On Dropping the First Sobol’ Point

Owen, Art B.

doi:10.1007/978-3-030-98319-2_4

Cited by 12 publications

(4 citation statements)

References 39 publications

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“…To evaluate the influence of Chl-a, depth, and R rs (560) variability on r b estimation, we generated five synthetic datasets using a revised Saltelli sampling sequence approach [28][29][30][31] (Table 2). This method produces quasi-random sequences of size n × (2p + 2), where p represents the number of input parameters, and n is the baseline sample size.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Global Chlorophyll Concentration Distribution and Effects on Bottom Reflectance of Coral Reefs

Bonelli,

Martin,

Noel

et al. 2024

Oceans

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Despite the limited coverage of coral reefs in the world’s oceans, they play a crucial role in global marine biodiversity and providing essential ecosystem services. This study explores the influence of chlorophyll-a (Chl-a) concentration in the water column on the estimation of bottom reflectance (rb) in coral reefs monitored by the Allen Coral Atlas coral reef monitoring system, using satellite imagery from a Sentinel-2 MSI sensor. We conducted a comprehensive analysis, considering Chl-a global distribution and variability, and its combined effect with water column depth over rb calculation. Our results demonstrated that the impact of Chl-a on rb estimation becomes significant when the water column depth exceeds 3 m. While suggesting the optionality of using regional Chl-a values, our study highlights potential overestimations of Chl-a in optically complex environments, such as along the Brazilian coast. This research contributes to refining coral reef monitoring systems and underscores the importance of accurate Chl-a assessments for robust environmental evaluations.

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Section: Sensitivity Analysismentioning

confidence: 99%

Global Chlorophyll Concentration Distribution and Effects on Bottom Reflectance of Coral Reefs

Bonelli,

Martin,

Noel

et al. 2024

Oceans

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“…QMC methods were added to SciPy (Virtanen et al, 2020) after an extensive review and discussion period (Roy et al, 2021) that lead to a very fruitful collaboration between SciPy's maintainers and renowned researchers in the field. For instance, our implementation inspired additional work on the importance of including the first point in the Sobol' sequence (Owen, 2020).…”

Section: Statement Of Needmentioning

confidence: 99%

Quasi-Monte Carlo Methods in Python

Roy¹,

Owen²,

Balandat³

et al. 2023

JOSS

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NumPy random number generators and SciPy distributions are widely used to generate random numbers. However, challenges might arise when sampling in high dimensions. Quasi-Monte Carlo (QMC) methods provide an answer to these problems but are arguably hard to use. Thanks to new developments in SciPy, a new submodule was introduced in version 1.7.0 making state-of-the-art QMC methods available: scipy.stats.qmc.

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“…We adopt the concepts of determinization (Somani et al, 2013) and common random numbers (Owen, 2013), a popular variance reduction technique: To sample states and observations for episodes on level l , we use a deterministic simulative model,that is, a function fl:S×A×[0,1]↦S×O such that, given a random variable ψ uniformly distributed in [0,1], ( s ’, o ) = f l ( s , a , ψ ) is distributed according to T l ( s , a , s ’) O ( s ’, a , o ). For an initial state s 0 ∼ b t and a sequence of actions, the states and observations of an episode on level l are then deterministically generated from f l using a sequence Ψ = ( ψ 0 , ψ 1 , …) of iid.…”

Section: Multilevel Pomdp Plannermentioning

confidence: 99%

Multilevel Monte Carlo for solving POMDPs on-line

Hoerger

Kurniawati

Elfes

2022

The International Journal of Robotics Research

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Planning under partial observability is essential for autonomous robots. A principled way to address such planning problems is the Partially Observable Markov Decision Process (POMDP). Although solving POMDPs is computationally intractable, substantial advancements have been achieved in developing approximate POMDP solvers in the past two decades. However, computing robust solutions for systems with complex dynamics remains challenging. Most on-line solvers rely on a large number of forward simulations and standard Monte Carlo methods to compute the expected outcomes of actions the robot can perform. For systems with complex dynamics, for example, those with non-linear dynamics that admit no closed-form solution, even a single forward simulation can be prohibitively expensive. Of course, this issue exacerbates for problems with long planning horizons. This paper aims to alleviate the above difficulty. To this end, we propose a new on-line POMDP solver, called Multilevel POMDP Planner (MLPP), that combines the commonly known Monte-Carlo-Tree-Search with the concept of Multilevel Monte Carlo to speed up our capability in generating approximately optimal solutions for POMDPs with complex dynamics. Experiments on four different problems involving torque control, navigation and grasping indicate that MLPP substantially outperforms state-of-the-art POMDP solvers.

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On Dropping the First Sobol’ Point

Cited by 12 publications

References 39 publications

Global Chlorophyll Concentration Distribution and Effects on Bottom Reflectance of Coral Reefs

Global Chlorophyll Concentration Distribution and Effects on Bottom Reflectance of Coral Reefs

Quasi-Monte Carlo Methods in Python

Multilevel Monte Carlo for solving POMDPs on-line

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