Mathematics

Time Series Analysis Part 5 – Oxford Temperature

Over the past 4 articles the focus was on applying time series techniques to generated time series data. The last article walked through a build up of a multiple linear regression model while incorporating time lags and trend as features. This resulted in a model with MSE comparable to the…

Time Series Analysis Part 4 – Multiple Linear Regression

byadmin June 2, 2022 Linear Regression Regression Statistics Time Series

Over the past 3 articles on time series we applied ARMA, ARIMA and SARIMA to time series examples and proceeded toward model selection via either AIC (Akaike Information Criterion) or MSE on unseen data. Here, we approach the same time series as found in Time Series Analysis Part 3 – Assessing Model Fit from a Linear Regression point of view

Time Series Analysis Part 3 – Assessing Model Fit

byadmin May 21, 2022 Statistics Time Series

In the previous articles we focused on time series structure and forecasting. We previously used AIC for model selection. Here, we focus on assessing model fit on unseen data by using the MSE as the quality of fit

Time Series Analysis Part 2 – Forecasting

byadmin May 8, 2022 Regression Statistics Time Series

This article will walk through the steps in Time Series Analysis 1 - Identifying Structure and use this knowledge to forecast. Here we will tackle the seasonality component as well.

Time Series Analysis 1 – Identifying Structure

byadmin April 23, 2022 Regression Statistics Time Series

In this article we tackle a generated set of progressively more complex time series datasets. From a random series to an ARIMA series with seasonality as well as a series with a structural change. For each of these time series we apply the traditional techniques used in time series analysis to ascertain the underlying structure. In a follow up article we will make the final step to use what we've learned to forecast into the future.

Naive Bayes

byadmin January 16, 2022 Classification Mathematics Statistics

Let’s focus on this table. Subscript, , is used to represent the feature/dimension. Superscript, , is used to represent the observation (here the observation). First, we make some basic assertions about the data. Distributions Each has a Categorical distribution: (1) The following is equivalent: (2) , and is the probability…

Gambler’s Ruin

byadmin February 8, 2020 Difference Equations Mathematics Python

Suppose I start gambling with $13 and with the goal of walking away with double my money. If I have 55% probability of winning $1 and 45% probability of losing $1 at each gamble, what's the probability that I will lose all my money before I double it? This is the Gambler's Ruin problem.

This article has 4 sections:

Introduction: Introduction to the gambler's ruin problem
Theory: The solution to the Gambler's Ruin problem
Methodology: How the simulation will be carried out
Pseudocode: Summary of the Python Code