scholarly journals Bayesian Nonparametric Modeling for Predicting Dynamic Dependencies in Multiple Object Tracking

Sensors ◽  
2022 ◽  
Vol 22 (1) ◽  
pp. 388
Author(s):  
Bahman Moraffah ◽  
Antonia Papandreou-Suppappola
Keyword(s):  
Dirichlet Process ◽  
Moving Objects ◽  
Object Identity ◽  
Bayesian Nonparametric ◽  
Nonparametric Modeling ◽  
Object State ◽  
Multiple Object ◽  
Dependent Dirichlet Process ◽  
Bernoulli Filter ◽  
Clustering Property

The paper considers the problem of tracking an unknown and time-varying number of unlabeled moving objects using multiple unordered measurements with unknown association to the objects. The proposed tracking approach integrates Bayesian nonparametric modeling with Markov chain Monte Carlo methods to estimate the parameters of each object when present in the tracking scene. In particular, we adopt the dependent Dirichlet process (DDP) to learn the multiple object state prior by exploiting inherent dynamic dependencies in the state transition using the dynamic clustering property of the DDP. Using the DDP to draw the mixing measures, Dirichlet process mixtures are used to learn and assign each measurement to its associated object identity. The Bayesian posterior to estimate the target trajectories is efficiently implemented using a Gibbs sampler inference scheme. A second tracking approach is proposed that replaces the DDP with the dependent Pitman–Yor process in order to allow for a higher flexibility in clustering. The improved tracking performance of the new approaches is demonstrated by comparison to the generalized labeled multi-Bernoulli filter.

scholarly journals Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis

2018 ◽  
Vol 11 (3) ◽  
pp. 52 ◽  
Author(s):  
Mark Jensen ◽  
John Maheu
Keyword(s):  
Dirichlet Process ◽  
Joint Distribution ◽  
Nonparametric Model ◽  
Bayesian Nonparametric ◽  
Excess Returns ◽  
Dirichlet Process Prior ◽  
Stock Market Returns ◽  
Conditional Mean ◽  
Risk Return ◽  
Volatility Feedback

In this paper, we let the data speak for itself about the existence of volatility feedback and the often debated risk–return relationship. We do this by modeling the contemporaneous relationship between market excess returns and log-realized variances with a nonparametric, infinitely-ordered, mixture representation of the observables’ joint distribution. Our nonparametric estimator allows for deviation from conditional Gaussianity through non-zero, higher ordered, moments, like asymmetric, fat-tailed behavior, along with smooth, nonlinear, risk–return relationships. We use the parsimonious and relatively uninformative Bayesian Dirichlet process prior to overcoming the problem of having too many unknowns and not enough observations. Applying our Bayesian nonparametric model to more than a century’s worth of monthly US stock market returns and realized variances, we find strong, robust evidence of volatility feedback. Once volatility feedback is accounted for, we find an unambiguous positive, nonlinear, relationship between expected excess returns and expected log-realized variance. In addition to the conditional mean, volatility feedback impacts the entire joint distribution.

Tracking Multiple Objects Is Limited Only by Object Spacing, Not by Speed, Time, or Capacity

2010 ◽  
Vol 21 (7) ◽  
pp. 920-925 ◽  
Author(s):  
S.L. Franconeri ◽  
S.V. Jonathan ◽  
J.M. Scimeca
Keyword(s):  
Object Tracking ◽  
Moving Objects ◽  
Multiple Object Tracking ◽  
Single Object ◽  
Multiple Objects ◽  
Performance Constraints ◽  
Root Cause ◽  
Multiple Object ◽  
Tracking Time ◽  
Environment Performance

In dealing with a dynamic world, people have the ability to maintain selective attention on a subset of moving objects in the environment. Performance in such multiple-object tracking is limited by three primary factors—the number of objects that one can track, the speed at which one can track them, and how close together they can be. We argue that this last limit, of object spacing, is the root cause of all performance constraints in multiple-object tracking. In two experiments, we found that as long as the distribution of object spacing is held constant, tracking performance is unaffected by large changes in object speed and tracking time. These results suggest that barring object-spacing constraints, people could reliably track an unlimited number of objects as fast as they could track a single object.

Bayesian Nonparametric Dynamic Methods: Applications to Linear and Nonlinear Advertising Models

2019 ◽  
Vol 56 (2) ◽  
pp. 211-229 ◽  
Author(s):  
Norris I. Bruce
Keyword(s):  
State Space ◽  
Diffusion Of Innovation ◽  
Dirichlet Process ◽  
Dynamic Models ◽  
Linear Models ◽  
State Space Models ◽  
Model Errors ◽  
Dynamic Discrete Choice ◽  
Bayesian Nonparametric ◽  
Advertising Models

Bayesian methods for dynamic models in marketing have so far been parametric. For instance, it is invariably assumed that model errors emerge from normal distributions. Yet using arbitrary distributional assumptions can result in false inference, which in turn misleads managers. The author therefore presents a set of flexible Bayesian nonparametric (NP) dynamic models that treat error densities as unknown but assume that they emerge from Dirichlet process mixtures. Although the methods address misspecification in dynamic linear models, the main innovation is a particle filter algorithm for nonlinear state-space models. The author used two advertising studies to confirm the benefits of the methods when strict error assumptions are untenable. In both studies, NP models markedly outperformed benchmarks in terms of fit and forecast results. In the first study, the benchmarks understated the effects of competitive advertising on own brand awareness. In the second study, the benchmark inflated ad quality, and consequently, the effects of past advertising appeared 36% higher than that predicted by the NP model. In general, these methods should be valuable wherever state-space models appear (e.g., brand and advertising dynamics, diffusion of innovation, dynamic discrete choice).

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