Analytic multivariate generating function for random multiplicative cascade processes

We have found an analytic expression for the multivariate generating function governing all n-point statistics of random multiplicative cascade processes. The variable appropriate for this generating function is the logarithm of the energy density, ln epsilon, rather than epsilon itself. All cumulant statistics become sums over derivatives of ``branching generating functions'' which are Laplace transforms of the splitting functions and completely determine the cascade process. We show that the branching generating function is a generalization of the multifractal mass exponents. Two simple models from fully developed turbulence illustrate the new formalism.Comment: REVTeX, 4 pages, 2 PostScript figs, submitted to PR

Determining source cumulants in femtoscopy with Gram-Charlier and Edgeworth series

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram-Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for nongaussian distributions.Comment: 11 pages, 2 figure

Spatial correlations of singularity strengths in multifractal branching processes

The n-point statistics of singularity strength variables for multiplicative branching processes is calculated from an analytic expression of the corresponding multivariate generating function. The key ingredient is a branching generating function which can be understood as a natural generalisation of the multifractal mass exponents. Various random multiplicative cascade processes pertaining to fully developed turbulence are discussed.Comment: REVTeX, 18 pages, 5 PS figs, submitted to PR

Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimation

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

Cumulant ratios in fully developed turbulence

In the context of random multiplicative cascade processes, we derive analytical solutions for one- and two-point cumulants with restored translational invariance. On taking ratios of cumulants in ln epsilon, geometrical effects due to spatial averaging cancel out. These ratios can successfully distinguish between splitting functions while multifractal scaling exponents and multiplier distributions cannot.Comment: 9th Workshop on Multiparticle Production (Torino), 9 pages latex, incl 9 figs and espcrc2.st

Stochastic energy-cascade model for 1+1 dimensional fully developed turbulence

Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as the energy dissipation in fully developed turbulence. We propose a dynamical generalization describing the energy dissipation in terms of a continuous and homogeneous stochastic field in one space and one time dimension. In the model, correlations originate in the overlap of the respective spacetime histories of field amplitudes. The theoretical two- and three-point correlation functions are found to be in good agreement with their equal-time counterparts extracted from wind tunnel turbulent shear flow data

Translationally invariant cumulants in energy cascade models of turbulence

In the context of random multiplicative energy cascade processes, we derive analytical expressions for translationally invariant one- and two-point cumulants in logarithmic field amplitudes. Such cumulants make it possible to distinguish between hitherto equally successful cascade generator models and hence supplement lowest-order multifractal scaling exponents and multiplier distributions.Comment: 11 pages, 3 figs, elsart.cls include