- Derive the equation for the posterior mean by expanding the square in the exponential for each i, collecting all similar power terms, and making a perfect square again. Note that the product of exponentials can be written as the exponential of a sum of terms.
For this exercise, we use the dataset corresponding to Smartphone-Based Recognition of Human Activities and Postural Transitions, from the UCI Machine Learning repository (https://archive.ics.uci.edu/ml/datasets/Smartphone-Based+Recognition+of+Human+Activities+and+Postural+Transitions). It contains values of acceleration taken from an accelerometer on a smartphone. The original dataset contains x, y, and z components of the acceleration and the corresponding timestamp values. For this exercise, we have used only the two horizontal components of the acceleration x and y. In this exercise, let's assume that the acceleration follows a normal distribution. Let's also assume a normal prior distribution for the mean values of...
Argentina
Australia
Austria
Belgium
Brazil
Bulgaria
Canada
Chile
Colombia
Cyprus
Czechia
Denmark
Ecuador
Egypt
Estonia
Finland
France
Germany
Great Britain
Greece
Hungary
India
Indonesia
Ireland
Italy
Japan
Latvia
Lithuania
Luxembourg
Malaysia
Malta
Mexico
Netherlands
New Zealand
Norway
Philippines
Poland
Portugal
Romania
Russia
Singapore
Slovakia
Slovenia
South Africa
South Korea
Spain
Sweden
Switzerland
Taiwan
Thailand
Turkey
Ukraine
United States