Browsing by Author "Eggers, Hans C."

Now showing 1 - 4 of 4
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    A class of spatio-temporal and causal stochastic processes, with application to multiscaling and multifractality
    (Academy of Science for South Africa, 2005) Schmiegel, Schmiegel; Barndorff-Nielsen, Ole E.; Eggers, Hans C.
    We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Lévy type whose weighted amplitudes are integrated within a causality cone. General n-point correlations are derived in closed form. As a special case of the general framework, we consider a causal multiscaling process in space and time in more detail. The latter is derived from, and completely specifed by, power-law two-point correlations, and gives rise to scaling behaviour of both purely temporal and spatial higher-order correlations. We further establish the connection to classical multifractality and prove the multifractal nature of the coarse-grained field amplitude.
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    From chi^2 to Bayesian model comparison : the example of Levy-based fits to e+e- correlations
    (Proceedings of Science, 2012) De Kock, Michiel B.; Eggers, Hans C.; Csorgo, Tamas
    The usual χ2 method of fit quality assessment is a special case of the more general method of Bayesian model comparison which involves integrals of the likelihood and prior over all possible values of all parameters. We introduce new parametrisations based on systematic expansions around the stretched exponential or Fourier-transformed Lévy source distribution, and utilise the increased discriminating power of the Bayesian approach to evaluate the relative probability of these models to be true representations of a recently measured Bose-Einstein correlation data in e +e− annihilations at LEP.
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    Rapid deconvolution of low-resolution time-of-flight data using Bayesian inference
    (AIP Publishing LLC, 2019) Pieterse, Cornelius L.; De Kock, Michiel B.; Robertson, Wesley D.; Eggers, Hans C.; Miller, R. J. Dwayne
    The deconvolution of low-resolution time-of-flight data has numerous advantages, including the ability to extract additional information from the experimental data. We augment the well-known Lucy-Richardson deconvolution algorithm using various Bayesian prior distributions and show that a prior of second-differences of the signal outperforms the standard Lucy-Richardson algorithm, accelerating the rate of convergence by more than a factor of four, while preserving the peak amplitude ratios of a similar fraction of the total peaks. A novel stopping criterion and boosting mechanism are implemented to ensure that these methods converge to a similar final entropy and local minima are avoided. Improvement by a factor of two in mass resolution allows more accurate quantification of the spectra. The general method is demonstrated in this paper through the deconvolution of fragmentation peaks of the 2,5-dihydroxybenzoic acid matrix and the benzyltriphenylphosphonium thermometer ion, following femtosecond ultraviolet laser desorption.
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    Stochastic gradient annealed importance sampling for efficient online marginal likelihood estimation
    (MDPI, 2019-11-12) Cameron, Scott A.; Eggers, Hans C.; Kroon, Steve
    We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by using stochastic gradient Markov Chain Monte Carlo techniques. This approach is far more efficient than traditional marginal likelihood estimation techniques such as nested sampling and annealed importance sampling due to its use of mini-batches to approximate the likelihood. Stability of the estimates is provided by an adaptive annealing schedule. The resulting stochastic gradient annealed importance sampling (SGAIS) technique, which is the key contribution of our paper, enables us to estimate the marginal likelihood of a number of models considerably faster than traditional approaches, with no noticeable loss of accuracy. An important benefit of our approach is that the marginal likelihood is calculated in an online fashion as data becomes available, allowing the estimates to be used for applications such as online weighted model combination.