A combined Bayesian Markovian approach for behaviour recognition

Numerous techniques exist which can be used for the task of behavioural analysis and recognition. Common amongst these are Bayesian networks and Hidden Markov Models. Although these techniques are extremely powerful and well developed, both have important limitations. By fusing these techniques together to form Bayes-Markov chains, the advantages of both techniques can be preserved, while reducing their limitations. The Bayes-Markov technique forms the basis of a common, flexible framework for supplementing Markov chains with additional features. This results in improved user output, and aids in the rapid development of flexible and efficient behaviour recognition systems.

Bayesian retrieval of complete posterior PDFs of oceanic rain rate from microwave observations

A new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) over the ocean is presented, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain-rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes’s theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance the understanding of theoretical benefits of the Bayesian approach, sensitivity analyses have been conducted based on two synthetic datasets for which the “true” conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism, but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak owing to saturation effects. It is also suggested that both the choice of the estimators and the prior information are crucial to the retrieval. In addition, the performance of the Bayesian algorithm herein is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

An analysis of the impact of R&D on productivity using Bayesian model averaging with a reversible jump algorithm.

A Bayesian Model Averaging approach to the estimation of lag structures is introduced, and applied to assess the impact of R&D on agricultural productivity in the US from 1889 to 1990. Lag and structural break coefficients are estimated using a reversible jump algorithm that traverses the model space. In addition to producing estimates and standard deviations for the coe¢ cients, the probability that a given lag (or break) enters the model is estimated. The approach is extended to select models populated with Gamma distributed lags of di¤erent frequencies. Results are consistent with the hypothesis that R&D positively drives productivity. Gamma lags are found to retain their usefulness in imposing a plausible structure on lag coe¢ cients, and their role is enhanced through the use of model averaging.

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Global trends and factors associated with the illegal killing of elephants: a hierarchical bayesian analysis of carcass encounter data

Elephant poaching and the ivory trade remain high on the agenda at meetings of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES). Well-informed debates require robust estimates of trends, the spatial distribution of poaching, and drivers of poaching. We present an analysis of trends and drivers of an indicator of elephant poaching of all elephant species. The site-based monitoring system known as Monitoring the Illegal Killing of Elephants (MIKE), set up by the 10th Conference of the Parties of CITES in 1997, produces carcass encounter data reported mainly by anti-poaching patrols. Data analyzed were site by year totals of 6,337 carcasses from 66 sites in Africa and Asia from 2002–2009. Analysis of these observational data is a serious challenge to traditional statistical methods because of the opportunistic and non-random nature of patrols, and the heterogeneity across sites. Adopting a Bayesian hierarchical modeling approach, we used the proportion of carcasses that were illegally killed (PIKE) as a poaching index, to estimate the trend and the effects of site- and country-level factors associated with poaching. Important drivers of illegal killing that emerged at country level were poor governance and low levels of human development, and at site level, forest cover and area of the site in regions where human population density is low. After a drop from 2002, PIKE remained fairly constant from 2003 until 2006, after which it increased until 2008. The results for 2009 indicate a decline. Sites with PIKE ranging from the lowest to the highest were identified. The results of the analysis provide a sound information base for scientific evidence-based decision making in the CITES process.

Quantitative precipitation estimation over ocean using Bayesian approach from microwave observations during the typhoon season

We have developed a new Bayesian approach to retrieve oceanic rain rate from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), with an emphasis on typhoon cases in the West Pacific. Retrieved rain rates are validated with measurements of rain gauges located on Japanese islands. To demonstrate improvement, retrievals are also compared with those from the TRMM/Precipitation Radar (PR), the Goddard Profiling Algorithm (GPROF), and a multi-channel linear regression statistical method (MLRS). We have found that qualitatively, all methods retrieved similar horizontal distributions in terms of locations of eyes and rain bands of typhoons. Quantitatively, our new Bayesian retrievals have the best linearity and the smallest root mean square (RMS) error against rain gauge data for 16 typhoon overpasses in 2004. The correlation coefficient and RMS of our retrievals are 0.95 and ~2 mm hr-1, respectively. In particular, at heavy rain rates, our Bayesian retrievals outperform those retrieved from GPROF and MLRS. Overall, the new Bayesian approach accurately retrieves surface rain rate for typhoon cases. Accurate rain rate estimates from this method can be assimilated in models to improve forecast and prevent potential damages in Taiwan during typhoon seasons.