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Fang, Youhan. "Efficient Markov Chain Monte Carlo Methods". Thesis, Purdue University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10809188.
Pełny tekst źródłaGenerating random samples from a prescribed distribution is one of the most important and challenging problems in machine learning, Bayesian statistics, and the simulation of materials. Markov Chain Monte Carlo (MCMC) methods are usually the required tool for this task, if the desired distribution is known only up to a multiplicative constant. Samples produced by an MCMC method are real values in N-dimensional space, called the configuration space. The distribution of such samples converges to the target distribution in the limit. However, existing MCMC methods still face many challenges that are not well resolved. Difficulties for sampling by using MCMC methods include, but not exclusively, dealing with high dimensional and multimodal problems, high computation cost due to extremely large datasets in Bayesian machine learning models, and lack of reliable indicators for detecting convergence and measuring the accuracy of sampling. This dissertation focuses on new theory and methodology for efficient MCMC methods that aim to overcome the aforementioned difficulties.
One contribution of this dissertation is generalizations of hybrid Monte Carlo (HMC). An HMC method combines a discretized dynamical system in an extended space, called the state space, and an acceptance test based on the Metropolis criterion. The discretized dynamical system used in HMC is volume preserving—meaning that in the state space, the absolute Jacobian of a map from one point on the trajectory to another is 1. Volume preservation is, however, not necessary for the general purpose of sampling. A general theory allowing the use of non-volume preserving dynamics for proposing MCMC moves is proposed. Examples including isokinetic dynamics and variable mass Hamiltonian dynamics with an explicit integrator, are all designed with fewer restrictions based on the general theory. Experiments show improvement in efficiency for sampling high dimensional multimodal problems. A second contribution is stochastic gradient samplers with reduced bias. An in-depth analysis of the noise introduced by the stochastic gradient is provided. Two methods to reduce the bias in the distribution of samples are proposed. One is to correct the dynamics by using an estimated noise based on subsampled data, and the other is to introduce additional variables and corresponding dynamics to adaptively reduce the bias. Extensive experiments show that both methods outperform existing methods. A third contribution is quasi-reliable estimates of effective sample size. Proposed is a more reliable indicator—the longest integrated autocorrelation time over all functions in the state space—for detecting the convergence and measuring the accuracy of MCMC methods. The superiority of the new indicator is supported by experiments on both synthetic and real problems.
Minor contributions include a general framework of changing variables, and a numerical integrator for the Hamiltonian dynamics with fourth order accuracy. The idea of changing variables is to transform the potential energy function as a function of the original variable to a function of the new variable, such that undesired properties can be removed. Two examples are provided and preliminary experimental results are obtained for supporting this idea. The fourth order integrator is constructed by combining the idea of the simplified Takahashi-Imada method and a two-stage Hessian-based integrator. The proposed method, called two-stage simplified Takahashi-Imada method, shows outstanding performance over existing methods in high-dimensional sampling problems.
Murray, Iain Andrew. "Advances in Markov chain Monte Carlo methods". Thesis, University College London (University of London), 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487199.
Pełny tekst źródłaGraham, Matthew McKenzie. "Auxiliary variable Markov chain Monte Carlo methods". Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/28962.
Pełny tekst źródłaXu, Jason Qian. "Markov Chain Monte Carlo and Non-Reversible Methods". Thesis, The University of Arizona, 2012. http://hdl.handle.net/10150/244823.
Pełny tekst źródłaZhang, Yichuan. "Scalable geometric Markov chain Monte Carlo". Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20978.
Pełny tekst źródłaPereira, Fernanda Chaves. "Bayesian Markov chain Monte Carlo methods in general insurance". Thesis, City University London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342720.
Pełny tekst źródłaCheal, Ryan. "Markov Chain Monte Carlo methods for simulation in pedigrees". Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362254.
Pełny tekst źródłaDurmus, Alain. "High dimensional Markov chain Monte Carlo methods : theory, methods and applications". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLT001/document.
Pełny tekst źródłaThe subject of this thesis is the analysis of Markov Chain Monte Carlo (MCMC) methods and the development of new methodologies to sample from a high dimensional distribution. Our work is divided into three main topics. The first problem addressed in this manuscript is the convergence of Markov chains in Wasserstein distance. Geometric and sub-geometric convergence with explicit constants, are derived under appropriate conditions. These results are then applied to thestudy of MCMC algorithms. The first analyzed algorithm is an alternative scheme to the Metropolis Adjusted Langevin algorithm for which explicit geometric convergence bounds are established. The second method is the pre-Conditioned Crank-Nicolson algorithm. It is shown that under mild assumption, the Markov chain associated with thisalgorithm is sub-geometrically ergodic in an appropriated Wasserstein distance. The second topic of this thesis is the study of the Unadjusted Langevin algorithm (ULA). We are first interested in explicit convergence bounds in total variation under different kinds of assumption on the potential associated with the target distribution. In particular, we pay attention to the dependence of the algorithm on the dimension of the state space. The case of fixed step sizes as well as the case of nonincreasing sequences of step sizes are dealt with. When the target density is strongly log-concave, explicit bounds in Wasserstein distance are established. These results are then used to derived new bounds in the total variation distance which improve the one previously derived under weaker conditions on the target density.The last part tackles new optimal scaling results for Metropolis-Hastings type algorithms. First, we extend the pioneer result on the optimal scaling of the random walk Metropolis algorithm to target densities which are differentiable in Lp mean for p ≥ 2. Then, we derive new Metropolis-Hastings type algorithms which have a better optimal scaling compared the MALA algorithm. Finally, the stability and the convergence in total variation of these new algorithms are studied
Wu, Miaodan. "Markov chain Monte Carlo methods applied to Bayesian data analysis". Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.625087.
Pełny tekst źródłaPaul, Rajib. "Theoretical And Algorithmic Developments In Markov Chain Monte Carlo". The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1218184168.
Pełny tekst źródłaKhedri, Shiler. "Markov chain Monte Carlo methods for exact tests in contingency tables". Thesis, Durham University, 2012. http://etheses.dur.ac.uk/5579/.
Pełny tekst źródłaIbrahim, Adriana Irawati Nur. "New methods for mode jumping in Markov chain Monte Carlo algorithms". Thesis, University of Bath, 2009. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500720.
Pełny tekst źródłaBarata, Teresa Cordeiro Ferreira Nunes. "Two examples of curve estimation using Markov Chain Monte Carlo methods". Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.612139.
Pełny tekst źródłaNemirovsky, Danil. "Monte Carlo methods and Markov chain based approaches for PageRank computation". Nice, 2010. http://www.theses.fr/2010NICE4018.
Pełny tekst źródłaVaičiulytė, Ingrida. "Study and application of Markov chain Monte Carlo method". Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141209_112440-55390.
Pełny tekst źródłaDisertacijoje nagrinėjami Markovo grandinės Monte-Karlo (MCMC) adaptavimo metodai, skirti efektyviems skaitiniams duomenų analizės sprendimų priėmimo su iš anksto nustatytu patikimumu algoritmams sudaryti. Suformuluoti ir išspręsti hierarchiniu būdu sudarytų daugiamačių skirstinių (asimetrinio t skirstinio, Puasono-Gauso modelio, stabiliojo simetrinio vektoriaus dėsnio) parametrų vertinimo uždaviniai. Adaptuotai MCMC procedūrai sukurti yra pritaikytas nuoseklaus Monte-Karlo imčių generavimo metodas, įvedant statistinį stabdymo kriterijų ir imties tūrio reguliavimą. Statistiniai uždaviniai išspręsti šiuo metodu leidžia atskleisti aktualias MCMC metodų skaitmeninimo problemų ypatybes. MCMC algoritmų efektyvumas tiriamas pasinaudojant disertacijoje sudarytu statistinio modeliavimo metodu. Atlikti eksperimentai su sportininkų duomenimis ir sveikatos industrijai priklausančių įmonių finansiniais duomenimis patvirtino, kad metodo skaitinės savybės atitinka teorinį modelį. Taip pat sukurti metodai ir algoritmai pritaikyti sociologinių duomenų analizės modeliui sudaryti. Atlikti tyrimai parodė, kad adaptuotas MCMC algoritmas leidžia gauti nagrinėjamų skirstinių parametrų įvertinius per mažesnį grandžių skaičių ir maždaug du kartus sumažinti skaičiavimų apimtį. Disertacijoje sukonstruoti algoritmai gali būti pritaikyti stochastinio pobūdžio sistemų tyrimui ir kitiems statistikos uždaviniams spręsti MCMC metodu.
Gausland, Eivind Blomholm. "Parameter Estimation in Extreme Value Models with Markov Chain Monte Carlo Methods". Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-10032.
Pełny tekst źródłaIn this thesis I have studied how to estimate parameters in an extreme value model with Markov Chain Monte Carlo (MCMC) given a data set. This is done with synthetic Gaussian time series generated by spectral densities, called spectrums, with a "box" shape. Three different spectrums have been used. In the acceptance probability in the MCMC algorithm, the likelihood have been built up by dividing the time series into blocks consisting of a constant number of points. In each block, only the maximum value, i.e. the extreme value, have been used. Each extreme value will then be interpreted as independent. Since the time series analysed are generated the way they are, there exists theoretical values for the parameters in the extreme value model. When the MCMC algorithm is tested to fit a model to the generated data, the true parameter values are already known. For the first and widest spectrum, the method is unable to find estimates matching the true values for the parameters in the extreme value model. For the two other spectrums, I obtained good estimates for some block lengths, others block lengths gave poor estimates compared to the true values. Finally, it looked like an increasing block length gave more accurate estimates as the spectrum became more narrow banded. A final simulation on a time series generated by a narrow banded spectrum, disproved this hypothesis.
Niederberger, Theresa. "Markov chain Monte Carlo methods for parameter identification in systems biology models". Diss., Ludwig-Maximilians-Universität München, 2012. http://nbn-resolving.de/urn:nbn:de:bvb:19-157798.
Pełny tekst źródłaXu, Xiaojin. "Methods in Hypothesis Testing, Markov Chain Monte Carlo and Neuroimaging Data Analysis". Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10927.
Pełny tekst źródłaStatistics
Demiris, Nikolaos. "Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods". Thesis, University of Nottingham, 2004. http://eprints.nottingham.ac.uk/10078/.
Pełny tekst źródłaSpade, David Allen. "Investigating Convergence of Markov Chain Monte Carlo Methods for Bayesian Phylogenetic Inference". The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1372173121.
Pełny tekst źródłaLi, Yuanzhi. "Bayesian Models for Repeated Measures Data Using Markov Chain Monte Carlo Methods". DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/6997.
Pełny tekst źródłaBrowne, William J. "Applying MCMC methods to multi-level models". Thesis, University of Bath, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268210.
Pełny tekst źródłaTu, Zhuowen. "Image Parsing by Data-Driven Markov Chain Monte Carlo". The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1038347031.
Pełny tekst źródłaVeitch, John D. "Applications of Markov Chain Monte Carlo methods to continuous gravitational wave data analysis". Thesis, Connect to e-thesis to view abstract. Move to record for print version, 2007. http://theses.gla.ac.uk/35/.
Pełny tekst źródłaPh.D. thesis submitted to Information and Mathematical Sciences Faculty, Department of Mathematics, University of Glasgow, 2007. Includes bibliographical references. Print version also available.
Walker, Neil Rawlinson. "A Bayesian approach to the job search model and its application to unemployment durations using MCMC methods". Thesis, University of Newcastle Upon Tyne, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299053.
Pełny tekst źródłaHigdon, David. "Spatial applications of Markov chain Monte Carlo for Bayesian inference /". Thesis, Connect to this title online; UW restricted, 1994. http://hdl.handle.net/1773/8942.
Pełny tekst źródłaOlvera, Astivia Oscar Lorenzo. "On the estimation of the polychoric correlation coefficient via Markov Chain Monte Carlo methods". Thesis, University of British Columbia, 2013. http://hdl.handle.net/2429/44349.
Pełny tekst źródłaBray, Isabelle Cella. "Modelling the prevalence of Down syndrome with applications of Markov chain Monte Carlo methods". Thesis, University of Plymouth, 1998. http://hdl.handle.net/10026.1/2408.
Pełny tekst źródłaWitte, Hugh Douglas. "Markov chain Monte Carlo and data augmentation methods for continuous-time stochastic volatility models". Diss., The University of Arizona, 1999. http://hdl.handle.net/10150/283976.
Pełny tekst źródłaByers, Simon. "Bayesian modeling of highly structured systems using Markov chain Monte Carlo /". Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/8980.
Pełny tekst źródłaOlsen, Andrew Nolan. "When Infinity is Too Long to Wait: On the Convergence of Markov Chain Monte Carlo Methods". The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1433770406.
Pełny tekst źródłaKarawatzki, Roman, Josef Leydold i Klaus Pötzelberger. "Automatic Markov Chain Monte Carlo Procedures for Sampling from Multivariate Distributions". Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2005. http://epub.wu.ac.at/1400/1/document.pdf.
Pełny tekst źródłaSeries: Research Report Series / Department of Statistics and Mathematics
Manrique, Garcia Aurora. "Econometric analysis of limited dependent time series". Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389797.
Pełny tekst źródłaLi, Min. "Bayesian discovery of regulatory motifs using reversible jump Markov chain Monte Carlo /". Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/9529.
Pełny tekst źródłaNilsson, Mats. "Building Reconstruction of Digital Height Models with the Markov Chain Monte Carlo Method". Thesis, Linköpings universitet, Datorseende, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-148886.
Pełny tekst źródłaFu, Jianlin. "A markov chain monte carlo method for inverse stochastic modeling and uncertainty assessment". Doctoral thesis, Universitat Politècnica de València, 2008. http://hdl.handle.net/10251/1969.
Pełny tekst źródłaFu, J. (2008). A markov chain monte carlo method for inverse stochastic modeling and uncertainty assessment [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1969
Palancia
Lindahl, John, i Douglas Persson. "Data-driven test case design of automatic test cases using Markov chains and a Markov chain Monte Carlo method". Thesis, Malmö universitet, Fakulteten för teknik och samhälle (TS), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-43498.
Pełny tekst źródłaFischer, Alexander. "An Uncoupling Coupling method for Markov chain Monte Carlo simulations with an application to biomolecules". [S.l. : s.n.], 2003. http://www.diss.fu-berlin.de/2003/234/index.html.
Pełny tekst źródłaYang, Chao. "ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN COMPLEX SYSTEMS". The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962.
Pełny tekst źródłaLewis, John Robert. "Bayesian Restricted Likelihood Methods". The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1407505392.
Pełny tekst źródłaHörmann, Wolfgang, i Josef Leydold. "Monte Carlo Integration Using Importance Sampling and Gibbs Sampling". Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, 2005. http://epub.wu.ac.at/1642/1/document.pdf.
Pełny tekst źródłaSeries: Preprint Series / Department of Applied Statistics and Data Processing
Walker, Matthew James. "Methods for Bayesian inversion of seismic data". Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10504.
Pełny tekst źródłaNiederberger, Theresa [Verfasser], i Patrick [Akademischer Betreuer] Cramer. "Markov chain Monte Carlo methods for parameter identification in systems biology models / Theresa Niederberger. Betreuer: Patrick Cramer". München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2012. http://d-nb.info/1036101029/34.
Pełny tekst źródłaMatsumoto, Nobuyuki. "Geometry of configuration space in Markov chain Monte Carlo methods and the worldvolume approach to the tempered Lefschetz thimble method". Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263464.
Pełny tekst źródłaAllchin, Lorraine Doreen May. "Statistical methods for mapping complex traits". Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:65f392ba-1b64-4b00-8871-7cee98809ce1.
Pełny tekst źródłaTiboaca, Oana D. "On the application of the reversible jump Markov chain Monte Carlo method within structural dynamics". Thesis, University of Sheffield, 2016. http://etheses.whiterose.ac.uk/17126/.
Pełny tekst źródłaDhulipala, Lakshmi Narasimha Somayajulu. "Bayesian Methods for Intensity Measure and Ground Motion Selection in Performance-Based Earthquake Engineering". Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/88493.
Pełny tekst źródłaDoctor of Philosophy
Earthquake ground shaking is a complex phenomenon since there is no unique way to assess its strength. Yet, the strength of ground motion (shaking) becomes an integral part for predicting the future earthquake performance of buildings using the Performance-Based Earthquake Engineering (PBEE) framework. The PBEE framework predicts building performance in terms of expected financial losses, possible downtime, the potential of the building to collapse under a future earthquake. Much prior research has shown that the predictions made by the PBEE framework are heavily dependent upon how the strength of a future earthquake ground motion is characterized. This dependency leads to uncertainty in the predicted building performance and hence its seismic design. The goal of this dissertation therefore is to employ Bayesian reasoning, which takes into account the alternative explanations or perspectives of a research problem, and propose robust quantitative methods that aid IM selection and ground motion selection in PBEE The fact that the local intensity of an earthquake can be characterized in multiple ways using Intensity Measures (IM; e.g., peak ground acceleration) is problematic for PBEE because it leads to different PBEE results for different choices of the IM. While formal procedures for selecting an optimal IM exist, they may be considered as being subjective and have multiple criteria making their use difficult and inconclusive. Bayes rule provides a mechanism called change of perspective using which a problem that is difficult to solve from one perspective could be tackled from a different perspective. This change of perspective mechanism is used to propose a quantitative, unified metric for rating alternative IMs. The immediate application of this metric is aiding the selection of the best IM that would predict the building earthquake performance with least bias. Structural analysis for performance assessment in PBEE is conducted by selecting ground motions which match a target response spectrum (a representation of future ground motions). The definition of a target response spectrum lacks general consensus and is dependent on the analysts’ preferences. To encompass all these preferences and requirements of analysts, a Bayesian target response spectrum which is general and flexible is proposed. While the generality of this Bayesian target response spectrum allow analysts select those ground motions to which their structures are the most sensitive, its flexibility permits the incorporation of additional information (preferences) into the target response spectrum development. This dissertation addresses four critical questions in PBEE: (1) how can we best define ground motion at a site?; (2) if ground motion can only be defined by multiple metrics, how can we easily derive the probability of such shaking at a site?; (3) how do we use these multiple metrics to select a set of ground motion records that best capture the site’s unique seismicity; (4) when those records are used to analyze the response of a structure, how can we be sure that a standard linear regression technique accurately captures the uncertainty in structural response at low and high levels of shaking?
Wang, Yinglu. "A Markov Chain Based Method for Time Series Data Modeling and Prediction". University of Cincinnati / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1592395278430805.
Pełny tekst źródłaChen, Yuting. "Inférence bayésienne dans les modèles de croissance de plantes pour la prévision et la caractérisation des incertitudes". Thesis, Châtenay-Malabry, Ecole centrale de Paris, 2014. http://www.theses.fr/2014ECAP0040/document.
Pełny tekst źródłaPlant growth models aim to describe plant development and functional processes in interaction with the environment. They offer promising perspectives for many applications, such as yield prediction for decision support or virtual experimentation inthe context of breeding. This PhD focuses on the solutions to enhance plant growth model predictive capacity with an emphasis on advanced statistical methods. Our contributions can be summarized in four parts. Firstly, from a model design perspective, the Log-Normal Allocation and Senescence (LNAS) crop model is proposed. It describes only the essential ecophysiological processes for biomass budget in a probabilistic framework, so as to avoid identification problems and to accentuate uncertainty assessment in model prediction. Secondly, a thorough research is conducted regarding model parameterization. In a Bayesian framework, both Sequential Monte Carlo (SMC) methods and Markov chain Monte Carlo (MCMC) based methods are investigated to address the parameterization issues in the context of plant growth models, which are frequently characterized by nonlinear dynamics, scarce data and a large number of parameters. Particularly, whenthe prior distribution is non-informative, with the objective to put more emphasis on the observation data while preserving the robustness of Bayesian methods, an iterative version of the SMC and MCMC methods is introduced. It can be regarded as a stochastic variant of an EM type algorithm. Thirdly, a three-step data assimilation approach is proposed to address model prediction issues. The most influential parameters are first identified by global sensitivity analysis and chosen by model selection. Subsequently, the model calibration is performed with special attention paid to the uncertainty assessment. The posterior distribution obtained from this estimation step is consequently considered as prior information for the prediction step, in which a SMC-based on-line estimation method such as Convolution Particle Filtering (CPF) is employed to perform data assimilation. Both state and parameter estimates are updated with the purpose of improving theprediction accuracy and reducing the associated uncertainty. Finally, from an application point of view, the proposed methodology is implemented and evaluated with two crop models, the LNAS model for sugar beet and the STICS model for winter wheat. Some indications are also given on the experimental design to optimize the quality of predictions. The applications to real case scenarios show encouraging predictive performances and open the way to potential tools for yield prediction in agriculture
Dahlin, Johan. "Accelerating Monte Carlo methods for Bayesian inference in dynamical models". Doctoral thesis, Linköpings universitet, Reglerteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-125992.
Pełny tekst źródłaBorde Riksbanken höja eller sänka reporäntan vid sitt nästa möte för att nå inflationsmålet? Vilka gener är förknippade med en viss sjukdom? Hur kan Netflix och Spotify veta vilka filmer och vilken musik som jag vill lyssna på härnäst? Dessa tre problem är exempel på frågor där statistiska modeller kan vara användbara för att ge hjälp och underlag för beslut. Statistiska modeller kombinerar teoretisk kunskap om exempelvis det svenska ekonomiska systemet med historisk data för att ge prognoser av framtida skeenden. Dessa prognoser kan sedan användas för att utvärdera exempelvis vad som skulle hända med inflationen i Sverige om arbetslösheten sjunker eller hur värdet på mitt pensionssparande förändras när Stockholmsbörsen rasar. Tillämpningar som dessa och många andra gör statistiska modeller viktiga för många delar av samhället. Ett sätt att ta fram statistiska modeller bygger på att kontinuerligt uppdatera en modell allteftersom mer information samlas in. Detta angreppssätt kallas för Bayesiansk statistik och är särskilt användbart när man sedan tidigare har bra insikter i modellen eller tillgång till endast lite historisk data för att bygga modellen. En nackdel med Bayesiansk statistik är att de beräkningar som krävs för att uppdatera modellen med den nya informationen ofta är mycket komplicerade. I sådana situationer kan man istället simulera utfallet från miljontals varianter av modellen och sedan jämföra dessa mot de historiska observationerna som finns till hands. Man kan sedan medelvärdesbilda över de varianter som gav bäst resultat för att på så sätt ta fram en slutlig modell. Det kan därför ibland ta dagar eller veckor för att ta fram en modell. Problemet blir särskilt stort när man använder mer avancerade modeller som skulle kunna ge bättre prognoser men som tar för lång tid för att bygga. I denna avhandling använder vi ett antal olika strategier för att underlätta eller förbättra dessa simuleringar. Vi föreslår exempelvis att ta hänsyn till fler insikter om systemet och därmed minska antalet varianter av modellen som behöver undersökas. Vi kan således redan utesluta vissa modeller eftersom vi har en bra uppfattning om ungefär hur en bra modell ska se ut. Vi kan också förändra simuleringen så att den enklare rör sig mellan olika typer av modeller. På detta sätt utforskas rymden av alla möjliga modeller på ett mer effektivt sätt. Vi föreslår ett antal olika kombinationer och förändringar av befintliga metoder för att snabba upp anpassningen av modellen till observationerna. Vi visar att beräkningstiden i vissa fall kan minska ifrån några dagar till någon timme. Förhoppningsvis kommer detta i framtiden leda till att man i praktiken kan använda mer avancerade modeller som i sin tur resulterar i bättre prognoser och beslut.