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On Nesting Monte Carlo Estimators [article]

Tom Rainforth, Robert Cornish, Hongseok Yang, Andrew Warrington, Frank Wood
2018 arXiv   pre-print
Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation.  ...  For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation.  ...  ) + 2A k y (0:k−1) + 2 A k y (0:k−1) 1 2 s 2 k y (0:k−1) + A k y (0:k−1) 1 2 N k + A k y (0:k−1) On Nesting Monte Carlo Estimators = s 2 k y (0:k−1) + 2K 2 k ω k y (0:k−1) N k + K 2 k ω k y (0:k−1) + 2K  ... 
arXiv:1709.06181v4 fatcat:b4oyiyf7hrblfmj4plvtugcyre

Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling [article]

Kei Ishikawa, Takashi Goda
2021 arXiv   pre-print
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods.  ...  than those of the previously known estimators.  ...  A nested Monte Carlo estimator is probably the most straightforward approach to estimate such a nested expectation.  ... 
arXiv:2001.04676v2 fatcat:qjk7nnxtnng33ggusrvgykpkyq

Calculating the Expected Value of Sample Information using Efficient Nested Monte Carlo: A Tutorial [article]

Anna Heath, Gianluca Baio
2018 arXiv   pre-print
Conclusions: This new method reduces the computational cost of estimating the EVSI by nested simulation.  ...  The EVSI estimation is more accurate if a greater number of nested samples are used, even for a fixed computational cost.  ...  To estimate the expected variance of the posterior INB, we use a nested Monte Carlo method.  ... 
arXiv:1709.02319v2 fatcat:4xbcws4pp5d7bjjgkzav7uuuqi

Faster Comparison of Stopping Times by Nested Conditional Monte Carlo [article]

Fabian Dickmann, Nikolaus Schweizer
2014 arXiv   pre-print
We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo.  ...  In these applications, our method allows to substantially increase the efficiency of other variance reduction techniques, namely, Quasi-Control Variates and Multilevel Monte Carlo.  ...  Since our method mimics Conditional Monte Carlo by Nested Simulation, we refer to it as Nested Conditional Monte Carlo.  ... 
arXiv:1402.0243v1 fatcat:pzyfoed5drd3zkkzdljstyjway

Unbiased Monte Carlo estimation for the expected value of partial perfect information [article]

Takashi Goda
2016 arXiv   pre-print
Numerical experiments show that even the convergence behaviors of our unbiased estimators are superior to that of the standard nested Monte Carlo estimator.  ...  In this paper we introduce two unbiased Monte Carlo estimators for the EVPPI based on multilevel Monte Carlo method, introduced by Heinrich (1998) and Giles (2008), and its extension by Rhee and Glynn  ...  decays to 0 much faster than that for the nested Monte Carlo estimator.  ... 
arXiv:1604.01120v1 fatcat:zpchumz445ekrp36nomzydfg4i

Faster comparison of stopping times by nested conditional Monte Carlo

Fabian Dickmann, Nikolaus Schweizer
2016 Journal of Computational Finance  
We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo.  ...  In these applications, our method allows to substantially increase the efficiency of other variance reduction techniques, namely, Quasi-Control Variates and Multilevel Monte Carlo.  ...  Since our method mimics Conditional Monte Carlo by Nested Simulation, we refer to it as Nested Conditional Monte Carlo.  ... 
doi:10.21314/jcf.2016.221 fatcat:6vmi5btnljabzeymheuv5h4cwi

Computing the variance of a conditional expectation via non-nested Monte Carlo [article]

Takashi Goda
2016 arXiv   pre-print
In this letter we construct unbiased non-nested Monte Carlo estimators based on the so-called pick-freeze scheme due to Sobol'.  ...  Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call 11/2-level simulation since the optimal inner-level sample size is bounded as the computational budget increases.  ...  In the next section, we introduce four straightforward non-nested Monte Carlo estimators; one based on Mauntz [3] and Kucherenko et al.  ... 
arXiv:1605.05454v2 fatcat:z3yicml4svdlpojiks2p3o6jla

Monte-Carlo Kakuro [chapter]

Tristan Cazenave
2010 Lecture Notes in Computer Science  
Monte-Carlo methods can improve on traditional search methods for Kakuro. We show that a Nested Monte-Carlo Search at level 2 gives good results.  ...  This is the first time a nested search of level 2 gives good results for a Constraint Satisfaction problem.  ...  Conclusion We have compared Forward Checking, Iterative Sampling and Nested Monte-Carlo Search on Kakuro problems. Nested Monte-Carlo search at level 2 gives the best results.  ... 
doi:10.1007/978-3-642-12993-3_5 fatcat:nibo6e3mkjfj7onlnhzpebribi

Calculating the Expected Value of Sample Information Using Efficient Nested Monte Carlo: A Tutorial

Anna Heath, Gianluca Baio
2018 Value in Health  
Conclusions: This new method reduces the computational cost of estimating the EVSI by nested simulation.  ...  The EVSI estimation is more accurate if a greater number of nested samples are used, even for a fixed computational cost.  ...  To estimate the expected variance of the posterior INB, we used a nested Monte Carlo method.  ... 
doi:10.1016/j.jval.2018.05.004 fatcat:lm5t7uvuxfawfctimloaix4duy

On the Pitfalls of Nested Monte Carlo [article]

Tom Rainforth, Robert Cornish, Hongseok Yang, Frank Wood
2016 arXiv   pre-print
In this paper, we analyse the behaviour of nested Monte Carlo (NMC) schemes, for which classical convergence proofs are insufficient.  ...  There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs.  ...  This paper examines convergence of such nested Monte Carlo (NMC) methods.  ... 
arXiv:1612.00951v1 fatcat:52itxlylyrfjdehveh5za2u4lu

Upper bounds for Bermudan options on Markovian data using nonparametric regression and a reduced number of nested Monte Carlo steps

Michael Kohler, Adam Krzyzak, Harro Walk
2009 Statistics & Decisions  
using only a reduced number of nested Monte Carlo steps.  ...  We use the dual approach to derive upper bounds on the price of such options using only a reduced number of nested Monte Carlo steps.  ...  In this article we introduce for general Markovian processes dual Monte Carlo estimates based on nonparametric regression which do not require many nested Monte Carlo steps.  ... 
doi:10.1524/stnd.2008.1014 fatcat:xnggvw3dm5dgdkq6ut6pzl6sye

Accelerated Option Pricing in Multiple Scenarios [article]

Stefan Dirnstorfer, Andreas J. Grau
2008 arXiv   pre-print
Instead of starting a separate nested Monte Carlo simulation for each scenario under consideration, the new method covers the utilization of very few representative nested simulations and estimating the  ...  This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives.  ...  Usage of variance reduction techniques in the nested Monte Carlo simulation.  ... 
arXiv:0807.5120v2 fatcat:zno7def63jfe5fqcnjgeujff4a

Multilevel and Quasi Monte Carlo methods for the calculation of the Expected Value of Partial Perfect Information [article]

Wei Fang, Zhenru Wang, Mike B Giles, Christopher H Jackson, Nicky J Welton, Christophe Andrieu, Howard Thom
2021 biorxiv/medrxiv   pre-print
Standard Monte Carlo (MC) estimation of EVPPI is computationally expensive as it requires nested simulation.  ...  In this paper, we explore the potential of Quasi Monte-Carlo (QMC) and Multilevel Monte-Carlo (MLMC) estimation to reduce computational cost of estimating EVPPI by reducing the variance compared with MC  ...  In addition, estimation based on the standard nested Monte Carlo method is biased [6, 7] .  ... 
doi:10.1101/2021.03.30.21254626 fatcat:2qxsoi57r5cqpoxoo7z6yfoviq

Nested Sampling with Constrained Hamiltonian Monte Carlo

M. J. Betancourt
2010 arXiv   pre-print
Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.  ...  An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution.  ...  Sampling Constrained Hamiltonian Monte Carlo (CHMC) naturally complements nested sampling by taking p (x) → π (α) C (x) → L (α) − L.  ... 
arXiv:1005.0157v1 fatcat:zf4zsk33rfed3ezig7wplby4pm

Combining UCT and Nested Monte Carlo Search for Single-Player General Game Playing

Jean Mehat, Tristan Cazenave
2010 IEEE Transactions on Computational Intelligence and AI in Games  
We compare Nested Monte-Carlo Search (NMC), Upper Confidence bounds for Trees (UCT-T), UCT with transposition tables (UCT+T) and a simple combination of NMC and UCT+T (MAX) on single-player games of the  ...  Monte-Carlo tree search has recently been very successful for game playing particularly for games where the evaluation of a state is difficult to compute, such as Go or General Games.  ...  Fig. 9 . 9 Average score with time at tpeg. tables (UCT+T), Nested Monte-Carlo Search (NMC) and a simple combination of UCT+T and Nested Monte-Carlo Search (MAX).  ... 
doi:10.1109/tciaig.2010.2088123 fatcat:hgp4ymfmyzelnbgpj5hgqhtija
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