Adaptive Markov Chain Monte Carlo (MCMC) algorithms attempt to 'learn' from the results of past iterations so the Markov chain can converge quicker. Unfortunately, adaptive MCMC algorithms are no longer Markovian, so their convergence is difficult to guarantee. In this paper, we develop new diagnostics to determine whether the adaption is still improving the convergence. We present an algorithm which automatically stops adapting once it determines further adaption will not increase the convergence speed. Our algorithm allows the computer to tune a 'good' Markov chain through multiple phases of adaption, and then run conventional non-adaptive MCMC. In this way, the efficiency gains of adaptive MCMC can be obtained while still ensuring convergence to the target distribution.

One of the most widely used samplers in practice is the component-wise Metropolis-Hastings (CMH) sampler that updates in turn the components of a vector valued Markov chain using accept-reject moves generated from a proposal distribution.When the target distribution of a Markov chain is irregularly shaped, a 'good' proposal distribution for one part of the state space might be a 'poor' one for another part of the state space. We consider a component-wise multiple-try Metropolis (CMTM) algorithm that can automatically choose from a set of candidate moves sampled from different distributions. The computational efficiency is increased using an adaptation rule for the CMTM algorithm that dynamically builds a better set of proposal distributions as the Markov chain runs. The ergodicity of the adaptive chain is demonstrated theoretically. The performance is studied via simulations and data examples.

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Energy consumption is a crucial issue of mobile surveillance cameras owing to limited battery capacity. The lifetime of the system is significantly extended by the eventdriven operation; the system mostly stays in sleep mode and wakes up only when an event is detected. In this paper, we propose a design of a low-energy surveillance camera that records events such as the abnormal movement of objects, or physical damage to the camera itself. Unlike conventional event-driven approaches, the proposed system records video from 10 seconds before the event detection because the most critical information is often before or at the moment of event detection, not after the detection. Two different encoders, a low-power encoder and a highcompression encoder, are employed together to implement the low-energy surveillance camera. Experimental results show that the energy consumption of the whole system is reduced by up to 74.9% (by 66.8% on average) compared with conventional always-on system.

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