Forgetting the starting distribution in finite interacting tempering

Markov chain Monte Carlo (MCMC) methods are frequently used to approximately simulate high-dimensional, multimodal probability distributions. In adaptive MCMC methods, the transition kernel is changed "on the fly" in the hope to speed up convergence. We study interacting tempering, an adaptive MCMC algorithm based on interacting Markov chains, that can be seen as a simplified version of the equi-energy sampler. Using a coupling argument, we show that under easy to verify assumptions on the target distribution (on a finite space), the interacting tempering process rapidly forgets its starting distribution. The result applies, among others, to exponential random graph models, the Ising and Potts models (in mean field or on a bounded degree graph), as well as (Edwards-Anderson) Ising spin glasses. As a cautionary note, we also exhibit an example of a target distribution for which the interacting tempering process rapidly forgets its starting distribution, but takes an exponential number of steps (in the dimension of the state space) to converge to its limiting distribution. As a consequence, we argue that convergence diagnostics that are based on demonstrating that the process has forgotten its starting distribution might be of limited use for adaptive MCMC algorithms like interacting tempering

Adaptive filtering techniques for gravitational wave interferometric data: Removing long-term sinusoidal disturbances and oscillatory transients

It is known by the experience gained from the gravitational wave detector proto-types that the interferometric output signal will be corrupted by a significant amount of non-Gaussian noise, large part of it being essentially composed of long-term sinusoids with slowly varying envelope (such as violin resonances in the suspensions, or main power harmonics) and short-term ringdown noise (which may emanate from servo control systems, electronics in a non-linear state, etc.). Since non-Gaussian noise components make the detection and estimation of the gravitational wave signature more difficult, a denoising algorithm based on adaptive filtering techniques (LMS methods) is proposed to separate and extract them from the stationary and Gaussian background noise. The strength of the method is that it does not require any precise model on the observed data: the signals are distinguished on the basis of their autocorrelation time. We believe that the robustness and simplicity of this method make it useful for data preparation and for the understanding of the first interferometric data. We present the detailed structure of the algorithm and its application to both simulated data and real data from the LIGO 40meter proto-type.Comment: 16 pages, 9 figures, submitted to Phys. Rev.

Patterns of Scalable Bayesian Inference

Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response to this challenge, there has been considerable recent work based on varying assumptions about model structure, underlying computational resources, and the importance of asymptotic correctness. As a result, there is a zoo of ideas with few clear overarching principles. In this paper, we seek to identify unifying principles, patterns, and intuitions for scaling Bayesian inference. We review existing work on utilizing modern computing resources with both MCMC and variational approximation techniques. From this taxonomy of ideas, we characterize the general principles that have proven successful for designing scalable inference procedures and comment on the path forward

A Bayesian approach to the study of white dwarf binaries in LISA data: The application of a reversible jump Markov chain Monte Carlo method

The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals "out of the box'', handling the total number of signals as an additional unknown parameter beside the unknown parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals.Comment: 18 pages, 9 figures, 3 tables, accepted for publication in PRD, revised versio

Wavelet-based response spectrum compatible synthesis of accelerograms-Eurocode application (EC8)

An integrated approach for addressing the problem of synthesizing artificial seismic accelerograms compatible with a given displacement design/target spectrum is presented in conjunction with aseismic design applications. Initially, a stochastic dynamics solution is used to obtain a family of simulated non-stationary earthquake records whose response spectrum is on the average in good agreement with the target spectrum. The degree of the agreement depends significantly on the adoption of an appropriate parametric evolutionary power spectral form, which is related to the target spectrum in an approximate manner. The performance of two commonly used spectral forms along with a newly proposed one is assessed with respect to the elastic displacement design spectrum defined by the European code regulations (EC8). Subsequently, the computational versatility of the family of harmonic wavelets is employed to modify iteratively the simulated records to satisfy the compatibility criteria for artificial accelerograms prescribed by EC8. In the process, baseline correction steps, ordinarily taken to ensure that the obtained accelerograms are characterized by physically meaningful velocity and displacement traces, are elucidated. Obviously, the presented approach can be used not only in the case of the EC8, for which extensive numerical results/examples are included, but also for any code provisions mandated by regulatory agencies. In any case, the presented numerical results can be quite useful in any aseismic design process dominated by the EC8 specifications