A bias in cosmic shear from galaxy selection: results from ray-tracing simulations

We identify and study a previously unknown systematic effect on cosmic shear measurements, caused by the selection of galaxies used for shape measurement, in particular the rejection of close (blended) galaxy pairs. We use ray-tracing simulations based on the Millennium Simulation and a semi-analytical model of galaxy formation to create realistic galaxy catalogues. From these, we quantify the bias in the shear correlation functions by comparing measurements made from galaxy catalogues with and without removal of close pairs. A likelihood analysis is used to quantify the resulting shift in estimates of cosmological parameters. The filtering of objects with close neighbours (a) changes the redshift distribution of the galaxies used for correlation function measurements, and (b) correlates the number density of sources in the background with the density field in the foreground. This leads to a scale-dependent bias of the correlation function of several percent, translating into biases of cosmological parameters of similar amplitude. This makes this new systematic effect potentially harmful for upcoming and planned cosmic shear surveys. As a remedy, we propose and test a weighting scheme that can significantly reduce the bias.Comment: 9 pages, 9 figures, version accepted for publication in Astronomy & Astrophysic

A Bayesian Approach toward Active Learning for Collaborative Filtering

Collaborative filtering is a useful technique for exploiting the preference patterns of a group of users to predict the utility of items for the active user. In general, the performance of collaborative filtering depends on the number of rated examples given by the active user. The more the number of rated examples given by the active user, the more accurate the predicted ratings will be. Active learning provides an effective way to acquire the most informative rated examples from active users. Previous work on active learning for collaborative filtering only considers the expected loss function based on the estimated model, which can be misleading when the estimated model is inaccurate. This paper takes one step further by taking into account of the posterior distribution of the estimated model, which results in more robust active learning algorithm. Empirical studies with datasets of movie ratings show that when the number of ratings from the active user is restricted to be small, active learning methods only based on the estimated model don't perform well while the active learning method using the model distribution achieves substantially better performance.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004

Iterated filtering methods for Markov process epidemic models

Dynamic epidemic models have proven valuable for public health decision makers as they provide useful insights into the understanding and prevention of infectious diseases. However, inference for these types of models can be difficult because the disease spread is typically only partially observed e.g. in form of reported incidences in given time periods. This chapter discusses how to perform likelihood-based inference for partially observed Markov epidemic models when it is relatively easy to generate samples from the Markov transmission model while the likelihood function is intractable. The first part of the chapter reviews the theoretical background of inference for partially observed Markov processes (POMP) via iterated filtering. In the second part of the chapter the performance of the method and associated practical difficulties are illustrated on two examples. In the first example a simulated outbreak data set consisting of the number of newly reported cases aggregated by week is fitted to a POMP where the underlying disease transmission model is assumed to be a simple Markovian SIR model. The second example illustrates possible model extensions such as seasonal forcing and over-dispersion in both, the transmission and observation model, which can be used, e.g., when analysing routinely collected rotavirus surveillance data. Both examples are implemented using the R-package pomp (King et al., 2016) and the code is made available online.Comment: This manuscript is a preprint of a chapter to appear in the Handbook of Infectious Disease Data Analysis, Held, L., Hens, N., O'Neill, P.D. and Wallinga, J. (Eds.). Chapman \& Hall/CRC, 2018. Please use the book for possible citations. Corrected typo in the references and modified second exampl

Approximate Bayesian Computation in State Space Models

A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data simulated from the true process; exact inference being feasible only if the statistics are sufficient. With finite sample sufficiency unattainable in the state space setting, we seek asymptotic sufficiency via the maximum likelihood estimator (MLE) of the parameters of an auxiliary model. We prove that this auxiliary model-based approach achieves Bayesian consistency, and that - in a precise limiting sense - the proximity to (asymptotic) sufficiency yielded by the MLE is replicated by the score. In multiple parameter settings a separate treatment of scalar parameters, based on integrated likelihood techniques, is advocated as a way of avoiding the curse of dimensionality. Some attention is given to a structure in which the state variable is driven by a continuous time process, with exact inference typically infeasible in this case as a result of intractable transitions. The ABC method is demonstrated using the unscented Kalman filter as a fast and simple way of producing an approximation in this setting, with a stochastic volatility model for financial returns used for illustration

Filtering and forecasting commodity futures prices under an HMM framework

We propose a model for the evolution of arbitrage-free futures prices under a regime-switching framework. The estimation of model parameters is carried out using the hidden Markov filtering algorithms. Comprehensive numerical experiments on real financial market data are provided to illustrate the effectiveness of our algorithm. In particular, the model is calibrated with data from heating oil futures and its forecasting performance as well as statistical validity is investigated. The proposed model is parsimonious, self-calibrating and can be very useful in predicting futures prices. © 2013 Elsevier B.V

Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models

A computationally simple approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics for the observed data with statistics computed from data simulated from the true process, based on parameter draws from the prior. Draws that produce a 'match' between observed and simulated summaries are retained, and used to estimate the inaccessible posterior. With no reduction to a low-dimensional set of sufficient statistics being possible in the state space setting, we define the summaries as the maximum of an auxiliary likelihood function, and thereby exploit the asymptotic sufficiency of this estimator for the auxiliary parameter vector. We derive conditions under which this approach - including a computationally efficient version based on the auxiliary score - achieves Bayesian consistency. To reduce the well-documented inaccuracy of ABC in multi-parameter settings, we propose the separate treatment of each parameter dimension using an integrated likelihood technique. Three stochastic volatility models for which exact Bayesian inference is either computationally challenging, or infeasible, are used for illustration. We demonstrate that our approach compares favorably against an extensive set of approximate and exact comparators. An empirical illustration completes the paper.Comment: This paper is forthcoming at the Journal of Computational and Graphical Statistics. It also supersedes the earlier arXiv paper "Approximate Bayesian Computation in State Space Models" (arXiv:1409.8363

Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes

We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully automated procedure that goes from raw data to an identified model. Both pre-processing parameters and GP hyper-parameters are tuned by maximizing the marginal likelihood of the probabilistic model. We obtain a Bayesian model of the system's dynamics which is able to report its uncertainty in regions where the data is scarce. The automated approach, the modeling of uncertainty and its relatively low computational cost make of GP-FNARX a good candidate for applications in robotics and adaptive control.Comment: Proceedings of the 52th IEEE International Conference on Decision and Control (CDC), Firenze, Italy, December 201