Theory of segmented particle filters

2016 ◽  
Vol 48 (1) ◽  
pp. 69-87 ◽  
Author(s):  
Hock Peng Chan ◽  
Chiang-Wee Heng ◽  
Ajay Jasra

AbstractWe study the asymptotic behavior of a new particle filter approach for the estimation of hidden Markov models. In particular, we develop an algorithm where the latent-state sequence is segmented into multiple shorter portions, with an estimation technique based upon a separate particle filter in each portion. The partitioning facilitates the use of parallel processing, which reduces the wall-clock computational time. Based upon this approach, we introduce new estimators of the latent states and likelihood which have similar or better variance properties compared to estimators derived from standard particle filters. We show that the likelihood function estimator is unbiased, and show asymptotic normality of the underlying estimators.

Author(s):  
Indah Agustien Siradjuddin ◽  
◽  
Muhammad Rahmat Widyanto ◽  

To track vehicle motion in data video, particle filter with Gaussian weighting is proposed. This method consists of four main stages. First, particles are generated to predict target’s location. Second, certain particles are searched and these particles are used to build Gaussian distribution. Third, weight of all particles is calculated based on Gaussian distribution. Fourth, particles are updated based on each weight. The proposed method could reduce computational time of tracking compared to that of conventional method of particle filter, since the proposed method does not have to calculate all particles weight using likelihood function. This method has been tested on video data with car as a target object. In average, this proposed method of particle filter is 60.61% times faster than particle filter method meanwhile the accuracy of tracking with this newmethod is comparable with particle filter method, which reach up to 86.87%. Hence this method is promising for real time object tracking application.


2015 ◽  
Vol 5 (1) ◽  
pp. 61
Author(s):  
Safaa K. Kadhem ◽  
Paul Hewson ◽  
Irene Kaimi

In Bayesian model selection, the deviance information criterion (DIC) has become a widely used criterion. It is however not defined for the hidden Markov models (HMMs). In particular, the main challenge of applying the DIC for HMMs is that the observed likelihood function of such models is not available in closed form. A closed form for the observed likelihood function can be obtained either by summing all possible hidden states of the complete likelihood using the so-called the forward recursion, or via integrating out the hidden states in the conditional likelihood. Hence, we propose two versions of the DIC to the model choice problem in HMMs context, namely, the recursive deviance-based DIC and the conditional likelihood-based DIC. In this paper, we compare several normal HMMs after they are estimated by Bayesian MCMC method. We conduct a simulation study based on synthetic data generated under two assumptions, namely diversity in the heterogeneity level and also the number of states. We show that the recursive deviance-based DIC performs well in selecting the correct model compared with the conditional likelihood-based DIC that prefers the more complicated models. A real application involving the waiting time of Old Faithful Geyser data was also used to check those criteria. All the simulations were conducted in Python v.2.7.10, available from first author on request.


Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide

This chapter combines the SMC algorithm with the particle filter approximation of the likelihood function to develop an SMC2 algorithm. As with the PFMH algorithm, the goal is to obtain a posterior sampler for the DSGE model parameters for settings in which the likelihood function of the DSGE model cannot be evaluated with the Kalman filter. The starting point is the SMC Algorithm 8. The chapter adds data sequentially to the likelihood function rather than tempering the entire likelihood function. Moreover, the evaluation of the incremental and the full likelihood function in the correction and mutation steps of Algorithm 8 are replaced by the evaluation of the respective particle filter approximations.


1996 ◽  
Vol 8 (1) ◽  
pp. 178-181 ◽  
Author(s):  
David J. C. MacKay

Several authors have studied the relationship between hidden Markov models and “Boltzmann chains” with a linear or “time-sliced” architecture. Boltzmann chains model sequences of states by defining state-state transition energies instead of probabilities. In this note I demonstrate that under the simple condition that the state sequence has a mandatory end state, the probability distribution assigned by a strictly linear Boltzmann chain is identical to that assigned by a hidden Markov model.


2019 ◽  
Vol 46 (4) ◽  
pp. 296
Author(s):  
Victoria L. Goodall ◽  
Sam M. Ferreira ◽  
Paul J. Funston ◽  
Nkabeng Maruping-Mzileni

Context Direct observations of animals are the most reliable way to define their behavioural characteristics; however, to obtain these observations is costly and often logistically challenging. GPS tracking allows finer-scale interpretation of animal responses by measuring movement patterns; however, the true behaviour of the animal during the period of observation is seldom known. Aims The aim of our research was to draw behavioural inferences for a lioness with a hidden Markov model and to validate the predicted latent-state sequence with field observations of the lion pride. Methods We used hidden Markov models to model the movement of a lioness in the Kruger National Park, South Africa. A three-state log-normal model was selected as the most suitable model. The model outputs are related to collected data by using an observational model, such as, for example, a distribution for the average movement rate and/or direction of movement that depends on the underlying model states that are taken to represent behavioural states of the animal. These inferred behavioural states are validated against direct observation of the pride’s behaviour. Key results Average movement rate provided a useful alternative for the application of hidden Markov models to irregularly spaced GPS locations. The movement model predicted resting as the dominant activity throughout the day, with a peak in the afternoon. The local-movement state occurred consistently throughout the day, with a decreased proportion during the afternoon, when more resting takes place, and an increase towards the early evening. The relocating state had three peaks, namely, during mid-morning, early evening and about midnight. Because of the differences in timing of the direct observations and the GPS locations, we had to compare point observations of the true behaviour with an interval prediction of the modelled behavioural state. In 75% of the cases, the model-predicted behaviour and the field-observed behaviour overlapped. Conclusions Our data suggest that the hidden Markov modelling approach is successful at predicting a realistic behaviour of lions on the basis of the GPS location coordinates and the average movement rate between locations. The present study provided a unique opportunity to uncover the hidden states and compare the true behaviour with the inferred behaviour from the predicted state sequence. Implications Our results illustrated the potential of using hidden Markov models with movement rate as an input to understand carnivore behavioural patterns that could inform conservation management practices.


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