8 results on '"target distribution"'
Search Results
2. The Self-Multiset Sampler
- Author
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Yuguo Chen, Juan Shen, and Weihong Huang
- Subjects
Statistics and Probability ,Multiset ,Generalization ,05 social sciences ,Sampling (statistics) ,Sample (statistics) ,01 natural sciences ,Target distribution ,Effective algorithm ,Markov chain monte carlo algorithm ,010104 statistics & probability ,Metropolis–Hastings algorithm ,0502 economics and business ,Statistics::Methodology ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Statistics, Probability and Uncertainty ,Algorithm ,050205 econometrics ,Mathematics - Abstract
The multiset sampler has been shown to be an effective algorithm to sample from complex multimodal distributions, but the multiset sampler requires that the parameters in the target distribution can be divided into two parts: the parameters of interest and the nuisance parameters. We propose a new self-multiset sampler (SMSS), which extends the multiset sampler to distributions without nuisance parameters. We also generalize our method to distributions with unbounded or infinite support. Numerical results show that the SMSS and its generalization have a substantial advantage in sampling multimodal distributions compared to the ordinary Markov chain Monte Carlo algorithm and some popular variants. Supplemental materials for the article are available online.
- Published
- 2017
- Full Text
- View/download PDF
3. Monitoring Joint Convergence of MCMC Samplers
- Author
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Douglas VanDerwerken and Scott C. Schmidler
- Subjects
0301 basic medicine ,Statistics and Probability ,Mathematical optimization ,Posterior probability ,Nonparametric statistics ,Markov chain Monte Carlo ,01 natural sciences ,Target distribution ,010104 statistics & probability ,03 medical and health sciences ,symbols.namesake ,Total variation ,030104 developmental biology ,Scalar projection ,symbols ,Discrete Mathematics and Combinatorics ,Partition (number theory) ,0101 mathematics ,Statistics, Probability and Uncertainty ,Cluster analysis ,Algorithm ,Mathematics - Abstract
We present a diagnostic for monitoring convergence of a Markov chain Monte Carlo (MCMC) sampler to its target distribution. In contrast to popular existing methods, we monitor convergence to the joint target distribution directly rather than a select scalar projection. The method uses a simple nonparametric posterior approximation based on a state-space partition obtained by clustering the pooled draws from multiple chains, and convergence is determined when the estimated posterior probabilities of partition elements under each chain are sufficiently similar. This framework applies to a wide variety of problems, and generalizes directly to non-Euclidean state spaces. Our method also provides approximate high-posterior-density regions, and a characterization of differences between nonconverged chains, all with little additional computational burden. We demonstrate this approach on applications to sampling posterior distributions over Rp, graphs, and partitions. Supplementary materials for this arti...
- Published
- 2017
- Full Text
- View/download PDF
4. Acquisition of a series of temperature-varied sample spectra to induce characteristic structural changes of components and selection of target-descriptive variables among them for multivariate analysis to improve accuracy
- Author
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Hoeil Chung, Junghye Lee, Chi-Hyuck Jun, and Kyeol Chang
- Subjects
Markov blanket ,Multivariate analysis ,business.industry ,Analytical chemistry ,Pattern recognition ,Feature selection ,02 engineering and technology ,021001 nanoscience & nanotechnology ,Spectral line ,Target distribution ,symbols.namesake ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Conditional independence test ,Snapshot (computer storage) ,020201 artificial intelligence & image processing ,Artificial intelligence ,0210 nano-technology ,business ,Raman spectroscopy ,Instrumentation ,Spectroscopy ,Mathematics - Abstract
As a means of improving the accuracy of Raman spectroscopic quantitative analysis, a strategy combining the generation of a series of temperature-varied spectra to make diverse and characteristic structural information of sample components widely available for calibration, and subsequent selection of more property-descriptive variables among these spectra, has been demonstrated. For the evaluation, Raman spectra of synthetic hydrocarbon mixtures, lube base oils (LBOs) and polyethylene (PE) pellets were acquired at regular intervals while the sample temperature gradually increased from cryogenic to near room temperature. To select target-descriptive variables from all of the snapshot (temperature-varied) spectra, a Markov blanket (MB) feature (variable) selection able to produce a minimal set of features without changing the original target distribution was adopted. The selection utilizes a conditional independence test to quickly obtain an optimal feature subset by simultaneously considering relev...
- Published
- 2016
- Full Text
- View/download PDF
5. Optimal chaotic selectors
- Author
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Paweł Góra, Abraham Boyarsky, and Zhenyang Li
- Subjects
Discrete mathematics ,Distribution function ,General Mathematics ,Bounded function ,Piecewise ,Chaotic ,Partition (number theory) ,Invariant (mathematics) ,Finite set ,Computer Science Applications ,Mathematics ,Target distribution - Abstract
Multivalued maps have many applications. We consider one-dimensional multivalued maps whose graphs are defined by lower and upper boundary maps. Let I = [0, 1] and let be a partition of I into a finite number of intervals. Let τl, τu: I → I be two piecewise expanding maps on such that τl ≤ τu. Let G ⊂ I×I be the region bounded by the graphs of τl and τu. Any map η: I → I that takes values in G is called a selector of the multivalued map defined by G. We assume that τl and τu as well as all the selectors we consider have invariant distribution functions. Let F* be a target distribution. We prove the existence of a selector η* which minimizes the functional , where η has invariant distribution Fη. Other results pertain to the functional , where Pη is the Frobenius–Perron operator of η acting on distribution functions. We present an algorithm for finding selectors which minimize J1(η).
- Published
- 2015
- Full Text
- View/download PDF
6. Two-Stage Importance Sampling With Mixture Proposals
- Author
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Wentao Li, Rong Chen, and Zhiqiang Tan
- Subjects
Statistics and Probability ,Sample size determination ,Maximum likelihood ,Statistics ,Econometrics ,Sampling (statistics) ,Estimator ,Sample (statistics) ,Stage (hydrology) ,Statistics, Probability and Uncertainty ,Importance sampling ,Mathematics ,Target distribution - Abstract
For importance sampling (IS), multiple proposals can be combined to address different aspects of a target distribution. There are various methods for IS with multiple proposals, including Hesterberg's stratified IS estimator, Owen and Zhou's regression estimator, and Tan's maximum likelihood estimator. For the problem of efficiently allocating samples to different proposals, it is natural to use a pilot sample to select the mixture proportions before the actual sampling and estimation. However, most current discussions are in an empirical sense for such a two-stage procedure. In this article, we establish a theoretical framework of applying the two-stage procedure for various methods, including the asymptotic properties and the choice of the pilot sample size. By our simulation studies, these two-stage estimators can outperform estimators with naive choices of mixture proportions. Furthermore, while Owen and Zhou's and Tan's estimators are designed for estimating normalizing constants, we extend their usa...
- Published
- 2013
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7. Adaptive tree bucking using group-guiding of harvesters: A simulation approach
- Author
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Lasse Tikkanen, Heikki Ovaskainen, and Teijo Palander
- Subjects
Tree (data structure) ,Cross-cutting ,Reference simulation ,Group (mathematics) ,Log-normal distribution ,Logging ,Statistics ,Forestry ,Mathematics ,Target distribution - Abstract
The objective of this study was to test harvester group-guiding methods by comparing how the total log output distribution of independent harvesters differs from the total log output distribution of group-guided harvesters. In this simulation study four harvesters worked in their own stands in the same region for an identical target, given by a sawmill. Group-guiding was done by utilizing other harvesters’ bucking outcomes to fulfil the target log distribution better. Harvesters were combined to form a group in an adapting phase where a new price list was formed. For group-guiding, four different price list adapting methods were developed. There were five different simulations: four with adaptation and one reference simulation without adaptation. Apportionment degree and log/pulpwood proportions were calculated to compare the difference between the methods and reference simulation. With group-guiding, by adapting the price list harvesters reached the target distribution better than working indepe...
- Published
- 2009
- Full Text
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8. Weighted Average Importance Sampling and Defensive Mixture Distributions
- Author
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Tim Hesterberg
- Subjects
Statistics and Probability ,Normalization (statistics) ,Applied Mathematics ,Modeling and Simulation ,Monte Carlo method ,Statistics ,Mixture distribution ,Variance reduction ,Weighted arithmetic mean ,Importance sampling ,Mathematics ,Target distribution ,Weighting - Abstract
Importance sampling uses observations from one distribution to estimate for another distribution by weighting the observations. Including the target distribution as one component of a mixture distribution bounds the weights and makes importance sampling more reliable. The usual importance-sampling estimate is a weighted average with weights that do not sum to 1. We discuss simple normalization and other, more efficient normalization methods. These innovations make importance sampling useful in a wider variety of problems. We demonstrate with a case study of oil-inventory reliability at a large utility.
- Published
- 1995
- Full Text
- View/download PDF
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