On inference for partially observed nonlinear diffusion models using the Metropolis–Hastings algorithm

By Gareth O. Roberts, Osnat Stramer. 2001

340 citations recorded by the source corpus.

Subfields: Finance, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a82efd78e2c602ec17e775f371817ab1b8c1d177

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Citations in the corpus

Black-Box Variational Inference for Stochastic Differential Equations (2018, methodology): “Bridge constructs can be used to produce proposals within Monte Carlo algorithms such as MCMC (see e.g. Roberts & Stramer 2001; Golightly & Wilkinson 2008; Fuchs 2013; van der Meulen et al. 2017).”
Analysis of the Gibbs Sampler for Hierarchical Inverse Problems (2013, methodology): “In order to alleviate the undesirable eﬀects of the strong dependence between the prior on u and δ , using intuition from [34, 37], we reparametrize the prior by writing u = δ − 12 v where v ∼ N (0 , C 0 ) and δ ∼ P ( δ ).”
Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion) (2006, methodology): “We fit the CIR model to a well-studied data set (used among others by Aït-Sahalia (1996), Elerian et al. (2001) and Roberts and Stramer (2001)) which contains daily euro–dollar rates between 1973 and 1995, to allow for comparisons with existing methods.”
Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes (2009, methodology): “Thus, inference is carried out using either non-likelihood approaches, such as estimating equations [10], efficient method of moments [20] and indirect inference [25], or approximate likelihood-based approaches, such as computationally intensive Markov chain Monte-Carlo imputation methods [17, 18, 3”
Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo (2011, methodology): “In the case where the model cannot be fitted exactly in continuous time (i.e. Euler discretizations are adopted), there is a vast literature concerning the difficulties of Markov chain Monte Carlo (MCMC) inference; see Roberts & Stramer (2001) and more recently Kalogeropoulos et al. (2007).”
A General Framework for the Parametrization of Hierarchical Models (2007, background): “Roberts and Stramer [38] suggested an alternative reparametrization X∗, which qualifies to be called noncentered only when b = 0 (a case, however, which has motivated the construction).”
Plug-and-play inference for disease dynamics: measles in large and small populations as a case study (2009, background): “…have been demonstrated for small populations with purely demographic stochasticity (Gibson & Renshaw 1998, 2001); however, these methods break down for large populations (Roberts & Stramer 2001; Beskos et al. 2006) or when environmental stochasticity is non-negligible (Bretó et al. 2009).”
Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions (2015, methodology): “Alternative methodology for nonparametric inference in diffusion models has been put forward recently, notably of a Bayesian flavour, see Roberts and Stramer [24], Papaspiliopoulos et al. [20], Pokern et al. [22], van der Meulen et al. [30], van Waaij and van Zanten [34] and references therein.”
Statistical inference for discretely observed Markov jump processes (2005, background): “A few recent references are Kessler and Sørensen (1999), Hoffmann (1999), Roberts and Stramer (2001), Elerian et al. (2001), Aı̈t-Sahalia (2002) and Bibby et al. (2004).”
On Simulated Likelihood of Discretely Observed Diffusion Processes and Comparison to Closed-Form Approximation (2007, methodology): “It has also been used in a Bayesian context to break the dependency between simulated paths and the volatility of the diffusions (Roberts and Stramer 2001).”
CHAPTER 4 – Estimating Functions for Discretely Sampled Diffusion-Type Models (2010, methodology): “Bayesian estimators with the same asymptotic properties as the maximum likelihood estimator can be obtained by Markov chain Monte Carlo methods, see Elerian, Chib & Shephard (2001), Eraker (2001), Roberts & Stramer (2001), and Johannes & Polson (2003).”
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster (2012, background): “In this case, understanding the problem in the limit where the augmented data (y, z) is a function is key to developing sampling algorithms which do not slow down as the amount of augmentation is increased [53]: naive algorithms for the sampling of the parameter u and latent function z are not ergod”
Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations (2006, methodology): “Bayesian analysis of discretely observed SDEs has been studied independently by Elerian, Chib and Shephard (2001), Eraker (2001), Roberts and Stramer (2001) and Jones (1998).”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, methodology): “…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 (Larget and Simon 1999; Huelsen-beck and Ronquist 2001; Chipman…”