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Spectral subsampling MCMC was recently proposed to speed up Markov chain Monte Carlo (MCMC) for long stationary univariate time series by subsampling periodogram observations in the frequency domain. This article extends the approach to multivariate time series using a multivariate generalisation of the Whittle likelihood. To assess the computational gains from spectral subsampling in challenging problems, a multivariate generalisation of the autoregressive tempered fractionally integrated moving average model (ARTFIMA) is introduced and some of its properties derived. Bayesian inference based on the Whittle likelihood is demonstrated to be a fast and accurate alternative to the exact time domain likelihood. Spectral subsampling is shown to provide up to two orders of magnitude additional speed-up, while retaining MCMC sampling efficiency and accuracy, compared to spectral methods using the full dataset. Keywords: Bayesian, Markov chain Monte Carlo, Semi-long memory, Spectral analysis, Whittle likelihood.

We show how to speed up sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is easy to sample from such as the prior and ending with the posterior distribution. Each update of the particle cloud consists of three steps: reweighting, resampling, and moving. In the move step, each particle is moved using a Markov kernel; this is typically the most computationally expensive part, particularly when the dataset is large. It is crucial to have an efficient move step to ensure particle diversity. Our article makes two important contributions. First, in order to speed up the SMC computation, we use an approximately unbiased and efficient annealed likelihood estimator based on data subsampling. The subsampling approach is more memory efficient than the corresponding full data SMC, which is an advantage for parallel computation. Second, we use a Metropolis within Gibbs kernel with two conditional updates. A Hamiltonian Monte Carlo update makes distant moves for the model parameters, and a block pseudo-marginal proposal is used for the particles corresponding to the auxiliary variables for the data subsampling. We demonstrate both the usefulness and limitations of the methodology for estimating four generalized linear models and a generalized additive model with large datasets.

The Keller–Segel (KS) model is a system of partial differential equations that describe chemotaxis—how cells move in response to chemical stimulus. Simulated data in the form of cell counts are used to carry out Bayesian inference on the ks model. A Bayesian analysis on the ks model is performed on three sets of initial conditions. First, the KS model is solved numerically using a finite difference method and Bayesian inference is performed on parameters of the model such as the cell diffusion and chemical sensitivity. We investigate the predictive posterior distribution of future data and the convergence of the 95% credible interval of cell diffusion at different grid sizes using the three different initial conditions. References D. Balding and D. L. S. McElwain. A mathematical model of tumour-induced capillary growth. J. Theor. Biol., 114(1):53–73, 1985. doi:10.1016/S0022-5193(85)80255-1. D. A. Brown and H. C. Berg. Temporal stimulation of chemotaxis in Escherichia coli. Proc. Nat. Acad. Sci., 71(4):1388–1392, 1974. doi:10.1073/pnas.71.4.1388. H. Chisholm. The Encyclop\T1\ae dia britannica: a dictionary of arts, sciences, literature and general information, volume 6. Encyclopaedia Britannica Co., 1910. F. W. Dahlquist, P. Lovely, and D. E. Koshland. Quantitative analysis of bacterial migration in chemotaxis. Nature New Biol., 236(65):120–123, 1972. doi:10.1038/newbio236120a0. J. Goodman and J. Weare. Ensemble samplers with affine invariance. Commun. Appl. Math. Comput. Sci., 5(1):65–80, 2010. URL https://projecteuclid.org/euclid.camcos/1513731992. K. Gustafson and T. Abe. The third boundary condition–-was it Robin's? Math. Intell., 20(1):63–71, 1998. doi:10.1007/BF03024402. L. Harvath and R. R. Aksamit. Oxidized n-formylmethionyl-leucyl-phenylalanine: Effect on the activation of human monocyte and neutrophil chemotaxis and superoxide production. J. Immun., 133(3):1471–1476, 1984. URL https://www.jimmunol.org/content/133/3/1471. E. F. Keller and L. A. Segel. Initiation of slime mold aggregation viewed as an instability. J. Theor. Bio., 26(3):399–415, 1970. doi:10.1016/0022-5193(70)90092-5. R. Mesibov, G. W. Ordal, and J. Adler. The range of attractant concentrations for bacterial chemotaxis and the threshold and size of response over this range: Weber law and related phenomena. J. Gen. Physiol., 62(2):203–223, 1973. doi:10.1085/jgp.62.2.203. J. A. Sherratt, E. H. Sage, and J. D. Murray. Chemical control of eukaryotic cell movement: A new model. J. Theor. Biol., 162(1):23–40, 1993. doi:10.1006/jtbi.1993.1074. R. T. Tranquillo, S. H. Zigmond, and D. A. Lauffenburger. Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay. Cell Motil. Cytoskel., 11(1):1–15, 1988. doi:10.1002/cm.970110102. A. W. van der Vaart. Asymptotic Statistics, volume 3. Cambridge University Press, 2000. doi:10.1017/CBO9780511802256.

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called Pseudo-Marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.

El Derecho Internacional de las Inversiones hoy en día se encuentra caracterizado por la fragmentación. Esto se debe principalmente a los diferentes estándares de garantía que los Estados otorgan a los inversionistas extranjeros, así como a las decisiones arbitrales al respecto. Si bien cada estándar de protección debe analizarse en cada caso concreto, la doctrina y los Tribunales internacionales han reconocido la existencia de ciertos estándares de protección clásicos como las Cláusulas de Nación Más Favorecida o las denominadas Cláusulas Paraguas. En el presente artículo, los autores buscan desarrollar la forma en que suelen operar estos dos estándares de protección y la posibilidad de invocar los beneficios de la cláusula paraguas por medio de una aplicación de la cláusula de nación más favorecida, de acuerdo a lo que ha sido resuelto por la jurisprudencia internacional sobre la materia.

Seagrass ecosystems are increasingly subjected to multiple interacting stressors, making the consequent trajectories difficult to predict. Here, we present a new process-based model of seagrass decline in response to cumulative light and temperature stress. The model is calibrated to laboratory datasets for Great Barrier Reef seagrasses using Bayesian inference. Our model, which is fit to both physiological and morphological data, supports the hypothesis that physiological carbon loss rate controls the shoot density decline rate of seagrasses. The model predicts the time to complete shoot loss, and a new, generalisable, cumulative stress index that indicates the potential seagrass shoot density decline based on the time period of cumulative stress. All model predictions include uncertainty estimates based on uncertainty in the model fit to the data. The calibrated model is packaged into a computer program that can forecast the potential declines of seagrasses due to cumulative light and temperature stress.

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smaller than that of the full log-likelihood in standard MCMC. The likelihood estimate is bias-corrected and used in two dependent pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to $n$ and $m$, respectively. We propose a practical estimator of the error and show that the error is negligible even for a very small $m$ in our applications. We demonstrate that Subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature., Comment: Main changes: The theory has been significantly revised

Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favourably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature., Comment: The main paper is 28 pages. The supplementary material is 28 pages

We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly effcient difference estimator from the survey sampling literature to estimate the log-likelihood accurately using only a small fraction of the data. Our algorithm improves on the O(n) complexity of regular MCMC by operating over local data clusters instead of the full sample when computing the likelihood. The likelihood estimate is used in a Pseudo-marginal framework to sample from a perturbed posterior which is within O(m -1/2) of the true posterior, where m is the subsample size. The method is applied to a logistic regression model to predict firm bankruptcy for a large data set. We document a significant speed up in comparison to the standard MCMC on the full dataset.

The complexity of Markov Chain Monte Carlo (MCMC) algorithms arises from the requirement of a likelihood evaluation for the full data set in each iteration. Payne and Mallick (2014) propose to speed up the Metropolis-Hastings algorithm by a delayed acceptance approach where the acceptance decision proceeds in two stages. In the first stage, an estimate of the likelihood based on a random subsample determines if it is likely that the draw will be accepted and, if so, the second stage uses the full data likelihood to decide upon final acceptance. Evaluating the full data likelihood is thus avoided for draws that are unlikely to be accepted. We propose a more precise likelihood estimator which incorporates auxiliary information about the full data likelihood while only operating on a sparse set of the data. It is proved that the resulting delayed acceptance MCMC is asymptotically more efficient compared to that of Payne and Mallick (2014). Furthermore, we adapt the method to handle data sets that are too large to fit in Random-Access Memory (RAM). This adaptation results in an algorithm that samples from an approximate posterior with well studied theoretical properties in the literature.

We propose a general class of flexible models for longitudinal data with special emphasis on discrete-time survival data. The model is a finite mixture model where the subjects are allowed to move ...