Academic literature on the topic 'Bootstrap'

In the simulation output analysis, there are some measures that should be calculated by time average concept such as the mean queue length. Especially, the confidence interval of those measures might be required for statistical analysis. In this situation, the traditional method that utilizes the central limit theorem (CLT) is inapplicable if the output data set has autocorrelation structure. The bootstrap is one of the most suitable methods which can reflect the autocorrelated phenomena in statistical analysis. Therefore, the confidence interval for a time averaged measure having autocorrelation structure can also be calculated by the bootstrap methods. This study introduces the method that constructs these confidence intervals applying the bootstraps. The bootstraps proposed are the threshold bootstrap (TB), the moving block bootstrap (MBB) and stationary bootstrap (SB). Finally, some numerical examples will be provided for verification.

Information dynamics and computational mechanics provide a suite of measures for assessing the information- and computation-theoretic properties of complex systems in the absence of mechanistic models. However, both approaches lack a core set of inferential tools needed to make them more broadly useful for analyzing real-world systems, namely reliable methods for constructing confidence sets and hypothesis tests for their underlying measures. We develop the computational mechanics bootstrap, a bootstrap method for constructing confidence sets and significance tests for information-dynamic measures via confidence distributions using estimates of ϵ -machines inferred via the Causal State Splitting Reconstruction (CSSR) algorithm. Via Monte Carlo simulation, we compare the inferential properties of the computational mechanics bootstrap to a Markov model bootstrap. The computational mechanics bootstrap is shown to have desirable inferential properties for a collection of model systems and generally outperforms the Markov model bootstrap. Finally, we perform an in silico experiment to assess the computational mechanics bootstrap’s performance on a corpus of ϵ -machines derived from the activity patterns of fifteen-thousand Twitter users.

Abstract. Bootstrap resamples can be used to investigate the tail of empirical distributions as well as return value estimates from the extremal behaviour of the sample. Specifically, the confidence intervals on return value estimates or bounds on in-sample tail statistics can be obtained using bootstrap techniques. However, non-parametric bootstrapping from the entire sample is expensive. It is shown here that it suffices to bootstrap from a small subset consisting of the highest entries in the sequence to make estimates that are essentially identical to bootstraps from the entire sample. Similarly, bootstrap estimates of confidence intervals of threshold return estimates are found to be well approximated by using a subset consisting of the highest entries. This has practical consequences in fields such as meteorology, oceanography and hydrology where return values are calculated from very large gridded model integrations spanning decades at high temporal resolution or from large ensembles of independent and identically distributed model fields. In such cases the computational savings are substantial.

Abstract. Sea-ice concentrations derived from satellite microwave brightness temperatures are less accurate during summer. In the Arctic Ocean the lack of accuracy is primarily caused by melt ponds, but also by changes in the properties of snow and the sea-ice surface itself. We investigate the sensitivity of eight sea-ice concentration retrieval algorithms to melt ponds by comparing sea-ice concentration with the melt-pond fraction. We derive gridded daily sea-ice concentrations from microwave brightness temperatures of summer 2009. We derive the daily fraction of melt ponds, open water between ice floes, and the ice-surface fraction from contemporary Moderate Resolution Spectroradiometer (MODIS) reflectance data. We only use grid cells where the MODIS sea-ice concentration, which is the melt-pond fraction plus the ice-surface fraction, exceeds 90 %. For one group of algorithms, e.g., Bristol and Comiso bootstrap frequency mode (Bootstrap_f), sea-ice concentrations are linearly related to the MODIS melt-pond fraction quite clearly after June. For other algorithms, e.g., Near90GHz and Comiso bootstrap polarization mode (Bootstrap_p), this relationship is weaker and develops later in summer. We attribute the variation of the sensitivity to the melt-pond fraction across the algorithms to a different sensitivity of the brightness temperatures to snow-property variations. We find an underestimation of the sea-ice concentration by between 14 % (Bootstrap_f) and 26 % (Bootstrap_p) for 100 % sea ice with a melt-pond fraction of 40 %. The underestimation reduces to 0 % for a melt-pond fraction of 20 %. In presence of real open water between ice floes, the sea-ice concentration is overestimated by between 26 % (Bootstrap_f) and 14 % (Bootstrap_p) at 60 % sea-ice concentration and by 20 % across all algorithms at 80 % sea-ice concentration. None of the algorithms investigated performs best based on our investigation of data from summer 2009. We suggest that those algorithms which are more sensitive to melt ponds could be optimized more easily because the influence of unknown snow and sea-ice surface property variations is less pronounced.