Relevant bibliographies by topics / Monte Carlo sampling and estimation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Monte Carlo sampling and estimation'

Author: Grafiati
Published: 21 December 2024

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Journal articles on the topic "Monte Carlo sampling and estimation"

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Liao, Meihao, Rong-Hua Li, Qiangqiang Dai, Hongyang Chen, Hongchao Qin, and Guoren Wang. "Efficient Personalized PageRank Computation: The Power of Variance-Reduced Monte Carlo Approaches." Proceedings of the ACM on Management of Data 1, no. 2 (June 13, 2023): 1–26. http://dx.doi.org/10.1145/3589305.

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Personalized PageRank (PPR) computation is a fundamental problem in graph analysis. The state-of-the-art algorithms for PPR computation are based on a bidirectional framework which include a deterministic forward push and a Monte Carlo sampling procedure. The Monte Carlo sampling procedure, however, often has a relatively-large variance, thus reducing the performance of the PPR computation algorithms. To overcome this issue, we develop two novel variance-reduced Monte Carlo techniques for PPR computation. Our first technique is to apply power iterations to reduce the variance of the Monte Carlo sampling procedure. We prove that conducting few power iterations can significantly reduce the variance of existing Monte Carlo estimators, only with few additional costs. Moreover, we show that such a simple and novel variance-reduced Monte Carlo technique can achieve comparable estimation accuracy and the same time complexity as the state-of-the-art bidirectional algorithms. Our second technique is a novel progressive sampling method which uses the historical information of former samples to reduce the variance of the Monte Carlo estimator. We develop several novel PPR computation algorithms by integrating both of these variance reduction techniques with two existing Monte Carlo sampling approaches, including random walk sampling and spanning forests sampling. Finally, we conduct extensive experiments on 5 real-life large graphs to evaluate our solutions. The results show that our algorithms can achieve much higher PPR estimation accuracy by using much less time, compared to the state-of-the-art bidirectional algorithms.
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Wolf, A. T., T. E. Burk, and J. G. Isebrands. "Estimation of daily and seasonal whole-tree photosynthesis using Monte Carlo integration techniques." Canadian Journal of Forest Research 25, no. 2 (February 1, 1995): 253–60. http://dx.doi.org/10.1139/x95-030.

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Monte Carlo estimation is explored as an alternative to traditional survey sampling techniques to estimate both daily and seasonal whole-tree photosynthesis of first-year Populus clones. Several methods, known in the literature as variance-reduction techniques, are applied to the problem of estimation and compared on the basis of relative root mean squared error. Also of interest is gain in precision over the simple expansion estimator (Monte Carlo estimation in its simplest form). Variance reduction is achieved by approximating the photosynthesis curve by some known, easily integrated function. The estimators retain their unbiasedness regardless of the appropriateness of this function. The authors show how these variance reduction techniques can be used to achieve greater precision when estimating both daily and seasonal whole-tree photosynthesis. These methods may be useful alternatives to current purposive sampling methods that have the potential for bias and high error.
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Morio, Jérôme, Baptiste Levasseur, and Sylvain Bertrand. "Drone Ground Impact Footprints with Importance Sampling: Estimation and Sensitivity Analysis." Applied Sciences 11, no. 9 (April 25, 2021): 3871. http://dx.doi.org/10.3390/app11093871.

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This paper addresses the estimation of accurate extreme ground impact footprints and probabilistic maps due to a total loss of control of fixed-wing unmanned aerial vehicles after a main engine failure. In this paper, we focus on the ground impact footprints that contains 95%, 99% and 99.9% of the drone impacts. These regions are defined here with density minimum volume sets and may be estimated by Monte Carlo methods. As Monte Carlo approaches lead to an underestimation of extreme ground impact footprints, we consider in this article multiple importance sampling to evaluate them. Then, we perform a reliability oriented sensitivity analysis, to estimate the most influential uncertain parameters on the ground impact position. We show the results of these estimations on a realistic drone flight scenario.
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Nawajah, Inad, Hassan Kanj, Yehia Kotb, Julian Hoxha, Mouhammad Alakkoumi, and Kamel Jebreen. "Bayesian Regression Analysis using Median Rank Set Sampling." European Journal of Pure and Applied Mathematics 17, no. 1 (January 31, 2024): 180–200. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.5015.

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Bayesian estimation of the linear regression parameter system is considered by deploying Median Rank Set Sampling (MRSS). The full conditional distributions and the associated posterior distribution are obtained. Therefore, based on Markov Chain Monte Carlo simulation, the Bayesian point estimates and credible intervals for the regression parameters are determined. To measure the efficiency of the obtained Bayesian estimates concerning the frequentist estimates we compute the asymptotic relative efficiency of the obtained Bayesian estimates using Markov Chain Monte Carlo simulation.
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Baker, Matthew J. "Adaptive Markov Chain Monte Carlo Sampling and Estimation in Mata." Stata Journal: Promoting communications on statistics and Stata 14, no. 3 (September 2014): 623–61. http://dx.doi.org/10.1177/1536867x1401400309.

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Thom, H., W. Fang, Z. Wang, NJ Welton, T. Goda, and M. Giles. "Advanced Monte-Carlo Sampling Schemes for Value of Information Estimation." Value in Health 20, no. 9 (October 2017): A772. http://dx.doi.org/10.1016/j.jval.2017.08.2219.

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Taverniers, Søren, and Daniel M. Tartakovsky. "Estimation of distributions via multilevel Monte Carlo with stratified sampling." Journal of Computational Physics 419 (October 2020): 109572. http://dx.doi.org/10.1016/j.jcp.2020.109572.

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Lang, Lixin, Wen-shiang Chen, Bhavik R. Bakshi, Prem K. Goel, and Sridhar Ungarala. "Bayesian estimation via sequential Monte Carlo sampling—Constrained dynamic systems." Automatica 43, no. 9 (September 2007): 1615–22. http://dx.doi.org/10.1016/j.automatica.2007.02.012.

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Magnussen, S., R. E. McRoberts, and E. O. Tomppo. "A resampling variance estimator for the k nearest neighbours technique." Canadian Journal of Forest Research 40, no. 4 (April 2010): 648–58. http://dx.doi.org/10.1139/x10-020.

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Current estimators of variance for the k nearest neighbours (kNN) technique are designed for estimates of population totals. Their efficiency in small-area estimation problems can be poor. In this study, we propose a modified balanced repeated replication estimator of variance (BRR) of a kNN total that performs well in small-area estimation problems and under both simple random and cluster sampling. The BRR estimate of variance is the sum of variances and covariances of unit-level kNN estimates in the area of interest. In Monte Carlo simulations of simple random and cluster sampling from seven artificial populations with real and simulated forest inventory data, the agreement between averages of BRR estimates of variance and Monte Carlo sampling variances was good both for population and for small-area totals. The modified BRR estimator is currently limited to sample sizes no larger than 1984. An accurate approximation to the proposed BRR estimator allows significant savings in computing time.
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Rulaningtyas, Riries, Yusrinourdi Muhammad Zuchruf, Akif Rahmatillah, Khusnul Ain, Alfian Pramudita Putra, Osmalina Nur Rahma, Limpat Salamat, and Rifai Chai. "ELBOW ANGLE ESTIMATION FROM EMG SIGNALS BASED ON MONTE CARLO SIMULATION." Jurnal Teknologi 84, no. 4 (May 30, 2022): 79–90. http://dx.doi.org/10.11113/jurnalteknologi.v84.17683.

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Monte Carlo simulation is defined as statistical sampling techniques which is used to estimate the solutions of quantitative problems. The aim of this study is to develop Monte Carlo algorithm for elbow angle estimation from EMG signal as preliminary study for further research in rehabilitation tool to make a breakthrough rehabilitation tool for post-stroke patients based on muscle signals to carry out rehabilitation independently and consistently. The Monte Carlo simulation is performed to approach the model’s angle from subject who takes 20 seconds lifting barbell repeatedly for 52 times. Monte Carlo simulations were carried out as many as 10,000 times because it was considered ideal testing for a model. In doing the estimation, the angle will be divided into four ranges, which are determined from the model’s trend value, the estimation of the previous angle, the estimated error angle, and the previous measured angle. Then an average calculation is performed on the Monte Carlo simulation, which enters the angle range to determine the estimated value of the angle. The most optimal estimation is obtained from this study with RMSE (root mean square error) was 8.96°, and the correlation coefficient between estimate angle and the measured angle was 0.96.
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Dissertations / Theses on the topic "Monte Carlo sampling and estimation"

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Chen, Wen-shiang. "Bayesian estimation by sequential Monte Carlo sampling for nonlinear dynamic systems." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1086146309.

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Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xiv, 117 p. : ill. (some col.). Advisors: Bhavik R. Bakshi and Prem K. Goel, Department of Chemical Engineering. Includes bibliographical references (p. 114-117).
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Gilabert, Navarro Joan Francesc. "Estimation of binding free energies with Monte Carlo atomistic simulations and enhanced sampling." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669282.

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The advances in computing power have motivated the hope that computational methods can accelerate the pace of drug discovery pipelines. For this, fast, reliable and user-friendly tools are required. One of the fields that has gotten more attentions is the prediction of binding affinities. Two main problems have been identified for such methods: insufficient sampling and inaccurate models. This thesis is focused on tackling the first problem. To this end, we present the development of efficient methods for the estimation of protein-ligand binding free energies. We have developed a protocol that combines enhanced sampling with more standard simulations methods to achieve higher efficiency. First, we run an exploratory enhanced sampling simulation, starting from the bound conformation and partially biased towards unbound poses. The we leverage the information gained from this short simulation to run, longer unbiased simulations to collect statistics. Thanks to the modularity and automation that the protocol offers we were able to test three different methods for the long simulations: PELE, molecular dynamics and AdaptivePELE. PELE and molecular dynamics showed similar results, although PELE used less computational resources. Both seemed to work well with small protein-fragment systems or proteins with not very flexible binding sites. Both failed to accurately reproduce the binding of a kinase, the Mitogen-activated protein kinase 1 (ERK2). On the other hand, AdaptivePELE did not show a great improvement over PELE, with positive results for the Urokinase-type plasminogen activator (URO) and a clear lack of sampling for the Progesterone receptor (PR). We demonstrated the importance of well-designed suite of test systems for the development of new methods. Through the use of a diverse benchmark of protein systems we have established the cases in which the protocol is expected to give accurate results, and which areas require further development. This benchmark consisted of four proteins, and over 30 ligands, much larger than the test systems typically used in the development of pathway-based free energy methods. In summary, the methodology developed in this work can contribute to the drug discovery process for a limited range of protein systems. For many other, we have observed that regular unbiased simulations are not efficient enough and more sophisticated, enhanced sampling methods are required.
Els grans avenços en la capacitat de computació han motivat l'esperança que els mètodes de simulacions per ordinador puguin accelerar el ritme de descobriment de nous fàrmacs. Per a què això sigui possible, es necessiten eines ràpides, acurades i fàcils d'utilitzar. Un dels problemes que han rebut més atenció és el de la predicció d'energies lliures d'unió entre proteïna i lligand. Dos grans problemes han estat identificats per a aquests mètodes: la falta de mostreig i les aproximacions dels models. Aquesta tesi està enfocada a resoldre el primer problema. Per a això, presentem el desenvolupament de mètodes eficients per a l'estimació de d'energies lliures d'unió entre proteïna i lligand. Hem desenvolupat un protocol que combina mètodes anomenats enhanced sampling amb simulació clàssiques per a obtenir una major eficiència. Els mètodes d'enhanced sampling són una classe d'eines que apliquen algun tipus de pertorbació externa al sistema que s'està estudiant per tal d'accelerar-ne el mostreig. En el nostre protocol, primer correm una simulació exploratòria d'enhanced sampling, començant per una mostra de la unió de la proteïna i el lligand. Aquesta simulació esta parcialment esbiaixada cap a aquells estats del sistema on els dos components es troben més separats. Després utilitzem la informació obtinguda d'aquesta primera simulació més curta per a córrer una segona simulació més llarga, amb mètodes sense biaix per obtenir una estadística fidedigna del sistema. Gràcies a la modularitat i el grau d'automatització que la implementació del protocol ofereix, hem pogut provar tres mètodes diferents per les simulacions llargues: PELE, dinàmica molecular i AdaptivePELE. PELE i dinàmica molecular han mostrat resultats similars, tot i que PELE utilitza menys recursos. Els dos han mostrat bons resultats en l'estudi de sistemes de fragments o amb proteïnes amb llocs d'unió poc flexibles. Però, els dos han fallat a l'hora de reproduir els resultats experimentals per a una quinasa, la Mitogen-activated protein kinase 1 (ERK2). D'altra banda, AdaptivePELE no ha mostrat una gran millora respecte a PELE, amb resultats positius per a la proteïna Urokinase-type plasminogen activator (URO) i una clara falta de mostreig per al receptor de progesterona (PR). En aquest treball hem demostrat la importància d'establir un banc de proves equilibrat durant el desenvolupament de nous mètodes. Mitjançant l'ús d'un banc de proves divers hem pogut establir en quins casos es pot esperar que el protocol obtingui resultats acurats, i quines àrees necessiten més desenvolupament. El banc de proves ha consistit de quatre proteïnes i més de trenta lligands, molt més dels que comunament s'utilitzen en el desenvolupament de mètodes per a la predicció d'energies d'unió mitjançant mètodes basats en camins (pathway-based). En resum, la metodologia desenvolupada durant aquesta tesi pot contribuir al procés de recerca de nous fàrmacs per a certs tipus de sistemes de proteïnes. Per a la resta, hem observat que els mètodes de simulació no esbiaixats no són prou eficients i tècniques més sofisticades són necessàries.
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Xu, Nuo. "A Monte Carlo Study of Single Imputation in Survey Sampling." Thesis, Örebro universitet, Handelshögskolan vid Örebro Universitet, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-30541.

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Missing values in sample survey can lead to biased estimation if not treated. Imputation was posted asa popular way to deal with missing values. In this paper, based on Särndal (1994, 2005)’s research, aMonte-Carlo simulation is conducted to study how the estimators work in different situations and howdifferent imputation methods work for different response distributions.
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Ptáček, Martin. "Spatial Function Estimation with Uncertain Sensor Locations." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2021. http://www.nusl.cz/ntk/nusl-449288.

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Tato práce se zabývá úlohou odhadování prostorové funkce z hlediska regrese pomocí Gaussovských procesů (GPR) za současné nejistoty tréninkových pozic (pozic senzorů). Nejdříve je zde popsána teorie v pozadí GPR metody pracující se známými tréninkovými pozicemi. Tato teorie je poté aplikována při odvození výrazů prediktivní distribuce GPR v testovací pozici při uvážení nejistoty tréninkových pozic. Kvůli absenci analytického řešení těchto výrazů byly výrazy aproximovány pomocí metody Monte Carlo. U odvozené metody bylo demonstrováno zlepšení kvality odhadu prostorové funkce oproti standardnímu použití GPR metody a také oproti zjednodušenému řešení uvedenému v literatuře. Dále se práce zabývá možností použití metody GPR s nejistými tréninkovými pozicemi v~kombinaci s výrazy s dostupným analytickým řešením. Ukazuje se, že k dosažení těchto výrazů je třeba zavést značné předpoklady, což má od počátku za následek nepřesnost prediktivní distribuce. Také se ukazuje, že výsledná metoda používá standardní výrazy GPR v~kombinaci s upravenou kovarianční funkcí. Simulace dokazují, že tato metoda produkuje velmi podobné odhady jako základní GPR metoda uvažující známé tréninkové pozice. Na druhou stranu prediktivní variance (nejistota odhadu) je u této metody zvýšena, což je žádaný efekt uvážení nejistoty tréninkových pozic.
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Diop, Khadim. "Estimation de la fiabilité d'un palier fluide." Thesis, Angers, 2015. http://www.theses.fr/2015ANGE0029/document.

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Les travaux de recherche constituent une contribution au développement de la théorie de la fiabilité en mécanique des fluides. Pour la conception de machines et de systèmes mécatroniques complexes, de nombreux composants fluides, difficiles à dimensionner, sont utilisés. Ces derniers ont des caractéristiques intrinsèques statiques et dynamiques sensibles et ont donc une grande importance sur la fiabilité et la durée de vie de la plupart des machines et des systèmes.Le développement effectué se concentre spécialement sur l'évaluation de la fiabilité d’un palier fluide grâce à un couplage « mécanique des fluides - fiabilité ». Ce couplage exige une définition propre de la fonction d’état limite permettant d’estimer la probabilité de défaillance d’un palier fluide. La modélisation par l'équation de Reynolds modifiée permet de déterminer la capacité de charge d’un palier fluide en fonction des conditions de fonctionnement. Plusieurs formes simples de paliers fluides ont été modélisées analytiquement et leurs probabilités de défaillance ont été estimées grâce à des méthodes d'approximation FORM/SORM (First Order Reliability, Second Order Reliability) et de simulation Monte Carlo
These research is a contribution to the development of reliability theory in fluid mechanics. For the machines design and complex mechatronic systems, many fluid components are used. These components have static and dynamic sensitive characteristics and thus have a great significance on the reliabilityand lifetime of the machines and systems. Development performed focuses specifically on the reliability evaluation of a fluid bearing using a"fluid mechanics - reliability" interaction approach. This coupling requires a specific definition of the limit state function for estimating the failure probability of a fluid bearing. The Reynolds equation permits to determine the fluid bearing load capacity according to the operating conditions. Several simple geometries of fluid bearings were modeled analytically and their failure probabilities were estimated using the approximation methods FORM / SORM (First Order Reliability Method,Second Order Reliability Method) and Monte Carlo simulation
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Greer, Brandi A. Young Dean M. "Bayesian and pseudo-likelihood interval estimation for comparing two Poisson rate parameters using under-reported data." Waco, Tex. : Baylor University, 2008. http://hdl.handle.net/2104/5283.

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Thajeel, Jawad. "Kriging-based Approaches for the Probabilistic Analysis of Strip Footings Resting on Spatially Varying Soils." Thesis, Nantes, 2017. http://www.theses.fr/2017NANT4111/document.

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L’analyse probabiliste des ouvrages géotechniques est généralement réalisée en utilisant la méthode de simulation de Monte Carlo. Cette méthode n’est pas adaptée pour le calcul des faibles probabilités de rupture rencontrées dans la pratique car elle devient très coûteuse dans ces cas en raison du grand nombre de simulations requises pour obtenir la probabilité de rupture. Dans cette thèse, nous avons développé trois méthodes probabilistes (appelées AK-MCS, AK-IS et AK-SS) basées sur une méthode d’apprentissage (Active learning) et combinant la technique de Krigeage et l’une des trois méthodes de simulation (i.e. Monte Carlo Simulation MCS, Importance Sampling IS ou Subset Simulation SS). Dans AK-MCS, la population est prédite en utilisant un méta-modèle de krigeage qui est défini en utilisant seulement quelques points de la population, ce qui réduit considérablement le temps de calcul par rapport à la méthode MCS. Dans AK-IS, une technique d'échantillonnage plus efficace 'IS' est utilisée. Dans le cadre de cette approche, la faible probabilité de rupture est estimée avec une précision similaire à celle de AK-MCS, mais en utilisant une taille beaucoup plus petite de la population initiale, ce qui réduit considérablement le temps de calcul. Enfin, dans AK-SS, une technique d'échantillonnage plus efficace 'SS' est proposée. Cette technique ne nécessite pas la recherche de points de conception et par conséquent, elle peut traiter des surfaces d’état limite de forme arbitraire. Toutes les trois méthodes ont été appliquées au cas d'une fondation filante chargée verticalement et reposant sur un sol spatialement variable. Les résultats obtenus sont présentés et discutés
The probabilistic analysis of geotechnical structures involving spatially varying soil properties is generally performed using Monte Carlo Simulation methodology. This method is not suitable for the computation of the small failure probabilities encountered in practice because it becomes very time-expensive in such cases due to the large number of simulations required to calculate accurate values of the failure probability. Three probabilistic approaches (named AK-MCS, AK-IS and AK-SS) based on an Active learning and combining Kriging and one of the three simulation techniques (i.e. Monte Carlo Simulation MCS, Importance Sampling IS or Subset Simulation SS) were developed. Within AK-MCS, a Monte Carlo simulation without evaluating the whole population is performed. Indeed, the population is predicted using a kriging meta-model which is defined using only a few points of the population thus significantly reducing the computation time with respect to the crude MCS. In AK-IS, a more efficient sampling technique ‘IS’ is used instead of ‘MCS’. In the framework of this approach, the small failure probability is estimated with a similar accuracy as AK-MCS but using a much smaller size of the initial population, thus significantly reducing the computation time. Finally, in AK-SS, a more efficient sampling technique ‘SS’ is proposed. This technique overcomes the search of the design points and thus it can deal with arbitrary shapes of the limit state surfaces. All the three methods were applied to the case of a vertically loaded strip footing resting on a spatially varying soil. The obtained results are presented and discussed
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Wu, Yi-Fang. "Accuracy and variability of item parameter estimates from marginal maximum a posteriori estimation and Bayesian inference via Gibbs samplers." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/5879.

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Item response theory (IRT) uses a family of statistical models for estimating stable characteristics of items and examinees and defining how these characteristics interact in describing item and test performance. With a focus on the three-parameter logistic IRT (Birnbaum, 1968; Lord, 1980) model, the current study examines the accuracy and variability of the item parameter estimates from the marginal maximum a posteriori estimation via an expectation-maximization algorithm (MMAP/EM) and the Markov chain Monte Carlo Gibbs sampling (MCMC/GS) approach. In the study, the various factors which have an impact on the accuracy and variability of the item parameter estimates are discussed, and then further evaluated through a large scale simulation. The factors of interest include the composition and length of tests, the distribution of underlying latent traits, the size of samples, and the prior distributions of discrimination, difficulty, and pseudo-guessing parameters. The results of the two estimation methods are compared to determine the lower limit--in terms of test length, sample size, test characteristics, and prior distributions of item parameters--at which the methods can satisfactorily recover item parameters and efficiently function in reality. For practitioners, the results help to define limits on the appropriate use of the BILOG-MG (which implements MMAP/EM) and also, to assist in deciding the utility of OpenBUGS (which carries out MCMC/GS) for item parameter estimation in practice.
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Argouarc, h. Elouan. "Contributions to posterior learning for likelihood-free Bayesian inference." Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. http://www.theses.fr/2024IPPAS021.

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L'inférence bayésienne a posteriori est utilisée dans de nombreuses applications scientifiques et constitue une méthodologie répandue pour la prise de décision en situation d'incertitude. Elle permet aux praticiens de confronter les observations du monde réel à des modèles d'observation pertinents, et d'inférer en retour la distribution d'une variable explicative. Dans de nombreux domaines et applications pratiques, nous considérons des modèles d'observation complexes pour leur pertinence scientifique, mais au prix de densités de probabilité incalculables. En conséquence, à la fois la vraisemblance et la distribution a posteriori sont indisponibles, rendant l'inférence Bayésienne à l'aide des méthodes de Monte Carlo habituelles irréalisable. Dans ce travail nous supposons que le modèle d'observation nous génère un jeu de données, et le contexte de cette thèse est de coupler les méthodes Bayésienne à l'apprentissage statistique afin de pallier cette limitation et permettre l'inférence a posteriori dans le cadre likelihood-free. Ce problème, formulé comme l'apprentissage d'une distribution de probabilité, inclut les tâches habituelles de classification et de régression, mais il peut également être une alternative aux méthodes “Approximate Bayesian Computation” dans le contexte de l'inférence basée sur la simulation, où le modèle d'observation est un modèle de simulation avec une densité implicite. L'objectif de cette thèse est de proposer des contributions méthodologiques pour l'apprentissage Bayésien a posteriori. Plus précisément, notre objectif principal est de comparer différentes méthodes d'apprentissage dans le cadre de l'échantillonnage Monte Carlo et de la quantification d'incertitude. Nous considérons d'abord l'approximation a posteriori basée sur le “likelihood-to-evidence-ratio”, qui a l'avantage principal de transformer un problème d'apprentissage de densité conditionnelle en un problème de classification. Dans le contexte de l'échantillonnage Monte Carlo, nous proposons une méthodologie pour échantillonner la distribution résultante d'une telle approximation. Nous tirons parti de la structure sous-jacente du modèle, compatible avec les algorithmes d'échantillonnage usuels basés sur un quotient de densités, pour obtenir des procédures d'échantillonnage simples, sans hyperparamètre et ne nécessitant d'évaluer aucune densité. Nous nous tournons ensuite vers le problème de la quantification de l'incertitude épistémique. D'une part, les modèles normalisés, tels que la construction discriminante, sont faciles à appliquer dans le contexte de la quantification de l'incertitude bayésienne. D'autre part, bien que les modèles non normalisés, comme le likelihood-to-evidence-ratio, ne soient pas facilement applicables dans les problèmes de quantification d'incertitude épistémique, une construction non normalisée spécifique, que nous appelons générative, est effectivement compatible avec la quantification de l'incertitude bayésienne via la distribution prédictive a posteriori. Dans ce contexte, nous expliquons comment réaliser cette quantification de l'incertitude dans les deux techniques de modélisation, générative et discriminante, puis nous proposons une comparaison des deux constructions dans le cadre de l'apprentissage bayésien. Enfin nous abordons le problème de la modélisation paramétrique avec densité tractable, qui est effectivement un prérequis pour la quantification de l'incertitude épistémique dans les méthodes générative et discriminante. Nous proposons une nouvelle construction d'un modèle paramétrique, qui est une double extension des modèles de mélange et des flots normalisant. Ce modèle peut être appliqué à de nombreux types de problèmes statistiques, tels que l'inférence variationnelle, l'estimation de densité et de densité conditionnelle, car il bénéficie d'une évaluation rapide et exacte de la fonction de densité, d'un schéma d'échantillonnage simple, et d'une approche de reparamétrisassions des gradients
Bayesian posterior inference is used in many scientific applications and is a prevalent methodology for decision-making under uncertainty. It enables practitioners to confront real-world observations with relevant observation models, and in turn, infer the distribution over an explanatory variable. In many fields and practical applications, we consider ever more intricate observation models for their otherwise scientific relevance, but at the cost of intractable probability density functions. As a result, both the likelihood and the posterior are unavailable, making posterior inference using the usual Monte Carlo methods unfeasible.In this thesis, we suppose that the observation model provides a recorded dataset, and our aim is to bring together Bayesian inference and statistical learning methods to perform posterior inference in a likelihood-free setting. This problem, formulated as learning an approximation of a posterior distribution, includes the usual statistical learning tasks of regression and classification modeling, but it can also be an alternative to Approximate Bayesian Computation methods in the context of simulation-based inference, where the observation model is instead a simulation model with implicit density.The aim of this thesis is to propose methodological contributions for Bayesian posterior learning. More precisely, our main goal is to compare different learning methods under the scope of Monte Carlo sampling and uncertainty quantification.We first consider the posterior approximation based on the likelihood-to-evidence ratio, which has the main advantage that it turns a problem of conditional density learning into a problem of binary classification. In the context of Monte Carlo sampling, we propose a methodology for sampling from such a posterior approximation. We leverage the structure of the underlying model, which is conveniently compatible with the usual ratio-based sampling algorithms, to obtain straightforward, parameter-free, and density-free sampling procedures.We then turn to the problem of uncertainty quantification. On the one hand, normalized models such as the discriminative construction are easy to apply in the context of Bayesian uncertainty quantification. On the other hand, while unnormalized models, such as the likelihood-to-evidence-ratio, are not easily applied in uncertainty-aware learning tasks, a specific unnormalized construction, which we refer to as generative, is indeed compatible with Bayesian uncertainty quantification via the posterior predictive distribution. In this context, we explain how to carry out uncertainty quantification in both modeling techniques, and we then propose a comparison of the two constructions under the scope of Bayesian learning.We finally turn to the problem of parametric modeling with tractable density, which is indeed a requirement for epistemic uncertainty quantification in generative and discriminative modeling methods. We propose a new construction of a parametric model, which is an extension of both mixture models and normalizing flows. This model can be applied to many different types of statistical problems, such as variational inference, density estimation, and conditional density estimation, as it benefits from rapid and exact density evaluation, a straightforward sampling scheme, and a gradient reparameterization approach
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Kastner, Gregor, and Sylvia Frühwirth-Schnatter. "Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models." WU Vienna University of Economics and Business, 2013. http://epub.wu.ac.at/3771/1/paper.pdf.

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Bayesian inference for stochastic volatility models using MCMC methods highly depends on actual parameter values in terms of sampling efficiency. While draws from the posterior utilizing the standard centered parameterization break down when the volatility of volatility parameter in the latent state equation is small, non-centered versions of the model show deficiencies for highly persistent latent variable series. The novel approach of ancillarity-sufficiency interweaving has recently been shown to aid in overcoming these issues for a broad class of multilevel models. In this paper, we demonstrate how such an interweaving strategy can be applied to stochastic volatility models in order to greatly improve sampling efficiency for all parameters and throughout the entire parameter range. Moreover, this method of "combining best of different worlds" allows for inference for parameter constellations that have previously been infeasible to estimate without the need to select a particular parameterization beforehand.
Series: Research Report Series / Department of Statistics and Mathematics
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Books on the topic "Monte Carlo sampling and estimation"

1

Lemieux, Christiane. Monte carlo and quasi-monte carlo sampling. New York: Springer, 2009.

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Fu, Michael. Conditional Monte Carlo: Gradient Estimation and Optimization Applications. Boston, MA: Springer US, 1997.

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Fu, Michael. Conditional Monte Carlo: Gradient estimation and optimization applications. Boston: Kluwer Academic Publishers, 1997.

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Evans, Michael J. Monte Carlo computation of marginal posterior qualities. Toronto: University of Toronto, Dept. of Statistics, 1988.

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Manly, Bryan F. J., 1944-, ed. Randomization, bootstrap and Monte Carlo methods in biology. 2nd ed. London: Chapman & Hall, 1997.

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Manly, Bryan F. J. Randomization, bootstrap and Monte Carlo methods in biology. 2nd ed. Boca Raton, Fla: Chapman and Hall/CRC, 2001.

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Evans, Michael J. Adaptive importance sampling and chaining. Toronto: University of Toronto, Dept. of Statistics, 1990.

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Bosá, Ivana. Exact property estimation from diffusion Monte Carlo with minimal stochastic reconfiguration. St. Catharines, Ont: Brock University, Dept. of Physics, 2004.

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Aït-Sahalia, Yacine. Maximum likelihood estimation of stochastic volatility models. Cambridge, MA: National Bureau of Economic Research, 2004.

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Petrone, Sonia. A note on convergence rates of Gibbs sampling for nonparametric mixtures. Toronto: University of Toronto, Dept. of Statistics, 1998.

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Book chapters on the topic "Monte Carlo sampling and estimation"

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Han, Chuan-Hsiang. "Importance Sampling Estimation of Joint Default Probability under Structural-Form Models with Stochastic Correlation." In Monte Carlo and Quasi-Monte Carlo Methods 2010, 409–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27440-4_22.

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Wypasek, C. J., J. V. Butera, and B. G. Fitzpatrick. "Monte Carlo Estimation of Diffusion Distributions at Inter-sampling Times." In Stochastic Analysis, Control, Optimization and Applications, 505–20. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1784-8_30.

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Keramat, Mansour, and Richard Kielbasa. "Latin Hypercube Sampling Monte Carlo Estimation of Average Quality Index for Integrated Circuits." In Analog Design Issues in Digital VLSI Circuits and Systems, 131–42. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6101-9_11.

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Tyagi, Anuj Kumar, Xavier Jonsson, Theo Beelen, and W. H. A. Schilders. "An Unbiased Hybrid Importance Sampling Monte Carlo Approach for Yield Estimation in Electronic Circuit Design." In Scientific Computing in Electrical Engineering, 233–42. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44101-2_22.

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Fastowicz, Jarosław, Dawid Bąk, Przemysław Mazurek, and Krzysztof Okarma. "Estimation of Geometrical Deformations of 3D Prints Using Local Cross-Correlation and Monte Carlo Sampling." In Image Processing and Communications Challenges 9, 67–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68720-9_9.

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Bocci, Chiara, and Emilia Rocco. "On the use of auxiliary information in spatial sampling." In Proceedings e report, 151–56. Florence: Firenze University Press and Genova University Press, 2023. http://dx.doi.org/10.36253/979-12-215-0106-3.27.

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Technology development has led to a growing availability of low-cost data ready-to-use, frequently derived from large scale observations (i.e. data from pervasive systems like GPS sensors, or remote sensing data from earth observation technologies). Oftentimes, these data can’t directly answer specific questions posed by researchers and data users, or even if they can they are subject to measurement errors or self-selection bias. In both cases it is still necessary to rely, at least partially, on ad-hoc probabilistic surveys. On the other hand, the precision and quality of surveys estimates can be improved by using the data derived from these new sources as auxiliary information in the design phase and/or in the estimation phase. We present a sequential sampling strategy, suitable to investigate a spatially-related phenomenon, which exploits the auxiliary information at design level in order to obtain efficient estimates when the relation between the auxiliary and study variables it is not completely known and/or is not univocally defined for the whole population under study. Using this strategy the final sample is obtained after two (or more) steps: (i) in the first step we collect an initial sample of observations on the target variable, which is used also to investigate the relation between the auxiliary and study variables; (ii) then, this relation is exploited to target and tailor the subsequent sampling step; (iii) additional steps can be included by applying the procedure iteratively. The performance of the suggested strategy is investigated through Monte Carlo experiments by considering several scenarios, which differ in the distributions of the auxiliary and study variables and in their relation.
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Kroese, Dirk P., and Joshua C. C. Chan. "Monte Carlo Sampling." In Statistical Modeling and Computation, 195–226. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8775-3_7.

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Kleijnen, Jack P. C., and Reuven Y. Rubinstein. "Monte Carlo sampling." In Encyclopedia of Operations Research and Management Science, 524–26. New York, NY: Springer US, 2001. http://dx.doi.org/10.1007/1-4020-0611-x_638.

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Barbu, Adrian, and Song-Chun Zhu. "Cluster Sampling Methods." In Monte Carlo Methods, 123–88. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-13-2971-5_6.

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Dupree, Stephen A., and Stanley K. Fraley. "Monte Carlo Sampling Techniques." In A Monte Carlo Primer, 21–56. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4419-8491-3_2.

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Conference papers on the topic "Monte Carlo sampling and estimation"

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Guibert, Alexandre, Álvaro Díaz-Flores, Anirban Chaudhuri, and H. Alicia Kim. "Multifidelity Uncertainty Quantification in Battery Performance for eVTOL Flights Under Material and Loading Uncertainties." In Vertical Flight Society 80th Annual Forum & Technology Display, 1–8. The Vertical Flight Society, 2024. http://dx.doi.org/10.4050/f-0080-2024-1167.

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This study addresses safety concerns within the rapidly evolving Electric Vertical Takeoff and Landing (eVTOL) aircraft domain, focusing on efficient tools to quantify uncertainties in lithium-ion battery behavior - a critical aspect of eVTOL. One major issue with quantifying uncertainty is the prohibitive computational cost associated with many queries of an expensive-to-evaluate computational model. This work employs three physics-based battery models models of varying fidelity and cost to estimate the mean and the variance of the selected quantities of interest through a multifidelity method to reduce the computation cost. By combining information from multiple cheaper, lower-fidelity models through the Multifidelity Monte Carlo method, we significantly reduce the number of high-fidelity samples required for a prescribed mean-squared error, consequently reducing computational costs down to a tractable level. The proposed methodology is applied to estimate the mean and the variance of the battery temperature and voltage, accounting for uncertainties in flight conditions and materials. The first example focuses on a 580-second flight and is benchmarked against a standard Monte Carlo sampling technique. Results indicate a notable fourfold speed-up using the Multifidelity Monte Carlo method compared to the standard Monte Carlo method for the same mean-squared error for the voltage estimate. To showcase the method's generality, the multifidelity method is then applied to a longer flight of 3580 seconds for estimating the mean and the variance and utilizing these statistics to approximately estimate the probability of the flight completion. This demonstrates the adaptability of the methodology to various power profiles and considered uncertainties, with potential extensions to any battery chemistry. In conclusion, the presented multifidelity method offers a robust approach to enhance eVTOL safety by efficiently estimating uncertainties in battery behavior.
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Haile, Mulugeta. "Data-Informed Structural Diagnostic Framework." In Vertical Flight Society 71st Annual Forum & Technology Display, 1–9. The Vertical Flight Society, 2015. http://dx.doi.org/10.4050/f-0071-2015-10199.

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Crack growth in airframe structures may be considered as a nonlinear dynamic process where the crack size at each time step is predicted by a physical damage model such as the Paris-Erdogan equation and updated by a sequence of noisy sensor measurements. The prediction-update implementation is a two stage recursive process that uses a sequential Monte Carlo sampling to obtain a posterior density of crack size at the desired inspection stage. The goal of this paper is to develop a datainformed diagnostic framework that combines the predictions of a physical damage model and evidence from ultrasonic sensor data to provide accurate estimation of crack-size in rotorcraft structures. The data-informed approach obtains the most probable crack-size (MPCS) at each inspection stage using a sequential Monte Carlo method known as Particle Filters. To validate the approach, two Al7075-T6 nested-angle plates were tested using rotorcraft spectrum loads. Results show that the prediction error of the data-informed method, as measured by root mean square deviation from the true value, is less than half of the error of both the Paris-Erdogan and NASGRO models.
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Frewen, Thomas, Bob LaBarre, Mark Gurvich, and Sergey Shishkin. "Enhancement of Reliability-Based Probabilistic Solutions for Rotorcraft Structural Analysis and Optimization." In Vertical Flight Society 72nd Annual Forum & Technology Display, 1–19. The Vertical Flight Society, 2016. http://dx.doi.org/10.4050/f-0072-2016-11538.

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This study addresses opportunities to dramatically increase computational efficiency of probabilistic solutions relevant to rotorcraft, i.e., focused on very low probabilities of failure (POF). Firstly, it is shown that down-selection of probabilistic solutions depends on problem definition, and a set of eight decision-based criteria is proposed. Next, limitations of typically used Monte Carlo simulation (MCS) and First- and Second-Order Reliability methods (FORM/SORM) are discussed in detail and demonstrated on numerical examples. Major efforts are focused on computational implementation of Cross-Entropy Importance Sampling (CE-IS) as an efficient alternative to both MCS and FORM/SORM. Remarkable computational enhancement in comparison with MCS is demonstrated on an example of probabilistic damage tolerance assessment for a representative composite structure: >1E+3 at POF = ∼1E-4; > 6E+4 at POF = ∼1E-6; and >1E+7 at POF = ∼1E-9. In addition, a simplified "engineering" variant is proposed based on estimation of a conservative, upper boundary of POF instead of its true value. Finally, possibilities of probabilistic optimization are highlighted according to the demonstrated CE-IS based capabilities.
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Chryssanthacopoulos, James, Mykel Kochenderfer, and Richard Williams. "Improved Monte Carlo Sampling for Conflict Probability Estimation." In 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
18th AIAA/ASME/AHS Adaptive Structures Conference
12th. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-3012.

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Dong, Hui, and Marvin K. Nakayama. "Quantile estimation using conditional Monte Carlo and Latin hypercube sampling." In 2017 Winter Simulation Conference (WSC). IEEE, 2017. http://dx.doi.org/10.1109/wsc.2017.8247933.

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Suresh, K., and J. Lagajac. "Fast Monte Carlo domain sampling for discrete field value estimation." In the fourth ACM symposium. New York, New York, USA: ACM Press, 1997. http://dx.doi.org/10.1145/267734.267817.

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Doorn, T. S., E. J. W. ter Maten, J. A. Croon, A. Di Bucchianico, and O. Wittich. "Importance sampling Monte Carlo simulations for accurate estimation of SRAM yield." In ESSCIRC 2008 - 34th European Solid-State Circuits Conference. IEEE, 2008. http://dx.doi.org/10.1109/esscirc.2008.4681834.

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Zhang, Pushi, Li Zhao, Guoqing Liu, Jiang Bian, Minlie Huang, Tao Qin, and Tie-Yan Liu. "Independence-aware Advantage Estimation." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/461.

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Most of existing advantage function estimation methods in reinforcement learning suffer from the problem of high variance, which scales unfavorably with the time horizon. To address this challenge, we propose to identify the independence property between current action and future states in environments, which can be further leveraged to effectively reduce the variance of the advantage estimation. In particular, the recognized independence property can be naturally utilized to construct a novel importance sampling advantage estimator with close-to-zero variance even when the Monte-Carlo return signal yields a large variance. To further remove the risk of the high variance introduced by the new estimator, we combine it with existing Monte-Carlo estimator via a reward decomposition model learned by minimizing the estimation variance. Experiments demonstrate that our method achieves higher sample efficiency compared with existing advantage estimation methods in complex environments.
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Djuric, Petar M., and Cagla Tasdemir. "Estimation of posterior distributions with population Monte Carlo sampling and graphical modeling." In 2012 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2012. http://dx.doi.org/10.1109/ssp.2012.6319677.

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Yi, Daqing, Shushman Choudhury, and Siddhartha Srinivasa. "Incorporating qualitative information into quantitative estimation via Sequentially Constrained Hamiltonian Monte Carlo sampling." In 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2017. http://dx.doi.org/10.1109/iros.2017.8206336.

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Reports on the topic "Monte Carlo sampling and estimation"

1

Herbst, Edward, and Frank Schorfheide. Sequential Monte Carlo Sampling for DSGE Models. Cambridge, MA: National Bureau of Economic Research, June 2013. http://dx.doi.org/10.3386/w19152.

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Kalos, M. H. Domain Green's Function Sampling in Diffusion Monte Carlo. Office of Scientific and Technical Information (OSTI), April 2000. http://dx.doi.org/10.2172/792336.

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John A. Krommes and Sharadini Rath. Monte Carlo Sampling of Negative-temperature Plasma States. Office of Scientific and Technical Information (OSTI), July 2002. http://dx.doi.org/10.2172/808375.

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Martz, R. L., R. C. Gast, and L. J. Tyburski. Monte Carlo next-event point flux estimation for RCP01. Office of Scientific and Technical Information (OSTI), December 1991. http://dx.doi.org/10.2172/10193014.

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Childers, David, Jesús Fernández-Villaverde, Jesse Perla, Christopher Rackauckas, and Peifan Wu. Differentiable State-Space Models and Hamiltonian Monte Carlo Estimation. Cambridge, MA: National Bureau of Economic Research, October 2022. http://dx.doi.org/10.3386/w30573.

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Devaney, J. Uniform versus random sampling in physical calculations: Monte Carlo. Office of Scientific and Technical Information (OSTI), September 1989. http://dx.doi.org/10.2172/5291731.

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Bond, Stephen, Brian Franke, Richard Lehoucq, and Scott McKinley. Sensitivity Analyses for Monte Carlo Sampling-Based Particle Simulations. Office of Scientific and Technical Information (OSTI), September 2022. http://dx.doi.org/10.2172/1889334.

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Üney, Murat, and Müjdat Çetin. Monte Carlo optimization approach for decentralized estimation networks under communication constraints. Sabanci University, November 2010. http://dx.doi.org/10.5900/su_fens_wp.2010.15985.

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Kuruvilla Verghese. Mammographic Imaging Studies Using the Monte Carlo Image Simulation-Differential Sampling (MCMIS-DS) Code. Office of Scientific and Technical Information (OSTI), April 2002. http://dx.doi.org/10.2172/793508.

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T.J. Donovan and Y. Danon. Application of Monte Carlo Chord-Length Sampling Algorithms to Transport Through a 2-D Binary Stochastic Mixture. Office of Scientific and Technical Information (OSTI), March 2002. http://dx.doi.org/10.2172/820707.

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