Objective Bayesian Model Selection

Frequentist and Bayesian approaches to statistics have long been seen as incompatible, but recent work has been done to try and unify them (Bayarri and Berger, 2004; Efron, 2005). Empirical Bayes, approximate Bayesian analysis, and the matching prior approach are examples of methods where prior elicitation is driven by a frequentist interpretation of the data. In this report, we review some standard frequentist and Bayesian model selection techniques and describe how objective Bayes theory can help in this decision-oriented framework, typically by enabling consideration of uncertainty in the model-building process. Objective Bayes mehtods are then used and compared with standard model selection methods on data from the financial sector in Switzerland, Greece, and the United States during 1999 to 2013; results show broad agreement between the methods, but conclusions are less clear-cut in the objective Bayes framework.

One Step Impulse Radio Ultra-WideBand Positioning Algorithm

John Farserotu, Jean-Yves Le Boudec, Hai Zhan

We consider the problem of positioning estimation with impulse radio (IR) ultra-wideband (UWB) radio under dense multipaths and additive Gaussian noise environments. Most popular positioning algorithms first estimate certain parameters (such as time of arrival (TOA), angle of arrival (AOA) and time difference of arrival (TDOA)) from the received signals. These parameters are then used to estimate the targeted position. In practice, the estimation of these parameters is not errors free and the distribution of the errors is difficult to model exactly. In contrast, we propose a novel one-step approach, which estimates the position and channels directly and jointly from the received signals of the used base stations. We use a Bayesian approach where the prior distribution of the channels follows the IEEE 802.15.4a channel model to estimate the joint posterior probability density function (pdf) of the channels, the targeted position and the transmit time. One application of the joint posterior pdf of the channels, the targeted position and the transmit time is the position determination with classical posterior estimator (such as minimum mean square error estimator (MMSE)). For computing the joint posterior pdf of the channels, the targeted position and the transmit time, we derived an algorithm which is based on sampling-importance resampling and the expectation maximization technique. Furthermore, we propose a reduced-complexity architecture of the proposed IR UWB localization system using our proposed algorithm. The algorithm can be easily implemented on hardware. Numerical evaluations under the IEEE 802.15.4a channel model are presented to demonstrate the good performance of the proposed estimator.

IEEE2009

A Novel Bayesian Impulse Radio Ultra-WideBand Ranging Algorithm

John Farserotu, Jean-Yves Le Boudec, Hai Zhan

We consider the problem of ranging with Impulse Radio (IR) Ultra-WideBand (UWB) radio under weak Line Of Sight (LOS) environments and additive Gaussian noise. We use a Bayesian approach where the prior distribution of the channel follows the IEEE 802.15.4a channel model, to estimate the joint posterior probability density function (pdf) of the channel and the targeted distance. One of applications of the joint posterior pdf of the channel and the targeted distance is the ranging determination with classical posterior estimators (such as Minimum Mean Square Error Estimator (MMSE)). For computing the joint posterior pdf of the channel and the targeted distance, we derived a novel algorithm which is based on importance sampling and expectation maximum techniques. Furthermore, we propose a reduced-complexity architecture of IR UWB ranging system using our proposed algorithm. The complexity analysis of the algorithm shows the proposed algorithm is a low-complexity one. Numerical evaluations under the IEEE 802.15.4a channel model are presented to demonstrate the good performance of the proposed estimator.

IEEE2009

Bayesian Inference for Spiking Neuron Models with a Sparsity Prior

Matthias Seeger

Generalized linear models are the most commonly used tools to describe the stimulus selectivity of sensory neurons. Here we present a Bayesian treatment of such models. Using the expectation propagation algorithm, we are able to approximate the full posterior distribution over all weights. In addition, we use a Laplacian prior to favor sparse solutions. Therefore, stimulus features that do not critically influence neural activity will be assigned zero weights and thus be effectively excluded by the model. This feature selection mechanism facilitates both the interpretation of the neuron model as well as its predictive abilities. The posterior distribution can be used to obtain confidence intervals which makes it possible to assess the statistical significance of the solution. In neural data analysis, the available amount of experimental measurements is often limited whereas the parameter space is large. In such a situation, both regularization by a sparsity prior and uncertainty estimates for the model parameters are essential. We apply our method to multi-electrode recordings of retinal ganglion cells and use our uncertainty estimate to test the statistical significance of functional couplings between neurons. Furthermore we used the sparsity of the Laplace prior to select those filters from a spike-triggered covariance analysis that are most informative about the neural response.

2008