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Wavelets unit root test vs DF test : A further investigation based on monte carlo experiments

Wavelets unit root test vs DF test : A further investigation based on monte carlo experiments

show that the e¤ects of initial value in the new tests must be considered. More concretely, we found that the new wavelets tests can appear signi…cantly more powerful than traditional ADF tests if the in‡uence of the initial value is ignored . But if the e¤ects of the initial value are considered, the two approaches give almost the same e¢ ciency. This paper is organized as follows: the second section presents the wavelets test. In the third section, the results of Monte Carlo simulation are analysed. The last section presents remarks and conclusion.

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Contributions to Monte Carlo Search

Contributions to Monte Carlo Search

in practice widely used in a totally different scenario, in which a significant amount of prior knowledge is available about the game or the sequential decision making problem to be solved. People applying MCS techniques typically spend plenty of time exploiting their knowledge of the target problem so as to design more efficient problem-tailored variants of MCS. Among the many ways to do this, one common practice is automatic hyper- parameter tuning. By way of example, the parameter C > 0 of UCT is in nearly all applications tuned through a more or less automated trial and error procedure. While hyper-parameter tuning is a simple form of problem-driven algorithm selection, most of the advanced algorithm selection work is done by humans, i.e., by researchers that modify or invent new algorithms to take the specificities of their problem into account. The comparison and development of new MCS algorithms given a target problem is mostly a manual search process that takes much human time and is error prone. Thanks to modern computing power, automatic discovery is becoming a credible approach for partly automating this process. In order to investigate this research direction, we focus on the simplest case of (fully-observable) deterministic single-player games. Our contribution is twofold. First, we introduce a grammar over algorithms that enables generating a rich space of MCS algorithms. It also describes several well-known MCS algorithms, using a particularly compact and elegant description. Second, we propose a methodology based on multi-armed bandits for identifying the best MCS algorithm in this space, for a given distribution over training problems. We test our approach on three different domains. The results show that it often enables discovering new variants of MCS that significantly outperform generic algorithms such as UCT or NMC. We further show the good robustness properties of the discovered algorithms by slightly changing the characteristics of the problem.
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Clock Monte Carlo methods

Clock Monte Carlo methods

compared to the Metropolis method, where N is the system size and the κ value depends on the nature of the energy extensivity. As a systematic test, we simulate long-range O(n) spin models in a wide parameter regime: for n = 1, 2, 3, with disordered algebraically decaying or oscillatory Ruderman-Kittel-Kasuya-Yosida-type interactions and with and without external fields, and in spa- tial dimensions from d = 1, 2, 3 to mean-field. The O(1) computational complexity is demonstrated, and the expected acceleration is confirmed. Its flexibility and its independence from the interac- tion range guarantee that the clock method would find decisive applications in systems with many interaction terms.
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Stochastic Quasi-Newton Langevin Monte Carlo

Stochastic Quasi-Newton Langevin Monte Carlo

2 x = 1. In these experiments, we use a constant step size for each method and discard the first 50 samples as burn-in. Note that for constant step size, we no longer have asymptotic unbiased- ness; however, the bias and MSE are still bounded. Fig. 5 shows the comparison of the algorithms in terms of the root mean squared-error (RMSE) that are obtained on the test set. We can observe that DSGLD and PSGLD have similar converges rates. On the other hand, HAMCMC converges faster than these methods while having almost the same computational requirements.

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Monte Carlo with Determinantal Point Processes

Monte Carlo with Determinantal Point Processes

have attracted attention in complex geometry [Berman, 2009a,b, 2013, 2014], in statistics [Lavancier et al., 2014, 2015, Møller et al., 2015], and in physics [Torquato et al., 2008, Scardicchio et al., 2009 ], it seems no CLT has been established yet when d > 3. Our first result for multivariate OP Ensembles is a CLT for C 1 test functions when the reference measure µ is a product of d Nevai-class probability measures on I. The exact definition of the Nevai class is postponed until Definition 4.1, but we now give a simple sufficient condition. As a consequence of Denisov–Rakhmanov’s theorem (see Theorem
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Nested Monte-Carlo Search

Nested Monte-Carlo Search

Figure 8: Distributions of the scores for Morpion Solitaire Figure 9: Distributions of the scores for Morpion Solitaire with memorization of the best sequence In Morpion Solitaire a nested search of level l is 200 times longer than a nested search of level l − 1. We can guess from the figure 9 that playing 200 games at level l − 1 is likely to give a worse score that playing one game at level l for l ≤ 4. In order to test this assumption, we computed the mean score of an iterated search for given times and levels. The results are depicted in figure 10. It is clear that a level 2 search is better than a level 1 search which is better than a level 0 search. Similarly to the left move problem, the increase in score is almost linear with the logarithm of the time. So given a time limit it is advisable to choose the highest level ≤ 4 that can be searched within the time limit, and to use iterative Nested Monte-Carlo Search.
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Line-sampling-based Monte Carlo method

Line-sampling-based Monte Carlo method

Beyond prospects of simulation, this approach offers an important versatility and possibility of analysis due to the fact that the computation does not rely on ”rigid” precomputed spectra. For instance, it becomes possible to easily study the effect of a given spectroscopic database, parameter or hypothesis on a radiative observable with the very same algorithm, without having to recompute a large set of spectra to cover the heterogeneity of the medium. Two examples applied to test-case 2 are given in Fig. 2 where the effects of the choice of database and line-wing truncation distance are evaluated.
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Monte Carlo Beam Search

Monte Carlo Beam Search

Monte-Carlo Beam Search Tristan Cazenave Abstract—Monte-Carlo Tree Search is state of the art for multiple games and for solving puzzles such as Morpion Solitaire. Nested Monte-Carlo Search is a Monte-Carlo Tree Search algorithm that works well for solving puzzles. We propose to enhance Nested Monte-Carlo Search with Beam Search. We test the algorithm on Morpion Solitaire. Thanks to beam search, our program has been able to match the record score of 82 moves. Monte-Carlo Beam Search achieves better scores in less time than Nested Monte-Carlo Search alone.
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Méthodes de Monte Carlo en Vision Stéréoscopique

Méthodes de Monte Carlo en Vision Stéréoscopique

Chapitre 7 Conclusion g´ en´ erale et perspectives Dans ce travail, nous nous sommes efforc´ es d’apporter une r´ eponse au probl` eme de l’incertitude en vision st´ er´ eoscopique. Une des difficult´ es majeures de cette probl´ ematique r´ eside dans le sens ` a donner au terme incertitude. La plupart du temps, ce probl` eme est abord´ e en terme d’efficacit´ e de l’algorithme de calcul, selon la d´ emarche suivante : ` a partir d’un jeu de donn´ ees de r´ ef´ erence, diff´ erents algorithmes de reconstruction 3D sont test´ es et class´ es en fonction de plusieurs crit` eres (´ ecart quadratique moyen, proportion d’erreurs sup´ erieures ` a un certain seuil, proportion de points non estim´ es...). Ce type d’´ evaluation fait mˆ eme l’objet d’un projet r´ ecent de recherche [104]. Or, il est assez frappant de constater que malgr´ e le nombre d’algorithmes test´ es et la vari´ et´ e des approches consid´ er´ ees, une limite semble ˆ etre atteinte : des erreurs subsistent. C’est que l’incertitude est une part inh´ erente du paradigme de la vision st´ er´ eoscopique, et qu’il convient de traiter le probl` eme en tant que tel. Il faut donc changer radicalement de point de vue, et abandonner la croyance illusoire qui consiste ` a vouloir reconstituer fid` element la r´ ealit´ e. En effet, les observations fournies par chaque image du couple sont imparfaites et partielles, et des ambigu¨ıt´es existent.
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Variance Analysis for Monte Carlo Integration

Variance Analysis for Monte Carlo Integration

function with fast power spectral decay rate (due to its C ∞ nature) whereas the Y m l basis function is bandwidth-limited. We compute variance of all the above integrands with different sampling patterns. The variance was computed over 1000 trials for cases where the samplers (white noise and jittered) are not prohibitively slow. For spherical CCVT and Poisson Disk, we kept the number of trials between 200 to 1000, depending on the speed of the sampler. As the spectral profile of these test integrands is known, our variance prediction model can be used to estimate the bounds on the variance in integration of each function by simply using the bounds derived from the corresponding sampling power spectra.
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Monte-Carlo Hex

Monte-Carlo Hex

When building our program Y OPT , we chose to test a completely different method that uses Monte-Carlo simulations. Back in 2000 when we first tried Monte-Carlo meth- ods with Hex, we did not use tree search and V. Anselevich virtual connections used to achieve better results. Recently however, the interest for Monte-Carlo methods for Hex raised with the success of methods developing trees along with Monte-Carlo simula- tions in the game of Go [10, 19, 13, 15]. R´emi Coulom, Lille 3 University, or Philip Henderson, Alberta University, among other researchers of this field have shown such an interest. As a consequence we developed a Monte-Carlo search program for Hex.
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Addressing nonlinearities in Monte Carlo

Addressing nonlinearities in Monte Carlo

Richard Fournier 3 , Mathieu Galtier 7 , Jacques Gautrais 8 , Anaïs Khuong 8 , Lionel Pelissier 9 , Benjamin Piaud 5 , Maxime Roger 7 , Guillaume Terrée 2 & Sebastian Weitz 1,2 Monte Carlo is famous for accepting model extensions and model refinements up to infinite dimension. However, this powerful incremental design is based on a premise which has severely limited its application so far: a state-variable can only be recursively defined as a function of underlying state- variables if this function is linear. Here we show that this premise can be alleviated by projecting nonlinearities onto a polynomial basis and increasing the configuration space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles, and concentrated solar power plant production, we prove the real-world usability of this advance in four test cases which were previously regarded as impracticable using Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to acute problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise on model refinement or system complexity, and convergence rates remain independent of dimension.
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Score Bounded Monte-Carlo Tree Search

Score Bounded Monte-Carlo Tree Search

Solving Seki problems has been addressed in [16]. We use more simple and easy to define problems than in [16]. Our aim is to show that Monte-Carlo with bounds can improve on Monte-Carlo without bounds as used in [19]. We used Seki problems with liberties for the players ranging from one to six lib- erties. The number of shared liberties is always two. The Max player (usually Black) plays first. The figure 4 shows the problem that has three liberties for Max (Black), four liberties for Min (White) and two shared liberties. The other problems of the test suite are very similar except for the number of liberties of Black and White. The results of these Seki problems are given in table 2. We can see that when Max has the same number of liberties than Min or one liberty less, the result is Draw.
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Étude des artefacts en tomodensitométrie par simulation Monte Carlo

Étude des artefacts en tomodensitométrie par simulation Monte Carlo

artefacts. Les simulations CBCT sont effectuées soit avec une source spectrale à 120 kVp pour mettre l’emphase sur le durcissement de faisceau ou soit avec une source mono- énergétique à 68 keV que l’on définit comme l’énergie effective d’un spectre à 120 kVp. Pour identifier l’impact du diffusé, les images CT sont comparées avec ou sans l’apport du rayonnement secondaire. L’analyse statistique permet d’évaluer l’erreur sur l’exac- titude des nombres CT. Généralement, on peut classer les erreurs selon deux types. L’erreur stochastique est associée à une dispersion statistique des données, telle que la présence d’un bruit gaussien dans une image. L’erreur systématique est un biais constant sur la valeur exacte. Dans ce contexte, on peut dire que le bruit présent dans les images reconstruites est une erreur stochastique que l’on attribue au nombre d’histoires uti- lisées dans les simulations Monte Carlo, l’algorithme de reconstruction et le compor- tement statistique des photons. Les ombres introduisent une erreur systématique qui sous-estime la valeur exacte dans la région ombragée. Les effets de cupping est un biais négatif ou positif pour une distance radiale donnée. La distorsion FDK est un biais qui dépend de l’élévation dans le fantôme. Les raies de volume partiel sous-estiment systématiquement la valeur exacte. Les effets de bord sont une source d’erreurs systé- matiques localisées aux interfaces. Finalement, les artefacts en anneaux est une erreur systématique qui oscille entre deux valeurs extrêmes, mais cette erreur devient nulle lorsque prise en moyenne.
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Monte Carlo method and sensitivity estimations

Monte Carlo method and sensitivity estimations

5. Example (2) To illustrate such a practical implementation, let us reconsider the preceding example, the layer being now both absorbing (absorption coe$cient k a ) and scattering (scattering coe$cient k s ). An example of the application of standard Monte Carlo algorithms consists of emitting bundles at the source and following them until they exit the layer by a random walk corresponding to the pure di"usion assumption [1]. The traveled length before exit is then used to compute the extinction of the bundle-power according to the pure-absorption exponential extinction. As before, the algorithm starts with the random sampling of an emission direction ˜u 1 for each of the N bundles of initial
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Comment on "Sequential Quasi-Monte Carlo Sampling"

Comment on "Sequential Quasi-Monte Carlo Sampling"

Comment on “Sequential Quasi-Monte Carlo Sampling” Pierre L’Ecuyer DIRO, Universit ´e de Montr ´eal, Canada Gerber and Chopin combine SMC with RQMC to accelerate convergence. They apply RQMC as in the array-RQMC method discussed below, for which convergence rate theory remains thin despite impressive empirical performance. Their proof of o(N −1/2 ) convergence rate is a remarkable contribution.

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Monte-Carlo and Domain-Deformation Sensitivities

Monte-Carlo and Domain-Deformation Sensitivities

k e = 0.5. Estimations of the absorbed radiative intensity density and its sensitivity are obtained for 2.10 6 realizations N of the corresponding Monte-Carlo weight function. Figure 4 displays the results of the algorithm presented in Figure 3. In order to validate the sensitivity model method, the finite differences are calculated from Monte-Carlo estimations of absorbed radiative intensity density. Figure 4 shows the difficulty to evaluate the sensitivities from finite differences. If δL value is chosen small in regards to L, the variance of finite difference becomes too large and the results does not converge. On the contrary if δL is chosen too large in regards to L, the calculation of the finite difference converges but the value of the sensitivity is not relevant. This difficulty is well known when gradients are estimated by differentiation, it is outlined in the gradient-based Kiefer-Wolfowitz method
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Monte Carlo Methods and stochastic approximations

Monte Carlo Methods and stochastic approximations

impl ement e ces formules. Les r esultats obtenus sont dans le T ableau 2. Q-CF d esigne le prix calcul e avec cette formule, et Brute repr esente le prix et l'erreur statistique de la m ethode de Monte Carlo standard. Une fois de plus la r eduction de variance obtenue par notre m ethode seule est signi cative. Mais pour souligner encore une fois

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Utilisation de la recherche arborescente Monte-Carlo au Hex

Utilisation de la recherche arborescente Monte-Carlo au Hex

Pour améliorer les simulations on peut utiliser des connaissances qui biaisent les choix aléatoires vers les bons coups (Coulom, 2006; Gelly et al., 2006; Cazenave, 2007). Au Go, par exemple, on interdit de jouer les coups qui bouchent les yeux dans les simulations. Ainsi, une partie se termine lorsqu’il n’y a plus que des chaînes vi- vantes et des yeux sur le goban. On peut alors précisément évaluer la position finale à l’aide des règles chinoises (le score d’un joueur est alors égal à la somme de ses pierres posées et de ses yeux). L’utilisation de connaissances dans les simulations n’est toute- fois pas toujours bénéfique. Ainsi, dans notre programme de Go, il est arrivé qu’un joueur A de simulations aléatoires gagne la plupart du temps ses simulations contre un joueur B de simulations aléatoires car le joueur A utilisait plus de connaissances. Cependant une fois intégré dans un algorithme Monte-Carlo, l’algorithme Monte- Carlo utilisant les simulations aléatoires de B gagnait largement contre l’algorithme utilisant les simulations aléatoires de A. Il est clair que l’utilisation de connaissances bien choisies améliore un algorithme de Monte-Carlo, il faut toutefois être prudent sur les connaissances à utiliser dans les simulations car certaines connaissances que l’on pourrait juger à priori bénéfiques peuvent se révéler contre-productives.
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methode monte carlo

methode monte carlo

Au sujet de la Méthode de Monte-Carlo Le terme méthode de Monte-Carlo désigne toute méthode visant à calculer une valeur numérique en utilisant des procédés aléatoires. Le nom de ces méthodes, qui fait allusion aux jeux de hasard pratiqués à Monte-Carlo, a été inventé en 1947 par Nicholas Metropolis. Le véritable développement des méthodes de Monte-Carlo s'est effectué sous l'impulsion de John von Neumann et Stanislas Ulam notamment, lors de la Seconde Guerre mondiale et des recherches sur la fabrication de la bombe atomique.
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