Skip to main content
Article thumbnail
Location of Repository

Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC.

By Paul Fearnhead


We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing convergence. Here we review three alternatives to MCMC methods: importance sampling, the forward-backward algorithm, and sequential Monte Carlo (SMC). We discuss how to design good proposal densities for importance sampling, show some of the range of models for which the forward-backward algorithm can be applied, and show how resampling ideas from SMC can be used to improve the efficiency of the other two methods. We demonstrate these methods on a range of examples, including estimating the transition density of a diffusion and of a discrete-state continuous-time Markov chain; inferring structure in population genetics; and segmenting genetic divergence data

Year: 2008
OAI identifier:
Provided by: Lancaster E-Prints

Suggested articles


  1. (1973). A Bayesian analysis of some nonparametric problems. doi
  2. (1996). A Hidden Markov Model approach to variation among sites in rate of evolution. Molecular Biology and Evolution, doi
  3. (1995). A new approach to maximum likelihood estimation of stochastic differential equations based on discrete observations.
  4. (2007). A randomized quasi-Monte carlo simulation method for Markov chains. doi
  5. (2003). A sequential Monte Carlo method for Bayesian analysis of massive datasets. Data Mining and Knowledge Discovery, doi
  6. (1986). An introduction to hidden Markov models. doi
  7. (2002). Approximate likelihood methods for estimating local recombination rates (with discussion). doi
  8. (2002). Assessing population differentiation and isolation from single-nucleotide polymorphism data.
  9. (2000). Association mapping in structured populations. doi
  10. (2007). Asymptotics of an efficient Monte Carlo estimation for the transition density of diffusion processes. doi
  11. (1999). Bayesian analysis of a two state Markov modulated Poisson process. doi
  12. (2007). Bayesian analysis of isochores. doi
  13. (2006). Bayesian analysis of Markov modulated Poisson processes. doi
  14. (1989). Bayesian forecasting and dynamic models. doi
  15. (2005). Bayesian inference for stochastic kinetic models using a diffusion approximation. doi
  16. (1999). Bayesian inference on biopolymer models. doi
  17. (2002). Bayesian methods for hidden Markov models: Recursive computing in the 21st century. doi
  18. (2006). Bayesian sequential inference for stochastic kinetic biochemical network models. doi
  19. (1998). Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. doi
  20. (1995). Blind deconvolution via sequential imputations. doi
  21. (2007). Calibrating the rate of evolution of campylobacter.
  22. (2007). Coalescent Theory: An Introduction. Roberts and Company, doi
  23. (2001). Combined parameter and state estimation in simulation based filtering. doi
  24. (1987). Construction of multilocus genetic linkage maps in humans. doi
  25. Equations of state calculations by fast computing machines. doi
  26. (2006). Equi-energy sampler with applications in statistical inference and statistical mechanics. doi
  27. (2001). Estimating recombination rates from population genetic data.
  28. (1984). Estimation of a noisy discrete-time step function: Bayes and empirical Bayes approaches. The Annals of Statistics, doi
  29. (2006). Exact and efficient inference for multiple changepoint problems. doi
  30. (2005). Exact Bayesian curve fitting and signal segmentation. doi
  31. (2004). Exact filtering for partially-observed continuoustime Markov models. doi
  32. (2001). Factor graphs and the sum-product algorithm. doi
  33. (1999). Filtering via simulation: auxiliary particle filters. doi
  34. (2001). Following a moving target - Monte Carlo inference for dynamic Bayesian models. doi
  35. (2002). Genetic structure of human populations.
  36. (1991). Hidden Markov models for speech recognition. doi
  37. (2000). Inference in molecular population genetics (with discussion). doi
  38. (2003). Inference of population structure using multilocus genotype data: Linked loci and correlated allele frequencies. doi
  39. (2000). Inference of population structure using multilocus genotype data. doi
  40. (2005). Joint Bayesian estimation of alignment and phylogeny. Systematic Biology, doi
  41. (2006). Markov Chain Monte Carlo: Stochastic Simulation For Bayesian Inference. doi
  42. (2003). Markov chain sampling for non-linear state space models using embedded hidden Markov models. Available from∼radford/embhmm.abstract.html.
  43. (2002). MCMC, sufficient statistics and particle filters. doi
  44. (1996). Metropolised independent sampling with comparisons to rejection sampling and importance sampling. doi
  45. Mismatch induced speciation in Salmonella: model and data. doi
  46. (1998). Monte Carlo approximations for general state-space models. doi
  47. (1996). Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. doi
  48. (2005). Monte Carlo filters:Algorithms and theoretical analysis. doi
  49. (2004). Monte Carlo smoothing for non-linear time series. doi
  50. (1998). Multilocus sequence typing: A portable approach to the identification of clones within populations of pathogenic microorganisms. doi
  51. (1961). New results in linear filtering and prediction theory. doi
  52. (2003). Non-centred parameterisations for hierarchical models and data augmentation (with discussion).
  53. (1993). Novel approach to nonlinear/nonGaussian Bayesian state estimation. doi
  54. (1992). Numerical solution of stochastic differential equations. doi
  55. (2002). Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes. doi
  56. (2001). On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm. doi
  57. (2007). On population-based simulation for statics inference. Statistics and Computing, doi
  58. (2007). On population-based simulation for statistical inference. Statistics and Computing. doi
  59. (2007). On simulated likelihood of discretely observed diffusion processes and comparison to closed form approximation. doi
  60. (2003). Online inference for hidden Markov models. doi
  61. (2007). Online inference for multiple changepoint problems. doi
  62. (1995). Origins and affinities of modern humans: a comparison of mitochondrial and nuclear genetic data.
  63. (2004). Particle filters for mixture models with an unknown number of components. doi
  64. (2007). Particle filters for partiallyobserved diffusions. doi
  65. (2002). Particle filters for state-space models with the presence of unknown static parameters. doi
  66. (1999). Problems with computational methods in population genetics. Contribution to the 52nd session of the International Statistical Institute.
  67. (1998). Rejection control and sequential importance sampling. doi
  68. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. doi
  69. (1994). Sequential imputations and Bayesian missing data problems. doi
  70. (1998). Sequential Monte Carlo methods for dynamic systems. doi
  71. (1996). Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statistica Sinica,
  72. (2007). Smooth particle filters for likelihood evaluation and maximisation. doi
  73. (2006). Stochastic Modelling for Systems Biology. doi
  74. (1987). Stochastic Simulation. doi
  75. (1982). The coalescent. Stochastic Processes and their Applications, doi
  76. (2002). The common ancestor at a non-neutral locus. doi
  77. (1964). The number of alleles that can be maintained in a finite population. doi
  78. (2000). Times on trees and the age of an allele. Theoretical Population Biology, doi
  79. (1994). Unrooted genealogical tree probabilities in the infinitelymany-sites model. doi
  80. (2005). Using random Quasi-Monte Carlo within particle filters, with application to financial time series. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.