Application of the extreme value theory to beam loss estimates in the SPIRAL2 linac based on large scale Monte Carlo computations

Extreme Value Theory (EVT) is an important tool to predict efficient gains and losses. Its main areas of analyses are economic and environmental. Initially, for that form of event, it was developed the use of patterns of parametric distribution such as Normal and Gamma. However, economic and environmental data presents, in most cases, a heavy-tailed distribution, in contrast to those distributions. Thus, it was faced a great difficult to frame extreme events. Furthermore, it was almost impossible to use conventional models, making predictions about non-observed events, which exceed the maximum of observations. In some situations EVT is used to analyse only the maximum of some dataset, which provide few observations, and in those cases it is more effective to use the r largest-order statistics. This paper aims to propose Bayesian estimators' for parameters of the r largest-order statistics. During the research, it was used Monte Carlo simulation to analyze the data, and it was observed some properties of those estimators, such as mean, variance, bias and Root Mean Square Error (RMSE). The estimation of the parameters provided inference for its parameters and return levels. This paper also shows a procedure to the choice of the r-optimal to the r largest-order statistics, based on the Bayesian approach applying Markov chains Monte Carlo (MCMC). Simulation results reveal that the Bayesian approach has a similar performance to the Maximum Likelihood Estimation, and the applications were developed using the Bayesian approach and showed a gain in accurary compared with otherestimators.

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Distribution Endpoint Estimation Assessment for the use in Metaheuristic Optimization Procedure

MENDEL ◽

10.13164/mendel.2018.1.093 ◽

2018 ◽

Vol 24 (1) ◽

pp. 93-100

Author(s):

Jan Holesovky

Keyword(s):

Extreme Value Theory ◽

Large Scale ◽

Optimization Problems ◽

Random Search ◽

Optimization Procedure ◽

Short Review ◽

Value Theory ◽

Extreme Value ◽

Mixed Integer ◽

Endpoint Estimation

Metaheuristic algorithms are often applied to numerous optimization problems, involving large-scale and mixed-integer instances, specifically. In this contribution we discuss some refinements from the extreme value theory to the lately proposed modification of partition-based random search. The partition-based approach performs iterative random sampling at given feasible subspaces in order to exclude the less favourable regions. The quality of particular regions is evaluated according to the promising index of a region. From statistical perspective, determining the promising index is equivalent to the endpoint estimation of a probability distribution induced by the objective function at the sampling subspace. In the following paper, we give a short review of the recent endpoint estimators derived on the basis of extreme value theory, and compare them by simulations. We discuss also the difficulties in their application and suitability of the estimators for various optimization instances.

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Extreme value theory as a framework for understanding mutation frequency distribution in cancer genomes

PLoS ONE ◽

10.1371/journal.pone.0243595 ◽

2021 ◽

Vol 16 (8) ◽

pp. e0243595

Author(s):

Natsuki Tokutomi ◽

Kenta Nakai ◽

Sumio Sugano

Keyword(s):

Population Dynamics ◽

Extreme Value Theory ◽

Large Scale ◽

Mutation Frequency ◽

Sequence Data ◽

Value Theory ◽

Extreme Value ◽

Cancer Genome ◽

Driver Mutation ◽

Cancer Genomes

Currently, the population dynamics of preclonal cancer cells before clonal expansion of tumors has not been sufficiently addressed thus far. By focusing on preclonal cancer cell population as a Darwinian evolutionary system, we formulated and analyzed the observed mutation frequency among tumors (MFaT) as a proxy for the hypothesized sequence read frequency and beneficial fitness effect of a cancer driver mutation. Analogous to intestinal crypts, we assumed that sample donor patients are separate culture tanks where proliferating cells follow certain population dynamics described by extreme value theory (EVT). To validate this, we analyzed three large-scale cancer genome datasets, each harboring > 10000 tumor samples and in total involving > 177898 observed mutation sites. We clarified the necessary premises for the application of EVT in the strong selection and weak mutation (SSWM) regime in relation to cancer genome sequences at scale. We also confirmed that the stochastic distribution of MFaT is likely of the Fréchet type, which challenges the well-known Gumbel hypothesis of beneficial fitness effects. Based on statistical data analysis, we demonstrated the potential of EVT as a population genetics framework to understand and explain the stochastic behavior of driver-mutation frequency in cancer genomes as well as its applicability in real cancer genome sequence data.

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Extreme value theory as a general framework for understanding mutation frequency distribution in cancer genomes

10.1101/2020.11.25.397562 ◽

2020 ◽

Author(s):

Natsuki Tokutomi ◽

Kenta Nakai ◽

Sumio Sugano

Keyword(s):

Population Genetics ◽

Population Dynamics ◽

Extreme Value Theory ◽

Large Scale ◽

Mutation Frequency ◽

Value Theory ◽

Extreme Value ◽

Cancer Genome ◽

Driver Mutation ◽

Cancer Genomes

AbstractCurrently, there is no recognized population genetics framework describing the population dynamics of cancer cells that is applicable to real cancer genome data. By focusing on cancer as a Darwinian evolutionary system, we formulated and analyzed the observed mutation frequency among tumors (MFaT) as a proxy for the hypothesized sequence read frequency and beneficial fitness effect of a cancer driver mutation. Analogous to intestinal crypts, we assumed that sample donor patients are separate culture tanks where proliferating cells follow certain population dynamics described by extreme value theory (EVT). To validate this, we analyzed three large-scale cancer genome datasets, each harboring > 10 000 tumor samples and in total involving > 177 898 observed mutation sites. We clarified the necessary premises for the application of EVT in the strong selection and weak mutation (SSWM) regime in relation to cancer genome sequences at scale. We also confirmed that the stochastic distribution of MFaT is likely of the Fréchet type, which challenges the well-known Gumbel hypothesis of beneficial fitness effects. Based on statistical data analysis, we demonstrated the potential of EVT as a population genetics framework to understand and explain the stochastic behavior of driver-mutation frequency in cancer genomes as well as its applicability in real cancer genome sequence data.

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