Nested sampling algorithm

About: Nested sampling algorithm is a research topic. Over the lifetime, 407 publications have been published within this topic receiving 19119 citations.

MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics

Abstract: We present further development and the first public release o f our multimodal nested sampling algorithm, called MULTINEST. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior s amples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantia l improvements in sampling efficiency and robustness, as compared to the original algorit hm presented in Feroz & Hobson (2008), which itself significantly outperformed existi ng MCMC techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MULTINEST algorithm is demonstrated by application to two toy problems and to a cosmological in

Data analysis : a Bayesian tutorial

Abstract: 1. The Basics 2. Parameter Estimation I 3. Parameter Estimation II 4. Model Selection 5. Assigning Probabilities 6. Non-parametric Estimation 7. Experimental Design 8. Least-Squares Extensions 9. Nested Sampling 10. Quantification Appendices Bibliography

A Typology of Mixed Methods Sampling Designs in Social Science Research

Abstract: This paper provides a framework for developing sampling designs in mixed methods research. First, we present sampling schemes that have been associated with quantitative and qualitative research. Second, we discuss sample size considerations and provide sample size recommendations for each of the major research designs for quantitative and qualitative approaches. Third, we provide a sampling design typology and we demonstrate how sampling designs can be classified according to time orientation of the components and relationship of the qualitative and quantitative sample. Fourth, we present four major crises to mixed methods research and indicate how each crisis may be used to guide sampling design considerations. Finally, we emphasize how sampling design impacts the extent to which researchers can generalize their findings. Key Words: Sampling Schemes, Qualitative Research, Generalization, Parallel Sampling Designs, Pairwise Sampling Designs, Subgroup Sampling Designs, Nested Sampling Designs, and Multilevel Sampling Designs

Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses

Abstract: In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional Markov Chain Monte Carlo (MCMC) sampling methods. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. The nested sampling method introduced by Skilling, has greatly reduced the computational expense of calculating evidence and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee, Parkinson & Liddle, but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw, Bridges & Hobson recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to two toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical data sets, and show that they significantly outperform existing MCMC techniques. An implementation of our methods will be publicly released shortly.

Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis

Abstract: In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional MCMC sampling methods. Second, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive. The nested sampling method introduced by Skilling (2004), has greatly reduced the computational expense of calculating evidences and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee et al. (2006), but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw et al. (2007), recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical datasets.