Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion)

By Alexandros Beskos, Omiros Papaspiliopoulos, Gareth O. Roberts, Paul Fearnhead. 2006

415 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cf43e1d50a7f8314f9a2bb8fef4c7fcb9d1172a3

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Citations in the corpus

To Center or Not to Center: That Is Not the Question—An Ancillarity–Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Efficiency (2011, background): “, NCP) for discretely observed diffusion processes (Papaspiliopoulos, Roberts, and Skold 2003; Beskos et al. 2006).”
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (2009, methodology): “First, even though VB methods seem often to approximate well the posterior mode (Wang and Titterington, 2006), the posterior variance can be (sometimes severely) underestimated; see Bishop (2006), chapter 10, and Wang and Titterington (2005).”
Statistical inference for dynamical systems: A review (2012, methodology): “Using this algorithm, the authors further develop a framework for statistical inference [12].”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, methodology): “…and artiﬁcial intelligence, to dynamical models driven by ODE’s (Wilkinson 2011b) and diﬀusions (Roberts and Stramer 2001; Dellaportas et al. 2004; Beskos et al. 2006), hidden trees (Larget and Simon 1999; Huelsen-beck and Ronquist 2001; Chipman et al. 2008; Aldous et al. 2008) and graphs, aside…”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, methodology): “1996) which were initially the focus, and graphical models that stemmed from image analysis (Geman and Geman 1984) and artificial intelligence, to dynamical models driven by ODE’s (Wilkinson 2011b) and diffusions (Roberts and Stramer 2001; Dellaportas et al. 2004; Beskos et al. 2006), hidden trees (”
Variational Inference for Diffusion Processes (2007, methodology): “In statistics the problem of Bayesian inference for both the state and parameters, within partially observed, non-linear diffusion processes has been tackled using Markov Chain Monte Carlo (MCMC) approaches based on data augmentation [17, 11], Monte Carlo exact simulation methods [6], or Langevin / ”
Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods (2014, methodology): “This problem is well-known to pose challenges for Bayesian computation and recent work in this direction includes (Beskos et al., 2006; Golightly and Wilkinson, 2008).”
Maximum-likelihood estimation for diffusion processes via closed-form density expansions (2013, methodology): “[16], Beskos, Papaspiliopoulos and Roberts [15] and Elerian, Chib and Shephard [28] advocated the application of various Monte Carlo simulation methods; Yu and Phillips [73] developed an exact Gaussian method for models with a linear drift function; Jensen and Poulsen [36] resorted to the techniques”
Nonparametric estimation of diffusions: a differential equations approach (2012, methodology): “In particular, we analyze the well- 16 known Eurodollar dataset, which consists of 5505 daily Eurodollar rates between 1973 and 1995, which are shown in Figure 3, and has been analyzed among others by Aı̈t-Sahalia (1996); Roberts & Stramer (2001); Beskos et al. (2006).”
Applied Stochastic Differential Equations (2019, neutral): “In so-called continuous-discrete filtering (continuous-time dynamics, discrete-time measurements), the theorem has turned out to be useful in constructing importance sampling and exact sampling methods for conditioned SDEs (Beskos et al., 2006a; Särkkä and Sottinen, 2008).”
Stochastic Normalizing Flows (2020, methodology): “This allows one to estimate the Kullback-Leibler divergence between densities of solutions to two SDEs (for the prior and posterior distributions) with diﬀering drift coeﬃcients (Beskos et al., 2006; Tzen & Raginsky, 2019).”
A General Framework for the Parametrization of Hierarchical Models (2007, methodology): “1 below has recently been found necessary in order to construct MCMC algorithms for inference for discretely observed diffusion processes in [2].”