Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAdaptive MCMC for Generalized Method of Moments with Many Moment Conditions
47
0
0.0
(
0
)
Added by
Masahiro Tanaka
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
Authors
Masahiro Tanaka
Ask ChatGPT about the research
No Arabic abstract
A generalized method of moments (GMM) estimator is unreliable for a large number of moment conditions, that is, it is comparable, or larger than the sample size. While classical GMM literature proposes several provisions to this problem, its Bayesian counterpart (i.e., Bayesian inference using a GMM criterion as a quasi-likelihood) almost totally ignores it. This study bridges this gap by proposing an adaptive Markov Chain Monte Carlo (MCMC) approach to a GMM inference with many moment conditions. Particularly, this study focuses on the adaptive tuning of a weighting matrix on the fly. Our proposal consists of two elements. The first is the use of the nonparametric eigenvalue-regularized precision matrix estimator, which contributes to numerical stability. The second is the random update of a weighting matrix, which substantially reduces computational cost, while maintaining the accuracy of the estimation. We then present a simulation study and real data application to compare the performance of the proposed approach with existing approaches.
rate research
Read More
It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly with dataset size. A popular class of methods for solving this issue is stochastic gradient MCMC. These methods use a noisy estimate of the gradient of the log posterior, which reduces the per iteration computational cost of the algorithm. Despite this, there are a number of results suggesting that stochastic gradient Langevin dynamics (SGLD), probably the most popular of these methods, still has computational cost proportional to the dataset size. We suggest an alternative log posterior gradient estimate for stochastic gradient MCMC, which uses control variates to reduce the variance. We analyse SGLD using this gradient estimate, and show that, under log-concavity assumptions on the target distribution, the computational cost required for a given level of accuracy is independent of the dataset size. Next we show that a different control variate technique, known as zero variance control variates can be applied to SGMCMC algorithms for free. This post-processing step improves the inference of the algorithm by reducing the variance of the MCMC output. Zero variance control variates rely on the gradient of the log posterior; we explore how the variance reduction is affected by replacing this with the noisy gradient estimate calculated by SGMCMC.
In this paper, we introduce efficient ensemble Markov Chain Monte Carlo (MCMC) sampling methods for Bayesian computations in the univariate stochastic volatility model. We compare the performance of our ensemble MCMC methods with an improved version of a recent sampler of Kastner and Fruwirth-Schnatter (2014). We show that ensemble samplers are more efficient than this state of the art sampler by a factor of about 3.1, on a data set simulated from the stochastic volatility model. This performance gain is achieved without the ensemble MCMC sampler relying on the assumption that the latent process is linear and Gaussian, unlike the sampler of Kastner and Fruwirth-Schnatter.
Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it also potentially induces a lengthy exploration of this target, with a requirement on the number of simulations that grows with the dimension of the problem and with the complexity of the data behind it. Several techniques are available towards accelerating the convergence of these Monte Carlo algorithms, either at the exploration level (as in tempering, Hamiltonian Monte Carlo and partly deterministic methods) or at the exploitation level (with Rao-Blackwellisation and scalable methods).
Motivated by the physics of strings and branes, we introduce a general suite of Markov chain Monte Carlo (MCMC) suburban samplers (i.e., spread out Metropolis). The suburban algorithm involves an ensemble of statistical agents connected together by a random network. Performance of the collective in reaching a fast and accurate inference depends primarily on the average number of nearest neighbor connections. Increasing the average number of neighbors above zero initially leads to an increase in performance, though there is a critical connectivity with effective dimension d_eff ~ 1, above which groupthink takes over, and the performance of the sampler declines.
We introduce an efficient MCMC sampling scheme to perform Bayesian inference in the M/G/1 queueing model given only observations of interdeparture times. Our MCMC scheme uses a combination of Gibbs sampling and simple Metropolis updates together with three novel shift and scale updates. We show that our novel updates improve the speed of sampling considerably, by factors of about 60 to about 180 on a variety of simulated data sets.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
