MTH522 Project Report

A Bayesian statistician approaches statistical inference using Bayesian probability, which represents a degree of belief or certainty. Bayesian statistics incorporates prior knowledge or beliefs about parameters and updates them based on observed data using Bayes’ theorem. This leads to the calculation of posterior probabilities, which express the probability of hypotheses given the data. Bayesian methods are particularly useful when dealing with small sample sizes or when incorporating existing knowledge into statistical analysis.

For example imagine a scenario where a pharmaceutical company wants to test the effectiveness of a new drug. A Bayesian statistician would start with prior beliefs about the drug’s effectiveness based on existing knowledge or previous studies. As new data from clinical trials becomes available, these prior beliefs are updated using Bayes’ theorem to calculate the posterior probability of the drug being effective. The Bayesian approach allows for the incorporation of prior knowledge into the analysis, making it especially useful when dealing with limited data.

Frequentist Statistician:

A frequentist statistician approaches statistical inference by focusing on the frequency or probability of events. In this framework, probabilities are associated with the frequency of events in repeated random sampling. Key concepts include point estimation, confidence intervals, and hypothesis testing. The emphasis is on using observed data to make inferences about the true values of population parameters. Frequentist methods do not assign probabilities to hypotheses; instead, they view hypotheses as fixed and the data as variable.

For example, Let’s say we want to estimate the average height of students in a school. A frequentist statistician would take random samples of students, calculate the average height in each sample, and use these averages to make inferences about the true average height of all students in the school. The focus is on using the observed data (sample means) to estimate and make statements about the population parameter (true average height).

Today I have learned about KNN (K Nearest Neighbors) algorithm, a handy tool for our Project 2 dataset. KNN excels at finding similarities in datasets where similar features tend to cluster together. The process involves addressing missing values, normalizing numerical features for equal importance, selecting relevant features like demographics and city data, splitting the dataset for training and testing, determining the optimal number of neighbors (K), training the model, evaluating its performance, and finally using it to predict categories for new data points. KNN’s focus on similarity makes it particularly useful for uncovering patterns in geographical dynamics.