Page 50 - Data Science Algorithms in a Week

Naive Bayes

Warm Strong Autumn No

Warm None Summer Yes
Hot None Spring No
Hot Breeze Autumn Yes

Warm Breeze Spring Yes
Cold Breeze Winter No

Cold None Spring Yes
Hot Strong Summer Yes
Warm None Autumn Yes

Warm Strong Spring ?
So, we wonder how the answer will change with this different data.

Analysis:
We may be tempted to use Bayesian probability to calculate the probability of our friend
playing chess with us in the park. However, we should be careful, and ask whether the
probability events are independent of each other.
In the previous example, where we used Bayesian probability, we were given the
probability variables Temperature, Wind, and Sunshine. These are reasonably independent.
Common sense tells us that a specific temperature or sunshine does not have a strong
correlation to a specific wind speed. It is true that sunny weather results in higher
temperatures, but sunny weather is common even when the temperatures are very low.
Hence, we considered even sunshine and temperature reasonably independent as random
variables and applied Bayes' theorem.
However, in this example, temperature and season are tightly related, especially in a
location such as the UK, where we stated that the park we are interested in was placed.
Unlike closer to the equator, temperatures in the UK vary greatly throughout the year.
Winters are cold and summers are hot. Spring and fall have temperatures in between.

Therefore, we cannot apply Bayes' theorem here, as the random variables are dependent.
However, we could still perform some analysis using Bayes' theorem on the partial data. By
eliminating sufficient dependent variables, the remaining ones could turn out to be
independent. Since temperature is a more specific variable than season, and the two
variables are dependent, let us keep only the temperature variable. The remaining two
variables, temperature and wind, are dependent.

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