time predictions for Bayesian cognitive models of sequential decision-making is proposed. The method is based on a Markov chain Monte Carlo algorithm that, by utilizing prior distributions and likelihood functions of possible action sequences, generates predictions about the time needed to choose one of these sequences. The plausibility of the reaction time predictions produced by this algorithm was investigated for simple exemplary distributions as well as for prior distributions and likelihood functions of a Bayesian model of habit learning. Simulations showed that the reaction time distributions generated by the Markov chain Monte Carlo sampler exhibit key characteristics of reaction time distributions typically observed in decision-making tasks. The introduced method can be easily applied to various Bayesian models for decision-making tasks with any number of choice alternatives. It thus provides the means to derive reaction time predictions for models where this has not been possible before. / In dieser Arbeit wird ein neuer Ansatz zum Generieren von Reaktionszeitvorhersagen für bayesianische Modelle sequenzieller Entscheidungsprozesse vorgestellt. Der Ansatz basiert auf einem Markov-Chain-Monte-Carlo-Algorithmus, der anhand von gegebenen A-priori-Verteilungen und Likelihood-Funktionen von möglichen Handlungssequenzen Vorhersagen über die Dauer einer Entscheidung für eine dieser Handlungssequenzen erstellt. Die Plausibilität der mit diesem Algorithmus generierten Reaktionszeitvorhersagen wurde für einfache Beispielverteilungen sowie für A-priori-Verteilungen und Likelihood-Funktionen eines bayesianischen Modells zur Beschreibung von Gewohnheitslernen untersucht. Simulationen zeigten, dass die vom Markov-Chain-Monte-Carlo-Sampler erzeugten Reaktionszeitverteilungen charakteristische Eigenschaften von typischen Reaktionszeitverteilungen im Kontext sequenzieller Entscheidungsprozesse aufweisen. Das Verfahren lässt sich problemlos auf verschiedene bayesianische Modelle für Entscheidungsparadigmen mit beliebig vielen Handlungsalternativen anwenden und eröffnet damit die Möglichkeit, Reaktionszeitvorhersagen für Modelle abzuleiten, für die dies bislang nicht möglich war.
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