An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

Why Monte Carlo Simulations are Inferences and not Experiments

Monte Carlo simulations arrive at their results by introducing randomness, sometimes derived from a physical randomizing device. Nonetheless, we argue, they open no new epistemic channels beyond that already employed by traditional simulations: the inference by ordinary argumentation of conclusions from assumptions built into the simulations. We show that Monte Carlo simulations cannot produce knowledge other than by inference, and that they resemble other computer simulations in the manner in which they derive their conclusions. Simple examples of Monte Carlo simulations are analysed to identify the underlying inferences.

More than just Good Luck. How to Explain the Success of Monte Carlo Simulations

Monte Carlo simulation is a powerful method in many natural and social sciences. But what sort of method is it? And where does its power come from? Are Monte Carlo simulations experiments, theories or something else? The aim of this talk is to answer these questions and to explain the power of Monte Carlo simulations. I provide a classification of Monte Carlo techniques and defend the claim that Monte Carlo simulation is a sort of inference.

Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

A critical evaluation of secondary cancer risk models applied to Monte Carlo dose distributions of 2-dimensional, 3-dimensional conformal and hybrid intensity-modulated radiation therapy for breast cancer

The comparison of radiotherapy techniques regarding secondary cancer risk has yielded contradictory results possibly stemming from the many different approaches used to estimate risk. The purpose of this study was to make a comprehensive evaluation of different available risk models applied to detailed whole-body dose distributions computed by Monte Carlo for various breast radiotherapy techniques including conventional open tangents, 3D conformal wedged tangents and hybrid intensity modulated radiation therapy (IMRT). First, organ-specific linear risk models developed by the International Commission on Radiological Protection (ICRP) and the Biological Effects of Ionizing Radiation (BEIR) VII committee were applied to mean doses for remote organs only and all solid organs. Then, different general non-linear risk models were applied to the whole body dose distribution. Finally, organ-specific non-linear risk models for the lung and breast were used to assess the secondary cancer risk for these two specific organs. A total of 32 different calculated absolute risks resulted in a broad range of values (between 0.1% and 48.5%) underlying the large uncertainties in absolute risk calculation. The ratio of risk between two techniques has often been proposed as a more robust assessment of risk than the absolute risk. We found that the ratio of risk between two techniques could also vary substantially considering the different approaches to risk estimation. Sometimes the ratio of risk between two techniques would range between values smaller and larger than one, which then translates into inconsistent results on the potential higher risk of one technique compared to another. We found however that the hybrid IMRT technique resulted in a systematic reduction of risk compared to the other techniques investigated even though the magnitude of this reduction varied substantially with the different approaches investigated. Based on the epidemiological data available, a reasonable approach to risk estimation would be to use organ-specific non-linear risk models applied to the dose distributions of organs within or near the treatment fields (lungs and contralateral breast in the case of breast radiotherapy) as the majority of radiation-induced secondary cancers are found in the beam-bordering regions.

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part I

This bipartite comparative study aims at inspecting the similarities and differences between the Jones and Stokes–Mueller formalisms when modeling polarized light propagation with numerical simulations of the Monte Carlo type. In this first part, we review the theoretical concepts that concern light propagation and detection with both pure and partially/totally unpolarized states. The latter case involving fluctuations, or “depolarizing effects,” is of special interest here: Jones and Stokes–Mueller are equally apt to model such effects and are expected to yield identical results. In a second, ensuing paper, empirical evidence is provided by means of numerical experiments, using both formalisms.

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part II

In this second part of our comparative study inspecting the (dis)similarities between “Stokes” and “Jones,” we present simulation results yielded by two independent Monte Carlo programs: (i) one developed in Bern with the Jones formalism and (ii) the other implemented in Ulm with the Stokes notation. The simulated polarimetric experiments involve suspensions of polystyrene spheres with varying size. Reflection and refraction at the sample/air interfaces are also considered. Both programs yield identical results when propagating pure polarization states, yet, with unpolarized illumination, second order statistical differences appear, thereby highlighting the pre-averaged nature of the Stokes parameters. This study serves as a validation for both programs and clarifies the misleading belief according to which “Jones cannot treat depolarizing effects.”

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

Monte-Carlo simulation of Callisto's exosphere

We model Callisto's exosphere based on its ice as well as non-ice surface via the use of a Monte-Carlo exosphere model. For the ice component we implement two putative compositions that have been computed from two possible extreme formation scenarios of the satellite. One composition represents the oxidizing state and is based on the assumption that the building blocks of Callisto were formed in the protosolar nebula and the other represents the reducing state of the gas, based on the assumption that the satellite accreted from solids condensed in the jovian sub-nebula. For the non-ice component we implemented the compositions of typical CI as well as L type chondrites. Both chondrite types have been suggested to represent Callisto's non-ice composition best. As release processes we consider surface sublimation, ion sputtering and photon-stimulated desorption. Particles are followed on their individual trajectories until they either escape Callisto's gravitational attraction, return to the surface, are ionized, or are fragmented. Our density profiles show that whereas the sublimated species dominate close to the surface on the sun-lit side, their density profiles (with the exception of H and H-2) decrease much more rapidly than the sputtered particles. The Neutral gas and Ion Mass (NIM) spectrometer, which is part of the Particle Environment Package (PEP), will investigate Callisto's exosphere during the JUICE mission. Our simulations show that NIM will be able to detect sublimated and sputtered particles from both the ice and non-ice surface. NIM's measured chemical composition will allow us to distinguish between different formation scenarios. (C) 2015 Elsevier Inc. All rights reserved.