Bootstrap Confidence Intervals for Significant Wave Height from Measurement Buoy Data

Project info

• Field of studyNaval Architecture and Ocean Engineering
• LevelMaster's thesis (S2)
• Method typeStatistics and Regression
• Estimated build time± 5 working days
• Toolsbootstrp, bootci (Statistics and Machine Learning Toolbox)
• PriceUS$22 - US$144

Research goal

Model significant wave height as a function of peak wave period and surface wind speed with Bootstrap and Confidence Intervals to test their significance.

Variables

Example result

• 39.188Sample mean
• 2.867Bootstrap SE
• 33.952CI lower
• 45.052CI upper
• 11.101CI width
• 0.052Bias

A 2000-replicate bootstrap gives a mean Significant wave height of 39.188 with a standard error of 2.867 and a 95% interval of [33.952, 45.052]; the classical normal interval [33.374, 45.002] is very close.

Computed from illustrative synthetic data, not from a real study.

About Bootstrap and Confidence Intervals

The bootstrap resamples the data with replacement to estimate the distribution of a statistic and its confidence interval without distributional assumptions. It suits small samples, complex statistics such as the median, or non-normal data.

Steps

1. 1Choose the statistic to estimate (mean, median, correlation)
2. 2Set the number of resamples (for example 2000)
3. 3Run bootstrp to get the bootstrap distribution
4. 4Compute the bootstrap standard error and bias
5. 5Compute a confidence interval with bootci (percentile or BCa)
6. 6Plot a histogram of the bootstrap distribution

Assumptions to check

• The original sample represents the population
• Observations are independent
• The number of resamples is large enough for stable intervals

Reading and reporting the results

Report the point estimate, bootstrap standard error, and 95 percent confidence interval with its type (percentile or BCa). Explain that the bootstrap does not fix a biased or too small sample.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(5);
significant_wave_height = exprnd(3, 40, 1);                          % skewed sample
peak_wave_period = 2000;                                      % number of resamples

est = median(significant_wave_height);
bs = bootstrp(peak_wave_period, @median, significant_wave_height);
fprintf('Sample median: %.3f\n', est);
fprintf('Bootstrap SE: %.3f, bias: %.3f\n', std(bs), mean(bs) - est);

ci_per = bootci(peak_wave_period, {@median, significant_wave_height}, 'Type', 'per');
ci_bca = bootci(peak_wave_period, {@median, significant_wave_height}, 'Type', 'bca');
fprintf('95%% percentile CI: [%.3f, %.3f]\n', ci_per(1), ci_per(2));
fprintf('95%% BCa CI: [%.3f, %.3f]\n', ci_bca(1), ci_bca(2));

figure;
histogram(bs, 40); hold on;
xline(est, 'r', 'LineWidth', 1.5);
xline(ci_per(1), 'k--'); xline(ci_per(2), 'k--');
xlabel('Bootstrap median'); ylabel('Frequency');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions