- Travel surveys gather socio-economic, demographic, and trip-making data from households and individuals to inform transportation planning. The author analyzes a 1996 survey of 1668 households and 18000 individuals. - The author explores whether females travel further than males using an exponential distribution and Monte Carlo sampling. Results show females have a 52.3% probability of traveling further. - Other questions examine which activities are more common for each gender given distance traveled, and which activities each gender is more likely to do at different ages.

1. Abstract
In transportation the travel surveys are one of the most important ways of obtaining the significant
information needed for transportation planning and decision making for a city, town, or state. These
surveys gather socio-economic, demographics, and trip-making characteristics of individual households;
whether these households have one individual or several. By gaining this information developers can
obtain a plan for travel forecasting using the travel relations to the types of choices, locations, and the
scheduling of daily activities. Travel forecasting is a method of predicting a travel pattern within the
zone, city, or state that is being studied.
The data that I have obtained is from 1996, and it studies the travel of 1668 different households and
18000 individuals. I randomly selected 5000 activities from the full data set to conduct this project.
Using this data, I will explore and answer several questions that might be useful for the planning of city
developers. The first question is whether females will travel further than males. This was done using a
Bayesian technique called Monte Carlo sampling and will use an Exponential distribution. The reason
that this might be important is to see whether a female is more willing to travel out of their zip code to
do certain activities than males are willing to do. This is important for the developers, since they may
decide to build more conveniently towards a female population verses a male population if it is found
that females travel further. The second question is given the gender and distance traveled, what activity
occurred, then comparing these to see which activities are more common for which gender. This was
done using a Bayesian method called Monte Carlo sampling using a Bernoulli distribution. This is
important for city planners that are deciding what types of businesses might be developed in a certain
zone (in our case zip code). The third question is to see whether a female or male is more likely to do a
certain activity given their age. This is also going to be done with a Bayesian technique called Gibbs
sampling and a probit regression. This is important for the city planners because they may be able to
build businesses which might attract a certain age group, and may want to see whether it is wise to do
so in a given area.
Results for Whether a Woman Travels More Than a Man Travels:

2. After looking at the data, the distances for both genders seemed to follow an exponential distribution
rather than any other distribution. I was able to examine this using a histogram, Figures 1.a for females
and 1.b for males. I decided to log the distances, since there seemed to be a large distance between the
values of the distance, and create a histogram with those plots, Figures 1.c for females and 1.d for
males. Since the plots seemed to have a curve to them, I decided that they must follow an exponential
distribution.
After fitting both sets of data to an exponential distribution, I then created the prior densities of each,
which turned out to both be gammas, and thus their posteriors also were gammas. I chose to have
and I decided to use a unit information prior, since I do not have any prior data to base
my prior on. So, therefore the distributions look like the following:
( )
} { } ∑
( )
} { } ∑
Next, I decided to check whether the data actually fitted an exponential distribution. I decided to do a
posterior predictive check. Out of 10,000 Monte Carlo datasets, about 50% had values of ( ) that
equaled or exceeded and the same was true for the males. Therefore, it appears that the
observed values are likely the result of an exponential model. Hence the exponential model is valid for
the test statistic t for the female distances and male distances. This is also shown with the histograms in
Figure 2.a and 2.b.
Also, I looked at the Monte Carlo mean =0.08 and found that the posterior mean approximately
equaled 0.08, therefore this shows also, that this model is a good fit.
After conducting a Monte Carlo sampling to answer my question, which was is the probability that a
female’s travel distance more than a male’s. To answer the question, I decided to first look at the
empirical probability, which was . Next, I decided to check the posterior

3. predictive data, which was ( ̃ ̃ ) So, this shows that the distributions of and are
quite similar, according to the scientific question, the probability of females traveling more than males is
0.523. Thus, my question is answered, women technically travel further than men.
Results for what activity, given the age and gender do males do more than females :
Results for what activity, given distance and gender do females do more than males: