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143
Bayesian Inference for Stochastic Kinetic Models Using a Diffusion Approximation
, 2005
"... This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white no ..."
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Cited by 60 (16 self)
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This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m − 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.
Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo
, 2011
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Parametric Inference for Diffusion Processes Observed At Discrete Points in Time: A Survey
"... This paper is a survey of existing estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and socalled simple es ..."
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Cited by 52 (1 self)
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This paper is a survey of existing estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and socalled simple estimating functions; (ii) analytical and numerical approximations of the likelihood which can in principle be made arbitrarily accurate; (iii) Bayesian analysis and MCMC methods; and (iv) indirect inference and EMM which both introduce auxiliary (but wrong) models and correct for the implied bias by simulation
Continuoustime methods in finance: A review and an assessment
 Journal of Finance
, 2000
"... I survey and assess the development of continuoustime methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. ..."
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Cited by 52 (0 self)
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I survey and assess the development of continuoustime methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. During the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance. This latter subperiod has seen significant progress in econometric theory, computational and estimation methods to test and implement continuoustime models. Capital market frictions and bargaining issues are being increasingly incorporated in continuoustime theory. THE ROOTS OF MODERN CONTINUOUSTIME METHODS in finance can be traced back to the seminal contributions of Merton ~1969, 1971, 1973b! in the late 1960s and early 1970s. Merton ~1969! pioneered the use of continuoustime modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting.
Bayesian sequential inference for nonlinear multivariate diffusions
 Statistics and Computing
, 2006
"... In this paper, we adapt recently developed simulationbased sequential algorithms to the problem concerning the Bayesian analysis of discretely observed diffusion processes. The estimation framework involves the introduction of m −1 latent data points between every pair of observations. Sequential ..."
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Cited by 51 (6 self)
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In this paper, we adapt recently developed simulationbased sequential algorithms to the problem concerning the Bayesian analysis of discretely observed diffusion processes. The estimation framework involves the introduction of m −1 latent data points between every pair of observations. Sequential MCMC methods are then used to sample the posterior distribution of the latent data and the model parameters online. The method is applied to the estimation of parameters in a simple stochastic volatility model (SV) of the U.S. shortterm interest rate. We also provide a simulation study to validate our method, using synthetic data generated by the SV model with parameters calibrated to match weekly observations of the U.S. shortterm interest rate. 1
Optimal filtering of jump diffusions: extracting latent states from asset prices
, 2007
"... This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing mo ..."
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Cited by 44 (8 self)
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This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines timediscretization schemes with Monte Carlo methods to compute the optimal filtering distribution. Our approach is very general, applying in multivariate jumpdiffusion models with nonlinear characteristics and even nonanalytic observation equations, such as those that arise when option prices are available. We provide a detailed analysis of the performance of the filter, and analyze four applications: disentangling jumps from stochastic volatility, forecasting realized volatility, likelihood based model comparison, and filtering using both option prices and underlying returns.
MCMC methods for continuoustime financial econometrics

, 2003
"... This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuoustime asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for explor ..."
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Cited by 41 (1 self)
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This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuoustime asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for exploring these highdimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the CliffordHammersley theorem, the Gibbs sampler, the MetropolisHastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuoustime asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regimeswitching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables.
Estimating Functions for Discretely Sampled DiffusionType Models
 IN FESTSCHRIFT FOR LUCIEN LE CAM: RESEARCH PAPERS IN PROBABILITY AND STATISTICS
, 2004
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Practical Filtering with Sequential Parameter Learning
, 2003
"... In this paper we develop a general simulationbased approach to filtering and sequential parameter learning. We begin with an algorithm for filtering in a general dynamic state space model and then extend this to incorporate sequential parameter learning. The key idea is to express the filtering ..."
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Cited by 40 (8 self)
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In this paper we develop a general simulationbased approach to filtering and sequential parameter learning. We begin with an algorithm for filtering in a general dynamic state space model and then extend this to incorporate sequential parameter learning. The key idea is to express the filtering distribution as a mixture of lagsmoothing distributions and to implement this sequentially. Our approach has a number of advantages over current methodologies. First, it allows for sequential parmeter learning where sequential importance sampling approaches have difficulties. Second
Bayesian estimation of continuoustime finance models
, 1999
"... A new Bayesian method is proposed for the analysis of discretely sampled diffusion processes. The method, which is termed high frequency augmentation (HFA), is a simple numerical method that is applicable to a wide variety of univariate or multivariate diffusion and jumpdiffusion processes. It is f ..."
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Cited by 39 (3 self)
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A new Bayesian method is proposed for the analysis of discretely sampled diffusion processes. The method, which is termed high frequency augmentation (HFA), is a simple numerical method that is applicable to a wide variety of univariate or multivariate diffusion and jumpdiffusion processes. It is furthermore useful when observations are irregularly observed, when one or more elements of the multivariate process are latent, or when microstructure effects add error to the observed data. The Markov chainMonte Carlobased procedure can be used to attain the posterior distributions of the parameters of the drift and diffusion functions as well as the posteriors of missing or latent data. Several examples are explored. First, posteriors of the parameters of a geometric Brownian motion are attained using HFA and compared with those obtained using standard analytical methods in a short Monte Carlo study. Second, a stochastic volatility model is estimated on a sample of S&P500 returns, a problem for which posteriors are analytically intractable. Third, it is shown how the method can be used to estimate an interest rate process using data that suffer from severe rounding. Finally, extension of the method to jumpdiffusions is described and applied to the analysis of the U.S dollar/German mark exchange rate.