Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothing-spline models, state-space models, semiparametric regression, spatial and spatio-temporal models, log-Gaussian Cox-processes, geostatistical and geoadditive models. In this paper we consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form due to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations

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[Read before The Royal Statistical Society at a meeting organized by the Research Section on

Recent developments in multi-electrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenges in computational neuroscience today. In this work, we develop a multivariate point-process model in which the observed activity of a network of neurons depends on three terms: 1) the experimentally-controlled stimulus; 2) the spiking history of the observed neurons; and 3) a latent noise source that corresponds, for example, to “common input ” from an unobserved population of neurons that is presynaptic to two or more cells in the observed population. We develop an expectation-maximization algorithm for fitting the model parameters; here the expectation step is based on a continuous-time implementation of the extended Kalman smoother, and the maximization step involves two concave maximization problems which may be solved in parallel. The techniques developed allow us to solve a variety of inference problems in a straightforward, computationally efficient fashion; for example, we may use the model to predict network activity given an arbitrary stimulus, infer a neuron’s firing rate given the stimulus and the activity of the other observed neurons, and perform optimal stimulus decoding and prediction. We present several detailed simulation studies which explore the strengths and limitations of our approach. 1

The problem of hypothesis testing against independence for a Gauss-Markov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, an expression for the log-likelihood ratio of detection is derived. Assuming random placement of nodes over a large region according to the Poisson or uniform distribution and nearest-neighbor dependency graph, the error exponent of the Neyman-Pearson detector is derived using large-deviations theory. The error exponent is expressed as a dependency-graph functional and the limit is evaluated through a special law of large numbers for stabilizing graph functionals. The exponent is analyzed for different values of the variance ratio and correlation. It is found that a more correlated GMRF has a higher exponent at low values of the variance ratio whereas the situation is reversed at high values of the variance ratio.

Understanding the characteristics of the Internet delay space (i.e., the all-pairs set of static round-trip propagation delays among edge networks in the Internet) is important for the design of global-scale distributed systems. For instance, algorithms used in overlay networks are often sensitive to violations of the triangle inequality and to the growth properties within the Internet delay space. Since designers of distributed systems often rely on simulation and emulation to study design alternatives, they need a realistic model of the Internet delay space. Our analysis shows that existing models do not adequately capture important properties of the Internet delay space. In this paper, we analyze measured delays among thousands of Internet edge networks and identify key properties that are important for distributed system design. Furthermore, we derive a simple model of the Internet delay space based on our analytical findings. This model preserves the relevant metrics far better than existing models, allows for a compact representation, and can be used to synthesize delay data for simulations and emulations at a scale where direct measurement and storage are impractical.

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Abstract: We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial non-homogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mix-ture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clus-tering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days.

The problem of optimal node density maximizing the Neyman-Pearson detection error exponent subject to a constraint on average (per node) energy consumption is analyzed. The spatial correlation among the sensor measurements is incorporated through a Gauss-Markov random field model with Euclidean nearest-neighbor dependency graph. A constant density deployment of sensors under the uniform or Poisson distribution is assumed. It is shown that the optimal node density crucially depends on the ratio between the measurement variances under the two hypotheses and displays a threshold behavior. Below the threshold value of the variance ratio, the optimal node density tends to infinity under any feasible average energy constraint. On the other hand, when the variance ratio is above the threshold, the optimal node density is the minimum value at which it is feasible to process and deliver the likelihood ratio (sufficient statistic) of the sensor measurements to the fusion center. In this regime of the variance ratio, an upper bound on the optimal node density based on a proposed 2-approximation fusion scheme and a lower bound based on the minimum spanning tree are established. Under an alternative formulation where the energy consumption per unit area is constrained, the optimal node density is shown to be strictly finite for all values of the variance ratio and bounds on this optimal node density are provided.

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