I have built a Markov chain with which I can simulate the daily routine of people (activity patterns). Each simulation day is divided into 144-time steps and the person can carry out one of fourteen activities. Those are: Away - work (1) Away - leisure (2) Away - shopping (3) Sleeping (4) Cooking (5) Using dishwasher (6) Doing laundry (7) Vacuuming (8) Watching TV (9) Using PC (10) Personal hygiene (11) Ironing (12) Listening to music (13) Other (14)
I calculated the transition probabilities for the Markov chain from a data set containing a total of 226 diaries of persons who documented their activities in a 10-minute interval. The data set can be found here: https://www.dropbox.com/s/tyjvh810eg5brkr/data?dl=0
I have now simulated 4000 days with the Markov chain and want to validate the results with the original data set.
For this purpose, I analyse the results for the activities individually and calculate the expected value as well as the 95% confidence interval for each time step. Then I check if the mean value for the activity from the original dataset lies within this interval and calculate the number of all points that do not lie within the upper or lower threshold of the confidence interval.
However, for each simulation I get deviations of different heights, sometimes in the 1% range, sometimes more than 10%.
I wonder now how this can be possible and whether it can be possible at all.
I have simulated 4x 4000 days and the results are:
I am happy for any feedback. Thanks! :)