A Discrete Bouncy Particle Sampler

Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of nonreversible Markov chains can be beneficial in many contexts. In particular, the recently-proposed bouncy particle sampler leverages a continuous-time and nonreversible Markov process and empirically shows state-of-the-art performances when used to explore certain probability densities; however, its implementation typically requires the computation of local upper bounds on the gradient of the log target density. We present the discrete bouncy particle sampler, a general algorithm based upon a guided random walk, a partial refreshment of direction, and a delayed-rejection step. We show that the bouncy particle sampler can be understood as a scaling limit of a special case of our algorithm. In contrast to the bouncy particle sampler, implementing the discrete bouncy particle sampler only requires point-wise evaluation of the target density and its gradient. We propose extensions of the basic algorithm for situations when the exact gradient of the target density is not available. In a Gaussian setting, we establish a scaling limit for the radial process as dimension increases to infinity. We leverage this result to obtain the theoretical efficiency of the discrete bouncy particle sampler as a function of the partial-refreshment parameter, which leads to a simple and robust tuning criterion. A further analysis in a more general setting suggests that this tuning criterion applies more generally. Theoretical and empirical efficiency curves are then compared for different targets and algorithm variations.

Selecting the Best Alternative Based on Its Quantile

A value-at-risk, or quantile, is widely used as an appropriate investment selection measure for risk-conscious decision makers. We present two quantile-based sequential procedures—with and without consideration of equivalency between alternatives—for selecting the best alternative from a set of simulated alternatives. These procedures asymptotically guarantee a user-defined target probability of correct selection within a prespecified indifference zone. Experimental results demonstrate the trade-off between the indifference-zone size and the number of simulation iterations needed to render a correct selection while satisfying a desired probability of correct selection.

Calibration of reliability-based safety factors for sand boiling in excavations

This study calibrated the required factors of safety of five analysis methods for sand boiling using reliability theory. The factors of safety computed by the five analysis methods were compared with the results of a series of sand boiling model tests. The comparison shows that rigorous methods (Terzaghi’s and Harza’s methods) were more accurate in predicting the factors of safety compared to the simplified methods (Harr’s, simplified Terzaghi’s, and simplified Harza’s methods). The statistics of the model factor for each method, defined as the actual factor of safety divided by the computed one, was calibrated by the model test results. These statistics were then used to establish the relationship between the target probability of failure and the required factor of safety by reliability theory. Verification using a full-scale sand boiling case history shows that the required factor of safety calibrated by the reliability theory was more reasonable than the required factors of safety in references and design codes.

Two Measurement Set Partitioning Algorithms for the Extended Target Probability Hypothesis Density Filter

The extended target probability hypothesis density (ET-PHD) filter cannot work well if the density of measurements varies from target to target, which is based on the measurement set partitioning algorithms employing the Mahalanobis distance between measurements. To tackle the problem, two measurement set partitioning approaches, the shared nearest neighbors similarity partitioning (SNNSP) and SNN density partitioning (SNNDP), are proposed in this paper. In SNNSP, the shared nearest neighbors (SNN) similarity, which incorporates the neighboring measurement information, is introduced to DP instead of the Mahalanobis distance between measurements. Furthermore, the SNNDP is developed by combining the DBSCAN algorithm with the SNN similarity together to enhance the reliability of partitions. Simulation results show that the ET-PHD filters based on the two proposed partitioning algorithms can achieve better tracking performance with less computation than the compared algorithms.

Implicit location probability learning does not induce baseline shifts of visuospatial attention

We tested whether implicit learning causes shifts of spatial attention in advance of or in response to stimulus onset. Participants completed randomly interspersed trials of letter search, which involved reporting the orientation of a T among Ls, and scene search, which involved identifying which of four scenes was from a target category (e.g., forest). In Experiment 1, an initial phase more often contained target letters in one screen quadrant, while the target scenes appeared equally often in all quadrants. Participants persistently prioritized letter targets in the more probable region, but the implicitly learned preference did not affect the unbiased scene task. In Experiment 2, the spatial probabilities of the scene and letter tasks reversed. Participants unaware of the probability manipulation acquired only a spatial bias to scene targets in the more probable region, with no effect on letter search. Instead of recruiting baseline shifts of spatial attention prior to stimulus onset, implicit learning of target probability yields task-dependent shifts of spatial attention following stimulus onset. Such shifts may involve attentional behaviors unique to certain task contexts.