Stochastic Gradient Markov Chain Monte Carlo

Nemeth, Christopher; Fearnhead, Paul

doi:10.1080/01621459.2020.1847120

Cited by 90 publications

(68 citation statements)

References 51 publications

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“…Zhou and Tartakovsky [13] proposed an adaptive MCMC method, in which a transmission model is replaced by a fast and accurate substitutive model that adopts a deep convolutional neural network to reduce calculation burden. For the shortcoming of MCMC, i.e., the huge amount of computation when the dataset is too large, Nemeth and Fearnhead [14] studied the latest development of scalable Monte Carlo algorithm for reducing computational cost of MCMC. In this paper, we focus on the stochastic gradient MCMC (SGMCMC), which uses the data subsampling technique to reduce the cost of each iteration of MCMC and to achieve good results.…”

Section: Introductionmentioning

confidence: 99%

A Fast and Efficient Markov Chain Monte Carlo Method for Market Microstructure Model

Sun

Peng

Xie

2021

Discrete Dynamics in Nature and Society

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The non-linear market microstructure (MM) model for financial time series modeling is a flexible stochastic volatility model with demand surplus and market liquidity. The estimation of the model is difficult, since the unobservable surplus demand is a time-varying stochastic variable in the return equation, and the market liquidity arises both in the mean term and in the variance term of the return equation in the MM model. A fast and efficient Markov Chain Monte Carlo (MCMC) approach based on an efficient simulation smoother algorithm and an acceptance-rejection Metropolis–Hastings algorithm is designed to estimate the non-linear MM model. Since the simulation smoother algorithm makes use of the band diagonal structure and positive definition of Hessian matrix of the logarithmic density, it can quickly draw the market liquidity. In addition, we discuss the MM model with Student-t heavy tail distribution that can be utilized to address the presence of outliers in typical financial time series. Using the presented modeling method to make analysis of daily income of the S&P 500 index through the point forecast and the density forecast, we find clear support for time-varying volatility, volatility feedback effect, market microstructure theory, and Student-t heavy tails in the financial time series. Through this method, one can use the estimated market liquidity and surplus demand which is much smoother than the strong stochastic return process to assist the transaction decision making in the financial market.

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Section: Introductionmentioning

confidence: 99%

A Fast and Efficient Markov Chain Monte Carlo Method for Market Microstructure Model

Sun

Peng

Xie

2021

Discrete Dynamics in Nature and Society

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“…Since we have introduced the randomness through the reparameterization trick in (3.9), as a remedy, we further exploit stochastic gradients instead to maximize the ELBO L. Stochastic gradients [14,18,145,151,163] are unbiased estimators of the exact gradients [5,15,129], but can be computed efficiently when the exact gradients cannot be calculated directly. In our case, we first draw a sample e from φ(e).…”

Section: Variational Bayesian Inference For Slammentioning

confidence: 99%

“…The gradients in (4.15) are referred to as stochastic gradients, and they are the unbiased expectations of the exact quantities in (4.13) [5,15,129]. With the stochastic gradients, we optimize the ELBO L in (4.12) iteratively.…”

Section: Stochastic Variational Bayesian Inference For Full Slam Problemmentioning

confidence: 99%

“…The covariance information is of great use in practical applications [16,25,57,64,143]. Stochastic gradients in Algorithm 1 can help to escape from poor solutions [5,15,129]. In addition, the uncertainty matrix simulates an annealing process [1,68] or smoothing-based optimization [202], contributing to a superior optimum [101,202].…”

Section: Algorithm Overview and Analysismentioning

confidence: 99%

“…This inference can be viewed as a smoothing-based optimization and can escape from shallow local extrema easily [101,202]. In addition, the employed stochastic gradients can also help to avoid poor solutions [5,15,129]. Considering the huge amount of points and real-time requirement, we further increase the processing speed via the SVRG method [73].…”

Section: Densitymentioning

confidence: 99%

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Visual and lidar-based SLAM by variational bayesian methods

Jiang¹

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The contributions of the co-authors are as follows:who has supported and encouraged me throughout the four years. His continuous support, immense knowledge, patience, and motivation helped me overcoming numerous obstacles I have been facing through my research. Also, his insightful suggestions and encouragement incented me to widen my research from various perspectives. When I am confused and depressed, he led me to the right path.Without his help, I could not have imagined completing this thesis. Very special gratitude goes out to NTU and STE-NTU corp lab for helping and providing the funding for my research work. My sincere thanks also go to Dr Hang Yu, Dr Michael Hoy, for their participation, feedback, cooperation and generous help in my research work. They guided and gave me a push when I am at a low ebb. I enjoyed working with them and learned a lot from them in those stimulating discussions. With their continuous help and hearty advice, I have arrived to the me who I am today. I am also grateful to my friends, who encouraged me to react positively under difficult conditions. Last but not least, I would like to thank my family: my parents and to my sister for supporting me spiritually throughout my PhD life. Love you, my family. All the experience in the four years, whatever sadness or joy, would be my treasure I cannot abandon in the rest of my life. ix "It always seems impossible until it's done."

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Discussion of “Specifying prior distributions in reliability applications”: Towards new formal rules for informative prior elicitation?

Bousquet¹

2023

Appl Stoch Models Bus & Ind

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SummaryThe article by Tian et al. (Appl. Stoch. Models Bus. Ind. 2023) takes an interesting look at the use of non‐informative priors adapted to several censoring processes, which are common in reliability. It proposes a continuum of modelling approaches that go as far as defining weakly informative priors to overcome the well‐known shortcomings of frequentist approaches to problems involving highly censored samples. In this commentary, I make some critical remarks and propose to link this work to a more generic vision of what could be a relevant Bayesian elicitation in reliability, taking advantage of recent theoretical and applied advances. Through tools like approximate posterior priors and prior equivalent sample sizes, and by illustrating them with simple reliability models, I suggest methodological avenues to formalize the elicitation of informative priors in a auditable, defensible way. By allowing a clear modulation of subjective information, this might respond to the authors' primary concern of constructing weakly informative priors and to a more general concern for precaution in Bayesian reliability.

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Stochastic Gradient Markov Chain Monte Carlo

Cited by 90 publications

References 51 publications

A Fast and Efficient Markov Chain Monte Carlo Method for Market Microstructure Model

A Fast and Efficient Markov Chain Monte Carlo Method for Market Microstructure Model

Visual and lidar-based SLAM by variational bayesian methods

Discussion of “Specifying prior distributions in reliability applications”: Towards new formal rules for informative prior elicitation?

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