Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods

Bauwens, Luc; Bos, Charles S.; Dijk, Herman K. van; Oest, Rutger D. van

doi:10.1016/j.jeconom.2003.12.002

Cited by 20 publications

(33 citation statements)

References 18 publications

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“…However, Bauwens et al (2004) show that actually any elliptically contoured candidate distribution can be considered without affecting the sampling results. After defining RMHS, we will define the adaptive RMHS algorithm [ARMHS], where µ and Σ are iteratively updated using the sample of draws from a previous round of the RMHS algorithm.…”

Section: Radial-based Metropolis-hastings Samplingmentioning

confidence: 99%

“…Adaptive radial-based direction sampling [ARDS] methods, due to Bauwens et al (2004), constitute a class of Monte Carlo integration methods that involve a transformation from the usual Carthesian coordinates to radial coordinates. The ARDS algorithms can be especially useful for Bayesian inference in models with non-elliptical, possibly multi-modal target distributions.…”

Section: Adaptive Radial-based Direction Samplingmentioning

confidence: 99%

“…In order to illustrate the advantages of the ARDS methods, we investigate a mixture model for the analysis of economic growth in the USA, which is also considered by Bauwens et al (2004). Bauwens et al (2004) compare the performance of the ARDS methods with the (independence chain) Metropolis-Hastings algorithm and importance sampling with a Student-t candidate distribution (with 5 degrees of freedom).…”

Section: Adaptive Radial-based Importance Samplingmentioning

confidence: 99%

“…Bauwens et al (2004) compare the performance of the ARDS methods with the (independence chain) Metropolis-Hastings algorithm and importance sampling with a Student-t candidate distribution (with 5 degrees of freedom). They compare estimation results after a given computing time with the 'true' results -estimation results after many more draws -and inspect the graphs of estimated marginal densities resulting from different sampling methods.…”

Section: Adaptive Radial-based Importance Samplingmentioning

confidence: 99%

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Simulation Based Bayesian Econometric Inference: Principles and Some Recent Computational Advances

2007

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In this paper we discuss several aspects of simulation based Bayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluating integrals by simulation methods is a crucial ingredient in Bayesian inference. Next, the most popular and well-known simulation techniques are discussed, the Metropolis-Hastings algorithm and Gibbs sampling (being the most popular Markov chain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed sampling methods: adaptive radial based direction sampling [ARDS], which makes use of a transformation to radial coordinates, and neural network sampling, which makes use of a neural network approximation to the posterior distribution of interest. Both methods are especially useful in cases where the posterior distribution is not well-behaved, in the sense of having highly non-elliptical shapes. The simulation techniques are illustrated in several example models, such as a model for the real US GNP and models for binary data of a US recession indicator.JEL classification: C11, C12, C15, C45, C52

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Section: Radial-based Metropolis-hastings Samplingmentioning

confidence: 99%

Section: Adaptive Radial-based Direction Samplingmentioning

confidence: 99%

Section: Adaptive Radial-based Importance Samplingmentioning

confidence: 99%

Section: Adaptive Radial-based Importance Samplingmentioning

confidence: 99%

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Simulation Based Bayesian Econometric Inference: Principles and Some Recent Computational Advances

2007

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“…Strachan (2003) employs this approach when has been identi…ed using restrictions related to those of the ML estimator of Johansen (1992). Alternatively one may use the Adaptive Radial based method of Bauwens, Bos, van Dijk and van Oest (2004) or the neural network mixture method of Hoogerheide, Kaashoek and van Dijk (2006). Bauwens and Lubrano (1996) and Strachan and Inder (2004) demonstrate other approaches.…”

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confidence: 99%

Bayesian Averaging over Many Dynamic Model Structures with Evidence on the Great Ratios and Liquidity Trap Risk

Strachan

Dijk

2008

SSRN Journal

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A Bayesian model averaging procedure is presented that makes use of a …nite mixture of many model structures within the class of vector autoregressive (VAR) processes. It is applied to two empirical issues. First, stability of the "Great Ratios" in U.S. macro-economic time series is investigated, together with the e¤ect of permanent shocks on business cycles. Second, the linear VAR model is extended to include a smooth transition function in a (monetary) equation and stochastic volatility in the disturbances. The risk of a liquidity trap in the USA and Japan is evaluated. Although this risk found to be reasonably high, we …nd only mild evidence that the monetary policy transmission mechanism is di¤erent and that central banks consider the expected cost of a liquidity trap in policy setting. Posterior probabilities of di¤erent models are evaluated using Markov chain Monte Carlo techniques.

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Simulation‐Based Bayesian Econometric Inference: Principles and Some Recent Computational Advances

Hoogerheide

Dijk

Oest

2009

Handbook of Computational Econometrics

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In this chapter we discuss several aspects of simulation-based Bayesian econometric inference (SBBEI). Broadly speaking, SBBEI deals with probabilistic inference on features of interest in econometric models, such as the probability of a recession, using simulation methods. In recent decades there has been a 'simulation revolution,' a huge increase in the use of simulation methods for SBBEI, which is to a large extent due to the advent of computers with increased computational power -see, for example, the discussions in Geweke (1999), Van Dijk (1999), andHamilton (2006). This computational power allows researchers to apply elaborate simulation techniques for Bayesian inference in which extensive use is made of pseudo-random numbers generated on computers.The basic principle in this line of research is that, in most cases of empirical econometric models, one cannot directly simulate from the distribution of interest, for example the distribution of the length of the business cycle. So one applies instead an indirect

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Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods

Cited by 20 publications

References 18 publications

Simulation Based Bayesian Econometric Inference: Principles and Some Recent Computational Advances

Simulation Based Bayesian Econometric Inference: Principles and Some Recent Computational Advances

Bayesian Averaging over Many Dynamic Model Structures with Evidence on the Great Ratios and Liquidity Trap Risk

Simulation‐Based Bayesian Econometric Inference: Principles and Some Recent Computational Advances

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