Monte Carlo estimation of the density of the sum of dependent random variables

Laub, Patrick J.; Salomone, Robert; Botev, Zdravko I.

doi:10.1016/j.matcom.2018.12.001

Cited by 10 publications

(10 citation statements)

References 19 publications

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“…It u is unknown; we can represent it through a prior density H (u ). Bayesian inference depends on the combined density in equation ( 31) (Laub et al, 2019):…”

Section: Monte Carlo Modelmentioning

confidence: 99%

“…Methods to estimate both H u (a 1 jb 1 ) and H u (b 1 ), then both H u (a 1:2 jb 1:2 ) and H u (b 1:2 ), and each subsequent step, is elaborated in equation ( 32) (Laub et al, 2019). Under the conditions of SMC techniques, the following dispersals are connected with densities.…”

Section: Monte Carlo Modelmentioning

confidence: 99%

“…It has been predicted that some of these 2 D materials (e.g. MoS2) possess strong intrinsic spin-orbit coupling, which could lead to enhanced spin lifetime and long spin diffusion length (Joshi and Ramachandran, 2019;Kim and Kim, 2008;L'Ecuyer et al, 2019;Laub et al, 2019). The use of 2 D materials will greatly benefit a wide variety of emerging spintronic device concepts, leading to a better manipulation of the spin.…”

Section: Introductionmentioning

confidence: 99%

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Modeling and implementation of spin diode based on two dimensional materials using Monte Carlo sampling method

Makdey

Patrikar

Hashmi

2020

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Purpose A “spin-diode” is the spintronics equivalent of an electrical diode: applying an external magnetic field greater than the limit of spin-diode BT flips the spin-diode between an isolating state and a conducting state [1]. While conventional electrical diodes are two-terminal devices with electrical current between the two terminals modulated by an electrical field, these two-terminal magneto resistive devices can generally be referred to as “spin-diodes” in which a magnetic field modulates the electrical current between the two terminals. Design/methodology/approach Current modulation and rectification are an important subject of electronics as well as spintronics spin diode is two-terminal magnetoresistive devices in which change in resistance in response to an applied magnetic field; this magnetoresistance occurs due to a variety of phenomena and with varying magnitudes and directions. Findings In this paper, an efficient rectifying spin diode is introduced. The resulting spin diode is formed from graphene gallium and indium quantum dots and antimony-doped molybdenum disulfide. Converting an alternating bias voltage to direct current is the main achievement of this model device with an additional profit of rectified spin-current. The non-equilibrium density functional theory with a Monte Carlo sampling method is used to evaluate the flow of electrons and rectification ratio of the system. Originality/value The results indicate that spin diode displaying both spin-current and charge-current rectification should be possible and may find practical application in nanoscale devices that combine logic and memory functions.

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“…It u is unknown; we can represent it through a prior density H (u ). Bayesian inference depends on the combined density in equation ( 31) (Laub et al, 2019):…”

Section: Monte Carlo Modelmentioning

confidence: 99%

Section: Monte Carlo Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling and implementation of spin diode based on two dimensional materials using Monte Carlo sampling method

Makdey

Patrikar

Hashmi

2020

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“…This includes the CDF of sums of Log-normal, Rayleigh, Nakagami, Rice, etc. The calculation of has been extensively investigated in the literature through either approximation methods [13]- [16] or efficient simulation techniques [3], [5], [17]- [20].…”

Section: A Cdf Of the Sum Of Independent Rvsmentioning

confidence: 99%

A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems

Rached

MacKinlay

Botev

et al. 2020

IEEE Trans. Wireless Commun.

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We propose a unified rare-event estimator for the performance evaluation of wireless communication systems. The estimator is derived from the well-known multilevel splitting algorithm. In its original form, the splitting algorithm cannot be applied to the simulation and estimation of time-independent problems, because splitting requires an underlying continuous-time Markov process whose trajectories can be split.We tackle this problem by embedding the static problem of interest within a continuous-time Markov process, so that the target time-independent distribution becomes the distribution of the Markov process at a given time instant. The main feature of the proposed multilevel splitting algorithm is its large scope of applicability. For illustration, we show how the same algorithm can be applied to the problem of estimating the cumulative distribution function (CDF) of sums of random variables (RVs), the CDF of partial sums of ordered RVs, the CDF of ratios of RVs, and the CDF of weighted sums of Poisson RVs. We investigate the computational efficiency of the proposed estimator via a number of simulation studies and find that it compares favorably with existing estimators.

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“…This produces a smoothing effect, illustrated by Figure 1.5 where the pdf of the sum of thirty iid Gamma(3, 2) random variables is estimated with and without CRN using the Monte Carlo estimator in [113]. 1 While using CRN creates a more realistic result for miniminal effort, the effect diminishes as R becomes larger.…”

Section: Common Random Numbersmentioning

confidence: 99%

Computational methods for sums of random variables

Laub¹

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A typical problem in the field of rare-event estimation is to find the probability P(S > γ) where S := X 1 + · · · + X d for a fixed d ∈ N + and where the γ ∈ R is large or increasing. In applications we often wish to understand the behaviour of a combination of random factors. Hence the random variable S is ubiquitous in real-world modeling problems. It can model, for example, aggregate risk or portfolio value for holding d risky assets [124,152], the aggregate losses for d insurance policy claims [14,107], and the combined signal interference from d wireless transmission sources [73]. Probabilities of this form are used to understand how a system would behave under extreme scenarios such as a market crash, a power surge, or a natural disaster. One is typically interested in, not just the quantity P(S > γ), but the behaviour of the summands when the extreme event {S > γ} occurs.

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Monte Carlo estimation of the density of the sum of dependent random variables

Cited by 10 publications

References 19 publications

Modeling and implementation of spin diode based on two dimensional materials using Monte Carlo sampling method

Modeling and implementation of spin diode based on two dimensional materials using Monte Carlo sampling method

A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems

Computational methods for sums of random variables

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