Math Python

Predicting Attributes/Demographics

Using probability to estimate demographics while managing uncertainty


Home Blog

Overview🔗

It’s common practice for websites,web analytics tools (like Google Analytics Demographics & Interests), and recommendation systems to collect information from users to create user demographics for analysis, recommending content, and audience targeting. However, this raises a couple of problems for different types of businesses:

  • These services do not indicate what data was used to make the prediction, nor provide a measure of uncertainty for the predictions.
  • Most websites do not have enough visitors to get a decent sample of their audience, which makes analysis difficult and audience segmentation nearly impossible.
  • For websites attempting to attract new visitors, discovering information about new visitors can be problematic. When a visitor comes to their website, they know little to nothing about them and over the course of their visit they learn more about them. How can they provide their visitor with content they will find most satisfying when they do not have much (or any data) about them?
  • Large scale websites can have issues maximizing use of their pages and their data. With many landing pages, new visitors can arrive to their website at many landing pages, many of which can provide different types of data on the user.. However, sites cannot predict which data points they will get about a user, due to the wide variety of entry points to the website. How can they progressively enhance their recommendations and user profile in real-time when they do not know where the user will land on their website, or the order in which they will receive information?

These problems can be mitigated by taking user data from and combining it with relevant statistics with data with larger sample sizes from reputable sources. Statistics based on a larger sample size can provide a more accurate measure regarding segments in a larger setting. While this measure also has flaws, it can provide a starting point for analysis and content recommendation.

I will start with of how to get probabilities from summary statistics of external data. Then cover how to use this output data for probability-based fuzzy segmentation, and to dynamically predict atttributes (in this case, demographics). These example will all be based on athletics demographics and segmentation.

Probability from External Data🔗

The data sets we will be using are sampled from the Running USA National Runner Survey and the Datalys publications, specifically those from the Journal of Athletic Training publication Epidemiology of National Collegiate Athletic Association Men’s and Women’s Cross-Country Injuries, 2009–2010 Through 2013–2014.

The data is divided into 2 files:

  • A total_statistics.csv file, which contains the top level statistics about each group
  • A runner_type_statistics.csv file, which contains probabilities for the same fields, but broken down by runner types (which will be covered shortly)

The total_statistics.csv file contains the following data (truncated for brevity):

category name probability
Gender Female 0.73
Gender Male 0.27

The `` file contains data in the following format (again, truncated for brevity):

category runner type name probability
Health serious & competitive Excellent 0.52
Health frequent/fitness Excellent 0.2
Health walker/jogger/recreational Excellent 0.2
Health obstacle event participant Excellent 0.19

Please use these samples as a reference for the Python code samples later in this post.

We will be loading these files into Pandas DataFrames to work with the data more efficiently and to reduce the boilerplate code to demonstrate the concept:

import pandas as pd

totals = pd.read_csv('total_statistics.csv')
runner_type_statistics = pd.read_csv('runner_type_statistics.csv')

For each of the category, name pairings in total_statistics.csv, we will calculate the probability of being of a particular runner type or a particular gender given that a person has a particular category-name pairing. We already know the likelihood of a person of a given gender or certain type of runner having a particular demographic. We know the probability of a person fits into a particular demographic given they are a particular gender/certain type of runner. But what about the other way around? Given that a person fits in a particular demographic, what is the likelihood that the person is a particular gender/is a certain type of runner?

The following script breaks down the data from both files using Baye’s Theorem to calculate the probability of

group_name = 'running type'
running_type_groups = runner_type_statistics.groupby(group_name)
for running_type_name, running_type_group in main_groups:
    # sum probabilities of being a particular type of runner
    running_type_total_rows = totals[totals['category'] == group_name]
    running_group_probability = running_type_total_rows[group_total_rows['name']==running_type_name]['probability'].sum()

    # break down types of runners by their demographics
    demographic_groups = running_type_group.groupby('category')
    for demographic_group_name, demographic_group_data in demographic_groups:

        for index, row in demographic_group_data.iterrows():
            if row['probability'] == 0.0:
                continue

            demographic_probability = totals[(totals['category'] == row['category']) & (totals['name']==row['name'])]['probability'].sum()

            if not demographic_probability:
                continue
            # calculate conditional probability using Baye's Theorem ( P(B|A) * P(A) ) / P(B)
            conditional_probability = (row['probability'] * running_group_probability) / demographic_probability
            print 'P(%s | %s: %s)' % (running_type_name, row['category'], row['name']), conditional_probability

"""
P(walker/jogger/recreational | training: I don't run if I'm not training for an event) 0.56
P(walker/jogger/recreational | training: I run a few weeks during the year) 0.608
P(walker/jogger/recreational | training: I run a few months during the year) 0.434285714286
P(walker/jogger/recreational | training: I run six months or more during the year) 0.16
P(walker/jogger/recreational | training: I run throughout the year; even if I'm not training for an event) 0.0842105263158
P(walker/jogger/recreational | volunteer for event: Yes) 0.131764705882
P(walker/jogger/recreational | volunteer for event: No) 0.174545454545
P(walker/jogger/recreational | weight: healthy) 0.11027027027
P(walker/jogger/recreational | weight: overweight) 0.292173913043
P(walker/jogger/recreational | weight: obese) 0.8
P(walker/jogger/recreational | weight: underweight) 0.08
P(walker/jogger/recreational | years running: 1-5) 0.21
P(walker/jogger/recreational | years running: 6-10) 0.131428571429
P(walker/jogger/recreational | years running: 11-25) 0.0973913043478
...
"""

The printed statements are the output probabilities in the format P( <unknown variable/variable being predicted> | <known variable/demographic> )

In order to convert probabilities to classifications, we need to set a probability threshold for the probability of category types. Setting a lower threshold means that we will get more information, but the information may be less reliable, but a higher threshold will provide less information, but the information will be more reliable. You may have to experiment with a threshold based on your acceptable level of risk. If no category types are above this threshold, we can conclude that we do not yet have enough information:

# probabilities of runner types
runner_types = {
    'Serious & competitive':	0.18,
    'frequent/fitness':	0.65,
    'walker/jogger/recreational':	0.16,
    'obstacle event participant':	0.01,
}
threshold = 0.6 # a very low threshold, for very low risk scenarios

most_likely_runner_type = max(runner_types, key=running_types.get)  #  'frequent/fitness'
if runner_types[most_likely_runner_type] >= threshold:
    running_type = most_likely_runner_type
else:
    running_type = None

Estimating demographics using larger datasets🔗

Small businesses and startups have to find their audiences in order to know who to market their products/services to. Many companies like MileStat, Flash Results, Inc., and RunCoach have niche audiences that their services are catered towards. But however small a niche is, they still need to identify audiences with highest conversion rates, and the ones who are not converting at all. Finding who the converting audiences are is possibly the easier of the two groups, this is because many of these services request demographic information from users when setting up their services, like gender, age, physical activity level, etc. This information is generally more trustworthy and accurate, because the user expects for this information to be used to provide a more useful service for them. Finding who the users are that are not converting is the harder problem. These visitors may not explicitly provide information to the company, and if they do they do not have incentives to do so truthfully. Business analysts have to manage this uncertainty in their predictions and classifications, which larger data sets help manage. These data sets should be a fairly accurate distribution of the total population, which (in the absence of significant customer data) can act as a crude but effective way of predicting visitor demographics. It does not matter that the distribution may not be exact, so long as the correlations are close to those of the actual population. While this method has its flaws its meant to be a temporary complement to a growing, but currently small, data set

Here is a relatively common example A race results website is trying to identify who their most active audiences are, but they have no visitor logins and only recently deployed tracking tools like Google Tag Manager / Google Analytics. Many smaller content-driven websites are in the same boat: Boatloads of content, but no way of finding out who is reading and who is bouncing from their website. There are a couple high-level demographics that will be useful for this website:

  • Gender
  • Role: Race Official, Coach, Athlete or Enthusiast
  • Event Preferences: Distance running vs Sprints vs Field events
  • Team Association (if any or if applicable)

We can use the Running USA 2012 Survey to enhance our predictions. But before we dive into solving our problem, let’s explore the data.

category subcategory dimension dimension name name probability
demographics gender all all female 0.37
demographics gender all all male 0.63
demographics age group all all 18-24 0.04
demographics age group all all 25-34 0.19
demographics age group all all 35-44 0.28
demographics age group all all 45-54 0.27
demographics age group all all 55-64 0.17
demographics age group all all 65-74 0.05
demographics age group all all >75 0.01
demographics marital status all all married 0.68
demographics marital status all all single, never married 0.2
demographics marital status all all divorced 0.08
demographics marital status all all domestic partner 0.03
demographics marital status all all widowed 0.01
demographics marital status all all separated 0.01
demographics household composition all all 1 0.14
demographics household composition all all 2 0.32
demographics household composition all all 3 0.16
demographics household composition all all 4 0.23
demographics household composition all all >5 0.14
demographics children under 19 all all 0 0.52
demographics children under 19 all all 1 0.16
demographics children under 19 all all 2 0.22
demographics children under 19 all all 3 0.08
demographics children under 19 all all >4 0.03
demographics education all all Currently full-time student and under 19 0.04
demographics education all all Attended college 1-3 years 0.08
demographics education all all Associate’s degree 0.06
demographics education all all Technical or Trade degree 0.02
demographics education all all Graduated from 4-year college 0.36
demographics education all all Post-grad study without degree 0.06
demographics education all all Master’s degree 0.29
demographics education all all Doctoral degree 0.08
demographics employment all all Employed full-time 0.87
demographics employment all all student 0.03
demographics employment all all retired 0.03
demographics employment all all homemaker 0.06
demographics employment all all unemployed 0.02
demographics ethnicity all all white/caucasian 0.84
demographics ethnicity all all black/african american 0.07
demographics ethnicity all all asian/pacific islander 0.06
demographics ethnicity all all hispanic 0.04
demographics ethnicity all all american indian 0.01
demographics ethnicity all all other 0.02
demographics annual income (employed) all all < $15,000 0.03
demographics annual income (employed) all all $15,000-$24,999 0.03
demographics annual income (employed) all all $25,000-$34,999 0.04
demographics annual income (employed) all all $35,000-$49,999 0.12
demographics annual income (employed) all all $50,000-$74,999 0.24
demographics annual income (employed) all all $75,000-$99,999 0.15
demographics annual income (employed) all all $100,000-$124,999 0.1
demographics annual income (employed) all all $125,000-$149,999 0.04
demographics annual income (employed) all all $150,000-$174,999 0.03
demographics annual income (employed) all all $175,000-$199,999 0.01
demographics annual income (employed) all all >$200,000 0.04
demographics annual income (employed) all all Don’t Know/Refused 0.17
demographics runner type all all Jogger / Recreational Runner 0.21
demographics runner type all all Serious & Competitive Runner 0.15
demographics runner type all all Frequent / Fitness Runner 0.62
habits time ran per year all all 12 months / year 0.76
habits time ran per week all all >= 4 days / week 0.56
motivators start running all all for exercise 0.24
motivators start running all all weight concerns 0.14
motivators start running all all Friend / family encouragement 0.09
motivators start running all all To enter a race 0.08
motivators start running all all Competed in school and never stopped 0.08
motivators start running all all Because I enjoy it 0.06
motivators start running all all Needed a new challenge 0.06
motivators start running all all To relieve stress 0.06
motivators start running all all Health concerns besides weight 0.05
motivators start running all all To get in shape for another sport 0.03
motivators continue to run all all staying healthy 0.77
motivators continue to run all all staying in shape 0.73
motivators continue to run all all relieving stress 0.62
motivators continue to run all all to enter / train for a race 0.62
motivators continue to run all all having fun 0.55
motivators continue to run all all achieving a goal 0.54
motivators continue to run all all meeting a personal challenge 0.53
motivators continue to run all all improving my state pf mind 0.53
motivators continue to run all all controlling my weight 0.53
motivators continue to run all all improving speed or endurance 0.46
motivators continue to run all all socializing with friends/family/others 0.41
motivators continue to run all all appreciating nature, scenery 0.39
motivators continue to run all all being by myself for awhile 0.39
motivators continue to run all all getting into the natural environment 0.31
motivators continue to run all all competing against others 0.22
motivators continue to run all all stay injury free 0.13
motivators goals all all stay healthy 0.68
motivators goals all all set a new PR 0.43
motivators goals all all Run a new race 0.4
motivators goals all all lose weight 0.32
motivators goals all all run a marathon 0.29
motivators goals all all keep a running streak 0.13
motivators goals all all Run 2017+ miles 0.05
motivators goals all all Run 1+ mile/day 0.03
activity regular activities as part of running all all warm up/stretch 0.55
activity regular activities as part of running all all use machines/weight 0.49
activity regular activities as part of running all all walk 0.47
activity regular activities as part of running all all bike 0.27
activity regular activities as part of running all all yoga/pilates 0.26
activity regular activities as part of running all all hike 0.21
activity regular activities as part of running all all HIIT Training 0.21
activity regular activities as part of running all all Spin 0.18
activity regular activities as part of running all all Swim 0.14
activity regular activities as part of running all all Aerobics 0.11
activity regular activities as part of running all all Crossfit 0.1
activity regular activities as part of running all all Form Drills 0.09
preferences time to run all all early AM 0.64
preferences time to run all all Mid-morning 0.25
preferences time to run all all Noon 0.06
preferences time to run all all Early afternoon 0.06
preferences time to run all all Mid-afternoon 0.11
preferences time to run all all Early evening 0.39
preferences time to run all all Late evening 0.09
preferences regular running workouts all all easy runs (aerobic) 0.86
preferences regular running workouts all all long runs (>1 hour) 0.79
preferences regular running workouts all all hill training 0.44
preferences regular running workouts all all pace workouts 0.44
preferences regular running workouts all all tempo runs 0.38
preferences regular running workouts all all recovery runs 0.31
preferences regular running workouts all all fartlek 0.17
preferences regular running workouts all all pickups 0.08
preferences social runs all all alone 0.55
preferences social runs all all with one other person 0.16
preferences social runs all all in a group 0.14
preferences social runs all all no preference 0.16
preferences venue/surface all all paved path 0.67
preferences venue/surface all all urban road 0.54
preferences venue/surface all all park 0.47
preferences venue/surface all all rural road 0.44
preferences venue/surface all all dirt trail 0.4
preferences venue/surface all all outdoor track 0.2
preferences venue/surface all all mountains 0.16
preferences venue/surface all all treadmill 0.14
preferences venue/surface all all beach 0.12
preferences season all all fall 0.46
preferences season all all winter 0.1
preferences season all all spring 0.34
preferences season all all summer 0.11
preferences prevent running outside all all too icy 0.69
preferences prevent running outside all all don’t feel safe 0.48
preferences prevent running outside all all windchill too low 0.44
preferences prevent running outside all all too rainy 0.35
preferences prevent running outside all all too dark 0.34
preferences prevent running outside all all too cold 0.31
preferences prevent running outside all all too hot 0.31
preferences prevent running outside all all nothing 0.07
preferences group involvement all all Local running club 0.34
preferences group involvement all all Social groups / informal groups 0.29
preferences group involvement all all running store group runs 0.18
preferences group involvement all all virtual running club / challenge group 0.11
preferences group involvement all all meetup running group 0.06
preferences group involvement all all rrca 0.06
preferences group involvement all all usa track & field 0.04
preferences group involvement all all none 0.4
preferences carrying items all all personal ID 0.34
preferences carrying items all all fitness tracker 0.3
preferences carrying items all all water bottle 0.28
preferences carrying items all all energy bars/gel 0.24
preferences carrying items all all portable audio sysem/ipod/MP3 0.23
preferences carrying items all all hydration accessories (belt, backpack) 0.21
preferences carrying items all all Spibelt (or similar waist belt) 0.21
preferences carrying items all all sunscreen 0.2
preferences carrying items all all reflective gear 0.19
preferences carrying items all all heart rate monitor 0.18
preferences carrying items all all cash/credit card 0.17
preferences carrying items all all chapstick/lipgloss 0.16
preferences carrying items all all compression gear 0.15
preferences carrying items all all sports drink 0.09
preferences carrying items all all sweatband 0.08
preferences carrying items all all dog 0.07
preferences carrying items all all pepper spray 0.07
preferences carrying items all all sleeves 0.04
preferences carrying items all all toilet paper 0.04
preferences carrying items all all inhaler 0.04
racing runner type all all competitor 0.56
racing runner type all all fun runner 0.52
racing runner type all all fitness participant 0.37
racing runner type all all outdoor enthusiast 0.15
racing Preferred distance all all 5k 0.14
racing Preferred distance all all 10k 0.18
racing Preferred distance all all 12k, 15k, 10 mile 0.06
racing Preferred distance all all half marathon 0.43
racing Preferred distance all all marathon 0.1
racing entered last 2 years all all 5k 0.82
racing entered last 2 years all all half marathon 0.8
racing entered last 2 years all all 10k 0.67
racing entered last 2 years all all marathon 0.43
racing entered last 2 years all all 12k, 15k, 10 mile 0.37
racing entered last 2 years all all 4 mile, 8k, or 5 mile 0.33
racing entered last 2 years all all fun run or untimed run 0.24
racing entered last 2 years all all trail race 0.23
racing entered last 2 years all all road running relay 0.13
racing entered last 2 years all all triathlon/duathlon 0.12
racing entered last 2 years all all mud/obstacle 0.1
racing entered last 2 years all all color 0.08
racing entered last 2 years all all 1 mile or 2 mile 0.11
racing entered last 2 years all all Glow / night 0.08
racing entered last 2 years all all 20k, 25k, or 30k 0.07
racing entered last 2 years all all ultra distance 0.08
racing entered last 2 years all all untimed walk event 0.06
racing entered last 2 years all all Cross-country race 0.05
racing most interested in upcoming year all all 5k 0.56
racing most interested in upcoming year all all half marathon 0.75
racing most interested in upcoming year all all 10k 0.56
racing most interested in upcoming year all all marathon 0.41
racing most interested in upcoming year all all 12k, 15k, 10 mile 0.3
racing most interested in upcoming year all all 4 mile, 8k, or 5 mile 0.21
racing most interested in upcoming year all all fun run or untimed run 0.08
racing most interested in upcoming year all all trail race 0.23
racing most interested in upcoming year all all road running relay 0.12
racing most interested in upcoming year all all triathlon/duathlon 0.13
racing most interested in upcoming year all all mud/obstacle 0.1
racing most interested in upcoming year all all color 0.05
racing most interested in upcoming year all all 1 mile or 2 mile 0.06
racing most interested in upcoming year all all Glow / night 0.07
racing most interested in upcoming year all all 20k, 25k, or 30k 0.08
racing most interested in upcoming year all all ultra distance 0.1
racing most interested in upcoming year all all untimed walk event 0.02
racing most interested in upcoming year all all Cross-country race 0.05
racing holiday event all all thanksgiving 0.54
racing holiday event all all fourth of july 0.26
racing holiday event all all st patrick’s day 0.2
racing holiday event all all new years 0.18
racing holiday event all all christmas 0.15
racing holiday event all all halloween 0.13
racing holiday event all all valentine’s day 0.08
racing participation change last year all all decrease 0.2
racing participation change last year all all same 0.5
racing participation change last year all all increase 0.3
racing Planned participation change next year all all decrease 0.08
racing Planned participation change next year all all same 0.56
racing Planned participation change next year all all increase 0.36
racing Half-marathons completed all all 0 0.1
racing Half-marathons completed all all 1 0.08
racing Half-marathons completed all all 2 0.07
racing Half-marathons completed all all 3-5 0.16
racing Half-marathons completed all all 6-10 0.2
racing Half-marathons completed all all 11-15 0.13
racing Half-marathons completed all all 16-20 0.09
racing Half-marathons completed all all 21-25 0.04
racing Half-marathons completed all all >=25 0.13
racing marathons completed all all 0 0.38
racing marathons completed all all 1 0.15
racing marathons completed all all 2 0.08
racing marathons completed all all 3-5 0.14
racing marathons completed all all 6-10 0.1
racing marathons completed all all 11-15 0.05
racing marathons completed all all 16-20 0.03
racing marathons completed all all 21-25 0.01
racing marathons completed all all >=25 0.05
racing Top factors effecting participation all all preferred distance 0.81
racing Top factors effecting participation all all date of event 0.78
racing Top factors effecting participation all all location is convenient 0.7
racing Top factors effecting participation all all have time to train 0.67
racing Top factors effecting participation all all health/injury 0.67
racing Top factors effecting participation all all sounds fun 0.66
racing Top factors effecting participation all all chip timed 0.65
racing Top factors effecting participation all all scenic course 0.61
racing Top factors effecting participation all all cost/entry fee 0.59
racing Top factors effecting participation all all reputation of event organizers 0.58
racing Other factors effecting participation all all accurate, vertified course 0.52
racing Other factors effecting participation all all medal or other momento for finishers 0.49
racing Other factors effecting participation all all quality t-shirt 0.44
racing Other factors effecting participation all all fun post-race experience 0.38
racing Other factors effecting participation all all it benefits an important cause 0.35
racing Other factors effecting participation all all no crowds/traffic/hassles expected 0.34
racing Other factors effecting participation all all my friends are doing it 0.34
racing Other factors effecting participation all all promise of a unique event 0.31
racing Other factors effecting participation all all It is an event I participated In before 0.29
racing Other factors effecting participation all all Fast course 0.26
racing Other factors effecting participation all all free race photos or videos 0.24
racing Other factors effecting participation all all entertainment on course or finish 0.24
racing Other factors effecting participation all all good age group awards 0.19
racing Other factors effecting participation all all sustainable event/ has an environmental initiative 0.18
racing Other factors effecting participation all all there Is an expo 0.15
racing Other factors effecting participation all all qualifier 0.15
racing Other factors effecting participation all all recycled/sustainable race t-shirt 0.12
racing Other factors effecting participation all all something offered to other family members 0.11
racing Other factors effecting participation all all it is a new event 0.1
racing Other factors effecting participation all all has a social media app / site for sharing experience 0.1
racing Other factors effecting participation all all random participant awards 0.1
racing Other factors effecting participation all all appropriate training group is available 0.06
racing Other factors effecting participation all all race Is part of a local grand prix 0.05
racing Other factors effecting participation all all elite runners in the field 0.05
racing Other factors effecting participation all all expo has guest speakers I am interested In meeting 0.04
racing Other factors effecting participation all all Women only event 0.04
racing primary source of information all all facebook 0.43
racing primary source of information all all word of mouth 0.37
racing primary source of information all all individual race website 0.35
racing primary source of information all all registration website 0.27
racing primary source of information all all running store group runs 0.23
racing primary source of information all all local club / city website 0.18
racing primary source of information all all race calendar apps 0.18
racing primary source of information all all national website 0.15
racing primary source of information all all Expos 0.11
racing primary source of information all all Regional / state website 0.1
racing primary source of information all all national magazine 0.09
racing primary source of information all all local publications 0.09
racing primary source of information all all instagram 0.05
racing primary source of information all all state or regional publication 0.04
racing primary source of information all all twitter 0.04
racing primary source of information all all GroupOn / Living Social / Rush 49 0.02
racing Attitudes & behaviors all all I prefer a tech finisher t-shirt to a cotton finisher t-shirt 0.73
racing Attitudes & behaviors all all It is easy to find an event I want to participate in 0.73
racing Attitudes & behaviors all all I would participate in more events if entry feeds were lower 0.62
racing Attitudes & behaviors all all I prefer traditional to non-traditional (i.e. mud, obstacle, color) running events 0.58
racing Attitudes & behaviors all all Race fees are too expensive 0.56
racing Attitudes & behaviors all all I receive good value for my race fee 0.51
racing Attitudes & behaviors all all I like participating in the same events every year 0.49
racing Attitudes & behaviors all all I am always looking for a new event experience 0.48
racing Attitudes & behaviors all all I like to share my race experience with others via social media 0.45
racing Attitudes & behaviors all all I wish races offered something other than a finisher t-shirt for SWAG 0.4
racing Attitudes & behaviors all all you should get a race finisher t-shirt for finishing shorter distances like a 5k or 10k 0.33
racing Attitudes & behaviors all all Social media is my first choice for event information 0.28
racing Attitudes & behaviors all all You should only get a race finisher medal for a half-marathon or marathon 0.27
racing Attitudes & behaviors all all I prefer larger races to smaller races 0.26
racing Attitudes & behaviors all all Race medals are getting too big 0.23
racing Attitudes & behaviors all all I like to take pictures while I am participating in an event 0.2
racing Attitudes & behaviors all all There are too many events to choose from 0.16
racing Attitudes & behaviors all all I would pay more for a VIP race experience (race day packet pickup, access to special porto potties, front on the starting line access, etc) 0.15
racing Attitudes & behaviors all all I don’t care about my race time 0.12
racing Attitudes & behaviors all all I would prefer to participate in events as a group vs individually 0.11
racing Attitudes & behaviors all all I like events where I can dress up in a costume / there is a theme 0.09
racing Attitudes & behaviors all all I prefer untimed events to times events 0.03
social media follows all all Running stores 0.4
social media follows all all Running brands 0.37
social media follows all all Local runners 0.32
social media follows all all Elite runners 0.29
social media follows all all Bloggers 0.19
social media follows all all Celebrities 0.05
social media follows all all None of these 0.16
social media follows all all I don’t follow any running-related accounts 0.21
technology app usage all all I like to have / track all of my running statistics 0.82
technology app usage all all It helps me train better 0.65
technology app usage all all It makes me feel good to see what I ran 0.61
technology app usage all all I like to share the information with others on social media 0.17
technology app usage all all I like to see how I compare to other runners 0.15
technology app usage all all I like to share the information with a running coach 0.07
technology app usage all all Everyone else is using them so I do too 0.02
technology tracking device Phone / app on phone track mileage 0.45
technology tracking device Phone / app on phone GPS 0.36
technology tracking device Phone / app on phone track nutrition / calories 0.29
technology tracking device Phone / app on phone track steps 0.21
technology tracking device Phone / app on phone map routes 0.38
technology tracking device Phone / app on phone play music 0.55
technology tracking device Phone / app on phone training programs 0.22
technology tracking device Phone / app on phone tracking workouts 0.4
technology tracking device Phone / app on phone interval training 0.17
technology tracking device Phone / app on phone virtual coach 0.11
technology tracking device Phone / app on phone none of these 0.08
technology tracking device watch track mileage 0.48
technology tracking device watch GPS 0.52
technology tracking device watch track nutrition / calories 0.07
technology tracking device watch track steps 0.28
technology tracking device watch map routes 0.17
technology tracking device watch play music 0.04
technology tracking device watch training programs 0.08
technology tracking device watch tracking workouts 0.34
technology tracking device watch interval training 0.27
technology tracking device watch virtual coach 0.04
technology tracking device watch none of these 0.08
technology tracking device wearable tracking device track mileage 0.23
technology tracking device wearable tracking device GPS 0.16
technology tracking device wearable tracking device track nutrition / calories 0.05
technology tracking device wearable tracking device track steps 0.26
technology tracking device wearable tracking device map routes 0.08
technology tracking device wearable tracking device play music 0.04
technology tracking device wearable tracking device training programs 0.04
technology tracking device wearable tracking device tracking workouts 0.17
technology tracking device wearable tracking device interval training 0.09
technology tracking device wearable tracking device virtual coach 0.02
technology tracking device wearable tracking device none of these 0.11
technology tracking device online website track mileage 0.12
technology tracking device online website GPS 0.04
technology tracking device online website track nutrition / calories 0.06
technology tracking device online website track steps 0.02
technology tracking device online website map routes 0.24
technology tracking device online website play music 0.01
technology tracking device online website training programs 0.18
technology tracking device online website tracking workouts 0.12
technology tracking device online website interval training 0.04
technology tracking device online website virtual coach 0.04
technology tracking device online website none of these 0.09
social media activity platform all fundraise for a charity event 0.62
social media activity platform all discuss running-related activities 0.62
social media activity platform all look for running motivation 0.49
social media activity platform all recruit others to join me at an upcoming race 0.49
social media activity platform all share your current training 0.47
social media activity platform all communicate with training partners 0.43
social media activity platform all recruit others to train with you 0.42
social media activity platform all post your race results 0.42
social media activity platform all follow events 0.4
social media activity platform all post general running photos and videos 0.38
social media activity platform all look for running training advice 0.37
social media activity platform all track friends / family in a race 0.33
social media activity platform all follow other runners (non-professional) 0.31
social media activity platform all Follow professional runners 0.29
social media activity platform all Post your mileage / running routes 0.29
social media activity platform all Post race photos and videos 0.26
social media activity platform all None of these 0.15
social media activity platform facebook fundraise for a charity event 0.07
social media activity platform facebook discuss running-related activities 0.11
social media activity platform facebook look for running motivation 0.06
social media activity platform facebook recruit others to join me at an upcoming race 0.06
social media activity platform facebook share your current training 0.06
social media activity platform facebook communicate with training partners 0.08
social media activity platform facebook recruit others to train with you 0.04
social media activity platform facebook post your race results 0.09
social media activity platform facebook follow events 0.05
social media activity platform facebook post general running photos and videos 0.06
social media activity platform facebook look for running training advice 0.03
social media activity platform facebook track friends / family in a race 0.05
social media activity platform facebook follow other runners (non-professional) 0.02
social media activity platform facebook Follow professional runners 0.04
social media activity platform facebook Post your mileage / running routes 0.04
social media activity platform facebook Post race photos and videos 0.11
social media activity platform facebook None of these 0.22
social media activity platform twitter fundraise for a charity event 0.26
social media activity platform twitter discuss running-related activities 0.16
social media activity platform twitter look for running motivation 0.21
social media activity platform twitter recruit others to join me at an upcoming race 0.16
social media activity platform twitter share your current training 0.1
social media activity platform twitter communicate with training partners 0.2
social media activity platform twitter recruit others to train with you 0.07
social media activity platform twitter post your race results 0.2
social media activity platform twitter follow events 0.07
social media activity platform twitter post general running photos and videos 0.09
social media activity platform twitter look for running training advice 0.06
social media activity platform twitter track friends / family in a race 0.12
social media activity platform twitter follow other runners (non-professional) 0.05
social media activity platform twitter Follow professional runners 0.1
social media activity platform twitter Post your mileage / running routes 0.06
social media activity platform twitter Post race photos and videos 0.18
social media activity platform twitter None of these 0.2
social media activity platform instagram fundraise for a charity event 0.01
social media activity platform instagram discuss running-related activities 0.01
social media activity platform instagram look for running motivation 0.01
social media activity platform instagram recruit others to join me at an upcoming race 0
social media activity platform instagram share your current training 0.01
social media activity platform instagram communicate with training partners 0.13
social media activity platform instagram recruit others to train with you 0
social media activity platform instagram post your race results 0.01
social media activity platform instagram follow events 0.01
social media activity platform instagram post general running photos and videos 0.08
social media activity platform instagram look for running training advice 0
social media activity platform instagram track friends / family in a race 0
social media activity platform instagram follow other runners (non-professional) 0
social media activity platform instagram Follow professional runners 0
social media activity platform instagram Post your mileage / running routes 0
social media activity platform instagram Post race photos and videos 0.01
social media activity platform instagram None of these 0.24
social media activity platform pinterest fundraise for a charity event 0.07
social media activity platform pinterest discuss running-related activities 0.07
social media activity platform pinterest look for running motivation 0.09
social media activity platform pinterest recruit others to join me at an upcoming race 0.11
social media activity platform pinterest share your current training 0.11
social media activity platform pinterest communicate with training partners 0.1
social media activity platform pinterest recruit others to train with you 0.13
social media activity platform pinterest post your race results 0.11
social media activity platform pinterest follow events 0.14
social media activity platform pinterest post general running photos and videos 0.13
social media activity platform pinterest look for running training advice 0.15
social media activity platform pinterest track friends / family in a race 0.15
social media activity platform pinterest follow other runners (non-professional) 0.17
social media activity platform pinterest Follow professional runners 0.16
social media activity platform pinterest Post your mileage / running routes 0.17
social media activity platform pinterest Post race photos and videos 0.15
social media activity platform pinterest None of these 0.12
technology tracking all all App on my phone 0.63
technology tracking all all hard copy log or journal 0.23
technology tracking all all computer software 0.15
technology tracking all all online software 0.14
technology tracking all all None, do not track at all 0.09
preferences general all all Run in a lower-cost, no frills, less swag race 0.55
preferences general all all Run in a higher-cost, fuller experience, more swag race 0.45
preferences general all all Run outside during harsher weather 0.57
preferences general all all Run inside during harsher weather 0.43
preferences general all all Only run as exercise 0.23
preferences general all all Supplement running with other exercise 0.77
preferences general all all Stretch 0.71
preferences general all all Not stretch 0.29
preferences general all all Run on trails 0.37
preferences general all all Run on the roads 0.64
preferences general all all Run with a watch or tracking device 0.93
preferences general all all Run without a watch or tracking device 0.07
preferences general all all Run with music 0.6
preferences general all all Run without music 0.4
preferences general all all Share your running with others on social media 0.35
preferences general all all Keep my running to myself and close friends 0.65
learning general all all Best places to run when on vacation 0.49
learning general all all Best places to run in your area 0.47
learning general all all How to avoid injuries 0.46
learning general all all How to cross train to supplement your running 0.42
learning general all all Easy ways to find races to partipicate in 0.38
learning general all all What to eat before a big race 0.35
learning general all all How to select the best running shoes 0.34
learning general all all What pace you should run when racing 0.31
learning general all all How to be safe when running 0.26
learning general all all How to run in inclement weather 0.2
learning general all all How to find a good running coach 0.14
learning general all all How to run at night 0.12
injuries Past 12 months all all blisters 0.29
injuries Past 12 months all all knee 0.22
injuries Past 12 months all all hips 0.14
injuries Past 12 months all all plantar fasciitis 0.14
injuries Past 12 months all all foot 0.13
injuries Past 12 months all all IT Band Syndrome 0.12
injuries Past 12 months all all Lower back 0.11
injuries Past 12 months all all shin splints 0.11
injuries Past 12 months all all hasmstring 0.1
injuries Past 12 months all all calf 0.09
injuries Past 12 months all all ankle 0.08
injuries Past 12 months all all achilles tendon 0.07
injuries Past 12 months all all stress fracture 0.03
injuries Past 12 months all all quadriceps 0.02
injuries Past 12 months all all None of these 0.23
injuries how to deal with all all take time off 0.66
injuries how to deal with all all take anti-inflammatory 0.58
injuries how to deal with all all stretch 0.57
injuries how to deal with all all ice 0.53
injuries how to deal with all all cross train 0.32
injuries how to deal with all all run through it 0.32
injuries how to deal with all all seek advice from other runners 0.29
injuries how to deal with all all seek advice online 0.27
injuries how to deal with all all see doctor 0.27

As you can see Gender can be estimated by tracking the gender of the races that the visitor views. For example if the visitor only views a number of women’s races, we can assume that the user has a strong affinity for women’s racing (through friendship, family, coaching, or themselves). According to the Running USA 2012 Survey, 63% of runners in the adult running community are female. Using this information, and the users trend of only looking a women’s races, we can estimate that the person is most likely a woman, or has a strong affinity for women’s running.

Runner Type can be estimated by looking at the types of race results that a visitor tends to view. Do they prefer looking at championship races, or do they prefer looking at Tough Mudder results? The Running USA survey divides runners into 4 groups:

  • Competitors - The people who enjoy running solely for the competition. These are the people who want to get a personal record, beat their friends, win their age group or win the whole race.
  • Fun Runners - People who enjoy running, and do it purely for the enjoyment of the activity and the events
  • Fitness Participants - Runners who participate in races to stay fit and keep a healthy lifestyle
  • Outdoor Enthusiasts - People who enjoy being outdoors and do many outdoor activities, not just running

These runners can be identified by the types of runs that they participate in, and more importantly for us, the race results that they view. IF a visitor only tends to look at championship events, college meets, or only tends to view the results at the top of the page (indicating they only looked at the winners), it likely that this person has an affinity for competitive racing. On the other hand, if the runner only tends to look at less competition-focused events, like Color Me Rad, or Tough Mudder races, it is possible they are more interested in less competitive, fun races. According to the Running USA Survey, the majority of runners tend to more strongly identify as competitive runners (56%) who run for fun (52%). The fewest runners, 15% identify as outdoor enthusiasts. So, if a person only tends to look at the NCAA championships, World Championships, and Rock N Roll Half Marathon results, it is likely this person strongly prefers competitive racing.

Preferred Event Types While the Running USA Survey has limited coverage of this dimension, this is a very simple dimension to identify without using other data sets. For example, a visitor who only looks at a specific type of event can be identified as an enthusiast for that event. For example, if a visitor only tends to look at sprinting events (races <= 400m), it is not likely that they will click on an ad for the Rock N Roll Half Marathon.

Name Events
Track & Field - Sprints Distance <=400m
Track & Field - Mid-Distance 400m < distance <= 1600m
Distance 1600 < Distance >= 5k
Field Events Distance >Pole Vault, Hammer Throw, etc

Team Affiliations/Interests Identifying what teams a user may be interested in can allow developers to recommend race results a user may be interested in based on the teams participating. While this approach also does not involve external datasets, it is incredibly simple to implement and (if done responsibly) can yield very informative information to visitors. This information can be found by finding the teams that participate in the races viewed by a visitor. If a user comes to the site and only looks at results for the Music City Challenge, the Tiger Paw Invitational, Penn Relays and the ACC Outdoor Championships, it is possible the visitor was looking at the Virginia Tech Hokies, as they attended 3/4 of those college track meets. We can also learn that they tend to enjoy competitive racing. This technique can also be used in non-team races to narrow down who a visitor may be a fan of (or who they may be), although, depending of the size of the races, may require many more race examples to adequately narrow down the potential list of participants.

def intersction(*sets):
    sets = [set(items) for items in sets]
    matches = set()
    [matches.union(items)for items in sets[1:]]
    for subset in sets:
        matches = matches.intersection(subset)
        if not matches:
            return matches
    return matches

Although, it is very unlikely that ALL the races that a visitor views will have their team in them. So we may want to use a softer, more forgiving approach by introducing an optional threshold argument:

from collections import Counter

def intersection(*sets, **kwargs):
    threshold = kwargs.get('threshold', 1)
    sets = [set(subset) for subset in sets]
    set_count = len(sets)
    # create a set containing all potential matches
    items = set()
    [items.union(item_set)for item_set in sets]
    counts = Counter()
    proportions = dict()
    [counts.update(subset) for subset in sets]
    for key, occurrence_count in counts.items():
        if occurrence_count / set_count >= threshold:
            proportions[key] = occurrence_count / set_count
    return proportions

Narrowing Down Attributes: Injuries🔗

The previous scenario allows us to predict a set of attributes about any visitor where every page allows us to learn about each attribute. But many scenarios do not provide information on all potential attributes simultaneously. we may only learn about a subset of attributes at a time. In fact, in many cases we can’t even predict the order in which we will learn information about an attribute. These uncertainties can be resolved using conditional probabilities. A perfect example of this is information regarding athletic injuries. Obtaining accurate information regarding injuries can be difficult, as some athletes cannot provide all the details of their injury. Fortunately we can use existing datasets to narrow down injury attributes. We will be using data from publications from the Datalys Center.

Let’s say that a female cross country athlete provides us with pieces of information regarding an injury she received but is having trouble remembering the details, so we don’t know they remember or when/if she will remember them. As she is collegiate cross country runner, we can use the publication Epidemiology of National Collegiate Athletic Association Men’s and Women’s Cross-Country Injuries, 2009–2010 Through 2013–2014 from the Journal of Athletic Training.

The first detail is that she injured her lower leg. We can cross-reference this information with the data extracted from the Datalys Journal:

gender part percent of sample rate per 1000 athlete exposures time loss (%) severe injuries (%)
female head/face 0.008 0.04 0 0
female neck 0.008 0.04 0 0
female shoulder/clavicle 0 0 0 0
female arm/elbow 0.004 0.02 0 0
female hand/wrist 0.004 0.02 0 0
female trunk 0.085 0.49 0.636 0.227
female hip/groin 0.112 0.65 0.586 0.138
female thigh 0.146 0.85 0.605 0.184
female knee 0.123 0.72 0.688 0.031
female lower leg 0.235 1.37 0.574 0.131
female ankle 0.05 0.29 0.615 0
female foot 0.154 0.9 0.525 0.225
female other 0.073 0.43 0.579 0
female total 1 5.83 0.588 0.131
male head/face 0.009 0.04 0 0
male neck 0 0 0 0
male shoulder/clavicle 0 0 0 0
male arm/elbow 0 0 0 0
male hand/wrist 0 0 0 0
male trunk 0.056 0.26 0.667 0.167
male hip/groin 0.032 0.15 0.571 0.143
male thigh 0.125 0.58 0.593 0.037
male knee 0.107 0.5 0.609 0.087
male lower leg 0.352 1.64 0.605 0.132
male ankle 0.13 0.6 0.464 0
male foot 0.157 0.73 0.765 0.059
male other 0.032 0.15 0.429 0
male total 1 4.66 0.611 0.083

According to the study, 23.5% of injuries to female collegiate cross country athletes are lower leg injuries. This calculation can be represented as P(Lower Leg | Female and College XC ) = 0.235 meaning the probability of a lower leg injury given being female and a collegiate cross country runner. According to this same study, 57% of female athletes with lower leg injuries were not able to compete for some length of time, but only 13%of lower leg injuries were serious injuries.

To take this a step further, of the 3 types of recorded injuries that occur to female cross country runners with lower leg injuries, inflammation is the most typical injury at 35% of injuries. The other injuries are only slightly less likely, making no injury type significantly likely.

gender part Injury percent of sample rate per 1000 athlete exposures time loss (%) severe injuries (%)
female thigh strain 0.065 0.38 0.588 0.059
female lower leg inflammation 0.065 0.38 0.706 0.059
female lower leg tendinitis 0.062 0.36 0.688 0.063
female lower leg strain 0.058 0.34 0.467 0.067
female foot inflammation 0.058 0.34 0.667 0.2
female thigh inflammation 0.05 0.29 0.769 0.231
female knee inflammation 0.05 0.29 0.692 0.077
female ankle sprain 0.042 0.25 0.545 0
female hip/groin strain 0.039 0.22 0.6 0.1
female respiratory respiratory 0.035 0.2 0.444 0
male ankle sprain 0.111 0.52 0.458 0
male lower leg tendinitis 0.097 0.45 0.571 0.048
male lower leg inflammation 0.083 0.39 0.889 0
male thigh strain 0.069 0.32 0.667 0
male lower leg strain 0.069 0.32 0.6 0.133
male foot inflammation 0.046 0.22 1 0
male knee inflammation 0.032 0.15 0.714 0
male hip/groin strain 0.028 0.13 0.667 0.167
male knee tendinitis 0.028 0.13 0.5 0.167
male lower leg stress fracture 0.023 0.11 0 0.4

At this point we have the following information:

  • A Female colliegiate athlete injured her lower leg, which is a fairly common injury
  • She will likely need to take/or has taken time off to recover
  • There is only a 13% chance that it is a severe injury

So we actually already know a fair amount of information. She later recalls that She thinks she got injured during a race. Using high-level data on the participation rate of female cross-country athletes in the NCAA across the Divisions, we can use this information to determine what the most likely division she is in using Baye’s theorem.

category division gender name rate per 1000 athlete exposures
injury rates 1 female practice 6.52
injury rates 1 male practice 5.7
injury rates 1 female competition 9.5
injury rates 1 male competition 3.41
injury rates 1 female total 6.75
injury rates 1 male total 5.53
injury rates 2 female practice 1.96
injury rates 2 male practice 1.62
injury rates 2 female competition 6.41
injury rates 2 male competition 2.82
injury rates 2 female total 2.28
injury rates 2 male total 1.71
injury rates 3 female practice 6.13
injury rates 3 male practice 5.14
injury rates 3 female competition 5.77
injury rates 3 male competition 5.77
injury rates 3 female total 6.09
injury rates 3 male total 5.21
injury rates overall female practice 5.69
injury rates overall male practice 4.7
injury rates overall female competition 7.46
injury rates overall male competition 4.22
injury rates overall female total 5.85
injury rates overall male total 4.66

Baye’s theorem allows us to still find probabilities, regardless of the order in which we receive information. In order to get a probability for a value, we just need the probability of a and b, and the conditional_probability of b given a to find the conditional probability ofa given b

def bayes(conditional_probability, a, b):
    return (conditional_probability * a) / b

print 'P(Division 1 | competition and female and cross country) = %s' % bayes(0.0095, 0.37, 0.00746)  # P(Division 1 | competition) = 0.4711796246648794
print 'P(Division 2 | competition and female and cross country) = %s' % bayes(0.0641, 0.23, 0.076)  # P(Division 2 | competition) = 0.19762734584450403
print 'P(Division 3 | competition and female and cross country) = %s' % bayes(0.0577, 0.388, 0.076)  # P(Division 3 | competition) = 0.3001018766756033

Based on Baye’s theorem, given that she was injured during competition, it is most likely that she competes for a Division 1 school or a Division 3 school (77%).

To be clear: I would never recommend using this as an actual method for making medical decisions. Please leave that to the certified professionals. I chose an example involving athletics because I enjoy the sport, not in order to advocate for using it. While this method of inference can be applied to just about any field, there are some (like individual health-care) where some restraint should be taken before applying this method. The above example is simply a demonstration of how these aggregate statistics can be used to infer knowledge in cases where uncertainty is very high.

Finding and selecting datasets🔗

Identifying reputable sources for data sets can be crucial for applying these techniques for narrowing down information.

The keys to a good dataset are this

  • Large datasets
  • Unbiased data
  • Population of data is directly relevant to what you are trying to predict

When you are finding datasets, be sure that the dataset is similar to the data you will be applying the produced statistics to. For example, if you are collecting demographic data to be used on estimating demographics of new users in Virginia, using demographics statistics from Virginia in the 1970’s or the state of North Carolina will most likely not provide very accurate estimations of Virginia users in the present day. Due to changes in job market, ease of travel, and immigration trends, Virginia does not have the same demographic as it did in the 1970s, so the predictions would reflect the demographics of the 1970s, not the demographics of the present day.

Conclusion🔗

Using Baye’s Theorem for predictive purposes can be useful, especially when only aggregate statistics are available. The areas of application for this technique are wide, but I would not recommend using it for making decisions where the risk of a wrong decision can have life-altering consequences (ex. cancer detection). This technique is for use in cases where the cost of making a wrong decision can be recovered from.

I have applied this technique to internal business processes for my work, predicting characteristics of individuals based on demographic information, and for analyzing extensive running data (as demonstrated above). I hope you find this technique as useful and as simple as I did.