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Carpooling is an integral component in smart carbon-neutral cities, in particular to facilitate homework commuting. We study an innovative carpooling service developed by the start-up Ecov which specialises in homework commutes in peri-urban and rural regions. When a passenger makes a carpooling request, a designated driver is not assigned as in a traditional carpooling service; rather the passenger waits for the first driver, from a population of non-professional drivers who are already en route, to arrive. We propose a two-stage Bayesian hierarchical model to overcome the considerable difficulties, due to the sparsely observed driver and passenger data from an embryonic stochastic carpooling service, to deliver high-quality predictions of driver flow and passenger waiting times. The first stage focuses on the driver flow, whose predictions are aggregated at the daily level to compensate the data sparsity. The second stage processes this single daily driver flow into sub-daily (e.g. hourly) predictions of the passenger waiting times. We demonstrate that our model mostly outperforms frequentist and non-hierarchical Bayesian methods for observed data from operational carpooling service in Lyon, France and we also validated our model on simulated data.

From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly focus on the case when the initial process is Gaussian. The challenge being that, although marginally remains Gaussian, the randomly sampled process will no longer be jointly Gaussian.

This paper develops a new global optimisation method that applies to a family of criteria that are not entirely known. This family includes the criteria obtained from the class of posteriors that have nor-malising constants that are analytically not tractable. The procedure applies to posterior probability densities that are continuously differen-tiable with respect to their parameters. The proposed approach avoids the re-sampling needed for the classical Monte Carlo maximum likelihood inference, while providing the missing convergence properties of the ABC based methods. Results on simulated data and real data are presented. The real data application fits an inhomogeneous area interaction point process to cosmological data. The obtained results validate two important aspects of the galaxies distribution in our Universe : proximity of the galaxies from the cosmic filament network together with territorial clustering at given range of interactions. Finally, conclusions and perspectives are depicted.

The intra-axonal water exchange time {\tau}i, a parameter associated with axonal permeability, could be an important biomarker for understanding demyelinating pathologies such as Multiple Sclerosis. Diffusion-Weighted MRI is sensitive to changes in permeability, however, the parameter has remained elusive due to the intractability of the mathematical models that incorporate it. Machine learning based computational models can potentially be used to estimate such parameters, and recently, a theoretical framework using a random forest (RF) suggests this is a promising approach. In this study, we adopt such an RF approach and experimentally investigate its suitability as a biomarker for demyelinating pathologies through direct comparison with histology. For this, we use an in-vivo cuprizone (CPZ) mouse model of demyelination with available ex-vivo electron microscopy (EM) data. We test our model on noise-free simulations and find very strong correlations between the predicted and ground truth parameters. For realistic noise levels as in our in-vivo data, the performance is affected, however, the parameters are still well estimated. We apply our RF model on in-vivo data from 8 CPZ and 8 wild-type (WT) mice and validate the RF estimates using histology. We find a strong correlation between the in-vivo RF estimates of {\tau}i and the EM measurements of myelin thickness ({\rho_\tau}i = 0.82), and between RF estimates and EM measurements of intra-axonal volume fraction ({\rho_f} = 0.98). When comparing {\tau}i in CPZ and WT mice we find a statistically significant decrease in the corpus callosum of the CPZ compared to the WT mice, in line with our expectations that {\tau}i is lower in regions where the myelin sheath is damaged. Overall, these results demonstrate the suitability of machine learning compartment models with permeability as a potential biomarker for demyelinating pathologies.

The present paper obtains a complete description of the limit distributions of sample covariances in N x n panel data when N and n jointly increase, possibly at different rate. The panel is formed by N independent samples of length n from random-coefficient AR(1) process with the tail distribution function of the random coefficient regularly varying at the unit root with exponent $\beta$ > 0. We show that for $\beta$ $\in$ (0, 2) the sample covariances may display a variety of stable and non-stable limit behaviors with stability parameter depending on $\beta$ and the mutual increase rate of N and n.

It is well-known that random-coefficient AR(1) process can have long memory depending on the index $\beta$ of the tail distribution function of the random coefficient, if it is a regularly varying function at unity. We discuss estimation of $\beta$ from panel data comprising N random-coefficient AR(1) series, each of length T. The estimator of $\beta$ is constructed as a version of the tail index estimator of Goldie and Smith (1987) applied to sample lag 1 autocorrelations of individual time series. Its asymptotic normality is derived under certain conditions on N, T and some parameters of our statistical model. Based on this result, we construct a statistical procedure to test if the panel random-coefficient AR(1) data exhibit long memory. A simulation study illustrates finite-sample performance of the introduced estimator and testing procedure.

We discuss nonparametric estimation of the distribution function $G(x)$ of the autoregressive coefficient $a \in (-1,1)$ from a panel of $N$ random-coefficient AR(1) data, each of length $n$, by the empirical distribution function of lag 1 sample autocorrelations of individual AR(1) processes. Consistency and asymptotic normality of the empirical distribution function and a class of kernel density estimators is established under some regularity conditions on $G(x)$ as $N$ and $n$ increase to infinity. The Kolmogorov-Smirnov goodness-of-fit test for simple and composite hypotheses of Beta distributed $a$ is discussed. A simulation study for goodness-of-fit testing compares the finite-sample performance of our nonparametric estimator to the performance of its parametric analogue discussed in Beran et al. (2010).

The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown distribution $\mu$. Two test procedures are investigated. The first one is devoted to testing if the transition matrix P of the Markov chain X satisfies specific affine constraints, covering a wide range of situations such as symmetry or sparsity. The second procedure is a goodness-of-fit test on the distribution $\mu$, which reveals to be consistent under mild assumptions even though the time gaps are not observed. The theoretical results are supported by a Monte Carlo simulation study to show the performance and robustness of the proposed methodologies on specific numerical examples.

It is well-known that the aggregated time series might have very different properties from those of the individual series, in particular, long memory. At the present time, aggregation has become one of the main tools for modelling of long memory processes. We review recent work on contemporaneous aggregation of random-coefficient AR(1) and related models, with particular focus on various long memory properties of the aggregated process.

We discuss contemporaneous aggregation of independent copies of a triangular array of random-coefficient AR(1) processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law W. The limiting aggregated process is shown to exist, under general assumptions on W and the mixing distribution, and is represented as a mixed infinitely divisible moving-average. Partial sums process of $ is discussed under the assumption E(W^2) is finite and a mixing density regularly varying at the "unit root" x=1 with exponent \beta >0. We show that the above partial sums process may exhibit four different limit behaviors depending on \beta and the L\'evy triplet of W. Finally, we study the disaggregation problem in spirit of Leipus et al. (2006) and obtain the weak consistency of the corresponding estimator of the mixing distribution in a suitable L_2-space.

We are interested in the online prediction of the electricity load, within the Bayesian framework of dynamic models. We offer a review of sequential Monte Carlo methods, and provide the calculations needed for the derivation of so-called particles filters. We also discuss the practical issues arising from their use, and some of the variants proposed in the literature to deal with them, giving detailed algorithms whenever possible for an easy implementation. We propose an additional step to help make basic particle filters more robust with regard to outlying observations. Finally we use such a particle filter to estimate a state-space model that includes exogenous variables in order to forecast the electricity load for the customers of the French electricity company \'Electricit\'e de France and discuss the various results obtained.

The characteristic feature of semi-selfsimilar process is the invariance of its finite dimensional distributions by certain dilation for specific scaling factor. Estimating the scale parameter $\lambda$ and the Hurst index of such processes is one of the fundamental problem in the literature. We present some iterative method for estimation of the scale and Hurst parameters which is addressed for semi-selfsimilar processes with stationary increments. This method is based on some flexible sampling scheme and evaluating sample variance of increments in each scale intervals $[\lambda^{n-1}, \lambda^n)$, $n\in \mathbb{N}$. For such iterative method we find the initial estimation for the scale parameter by evaluating cumulative sum of moving sample variances and also by evaluating sample variance of preceding and succeeding moving sample variance of increments. We also present a new efficient method for estimation of Hurst parameter of selfsimilar processes. As an example we introduce simple fractional Brownian motion (sfBm) which is semi-selfsimilar with stationary increments. We present some simulations and numerical evaluation to illustrate the results and to estimate the scale for sfBm as a semi-selfsimilar process. We also present another simulation and show the efficiency of our method in estimation of Hurst parameter by comparing its performance with some previous methods., Comment: 15 pages

We prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression mdoel where the break-point is unknown. The non-differentiability of the likelihood of the model with regard to the break- point parameter induces technical difficulties that we overcome by creating a regularised version of the problem at hand. We first recover the strong consistency of the quantities of interest for the regularised version, using results about the MLE, and we then prove that the regularised version and the original version of the problem share the same asymptotic properties.

This article deals with detection of nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with constant long memory parameter, typically an I(d) series with d>-.5. The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I(d_1) to I(d_2).

We are interested in the estimation and prediction of a parametric model on a short dataset upon which it is expected to overfit and perform badly. To overcome the lack of data (relatively to the dimension of the model) we propose the construction of an informative hierarchical Bayesian prior based upon another longer dataset which is assumed to share some similarities with the original, short dataset. We illustrate the performance of our prior on simulated dataset from three standard models. Then we apply the methodology to a working model for the electricity load forecasting on real datasets, where it leads to a substantial improvement of the quality of the predictions.

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) to the stationary processes for which the singularities of the spectral density are not limited to the origin. We show that the convergence rates and the limit distribution may be different in this context.

This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and spectral analyses of the increments are investigated. On the other hand we show that (almost) all mfBm's may be reached as the limit of partial sums of (super)linear processes. Finally, an algorithm to perfectly simulate the mfBm is presented and illustrated by some simulations., Comment: D\'epartement Images et Signal

We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in [Giraitis L., Leipus, R., Philippe, A., 2006. A test for stationarity versus trends and unit roots for a wide class of dependent errors. Econometric Theory 21, 989--1029]. The two samples have the same length and can be mutually independent or dependent. In the latter case, the test statistic is modified to make it asymptotically free of the long-run correlation coefficient between the samples. To diminish the sensitivity of the test on the choice of the bandwidth parameter, an adaptive formula for the bandwidth parameter is derived using the asymptotic expansion in [Abadir, K., Distaso, W., Giraitis, L., 2009. Two estimators of the long-run variance: Beyond short memory. Journal of Econometrics 150, 56--70]. A simulation study shows that the above choice of bandwidth leads to a good size of our comparison test for most values of fractional and ARMA parameters of the simulated series.

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices.

Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our limit theorems and those of Ginovian (99) to obtain the asymptotic behavior of the empirical covariances of Gaussian fields, which is a particular example of quadratic forms. We show that it is possible to obtain a Gaussian limit when the spectral density is not in $L^2$. Therefore the dichotomy observed in dimension $d=1$ between central and non central limit theorems cannot be stated so easily due to possible anisotropic strong dependence in $d>1$.

In the focus of our attention is the asymptotic properties of the sequence of convex hulls which arise as a result of a peeling procedure applied to the convex hull generated by a Poisson point process. Processes of the considered type are tightly connected with empirical point processes and stable random vectors. Results are given about the limit shape of the convex hulls in the case of a discrete spectral measure. We give some numerical experiments to illustrate the peeling procedure for a more large class of Poisson point processes.

This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy enough tails. We prove that under rather general conditions the existence of the spectral density is preserved by random sampling. We also investigate the effects of deterministic sampling on seasonal long-memory.

The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Oppenheim et al 2006, in the aggregation/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the (semiparametric) form of the mixture density, the estimator is asymptotically normal. The proof is based on the limit theory for the quadratic form in linear random variables developed by Bhansali et al 2007. The moving average representation of the aggregated process is investigated. A small simulation study illustrates the result.

We study the aggregation/disaggregation problem of random parameter AR(1) processes and its relation to the long memory phenomenon. We give a characterization of a subclass of aggregated processes which can be obtained from simpler, "elementary", cases. In particular cases of the mixture densities, the structure (moving average representation) of the aggregated process is investigated.