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Bootstrapping is a statistical resampling method used to estimate the distribution of a sample statistic (like the mean, median, variance) by repeatedly sampling from the original dataset with replacement. The primary idea is to generate "new" samples (called bootstrap samples) by randomly selecting data points from the original sample, allowing some points to be selected multiple times while others may not be selected at all.

Steps of Bootstrapping:

1. Original sample: Start with a dataset of size n.

2. Resampling: Generate multiple new datasets (bootstrap samples) of the same size n by sampling with replacement from the original dataset.

3. Statistic calculation: For each bootstrap sample, calculate the statistic of interest (e.g., the mean).

4. Aggregation: After many resamplings (typically thousands), aggregate these statistics to estimate properties like confidence intervals, standard errors, or the distribution of the statistic.

Efficacy in Augmenting Sample Size:

While bootstrapping doesn’t actually create new, independent data, it is effective at enhancing statistical insights from small samples by simulating variability and giving a better approximation of the underlying population’s distribution. Its efficacy is most pronounced when:

• Small samples: Bootstrapping is especially useful for datasets where traditional parametric methods may not be applicable due to the small sample size or assumptions (like normality).

• Non-parametric nature: It does not require assumptions about the distribution of the data, making it versatile.

• Uncertainty Estimation: It helps estimate confidence intervals, standard errors, and biases for small samples when direct analytical solutions are difficult.

However, since bootstrapping is based on the assumption that the original sample is representative of the population, its effectiveness can be limited when the original sample is biased or unrepresentative. It’s not a substitute for truly increasing the sample size but is a powerful technique for making the most of available data.

Bias means underfitting. The model is too simple that it does not learn all the patterns in the training data. When using it in the testing dataset, it will miss several patterns. Variance means overfitting. The model learns even noise data, causing it to be sensitive to outliers during testing. The general pattern is impacted by noise in testing data.