## Bayesian Modelling in Python¶

Mark Regan

### Section 0: Introduction¶

Welcome to "Bayesian Modelling in Python" - a tutorial for those interested in learning Bayesian statistics in Python. You can find a list of all tutorial sections on the project's homepage.

Statistics is a topic that never resonated with me throughout my years in university. The frequentist techniques that we were taught (p-values, etc.) felt contrived and ultimately, I turned my back on statistics as a topic that I wasn't interested in.

That was until I stumbled upon Bayesian statistics - a branch of statistics quite different from the traditional frequentist statistics that most universities teach. I was inspired by a number of different publications, blogs & videos that I would highly recommend any newbies to Bayesian stats to begin with. They include:

I created this tutorial in the hope that others find it useful and it helps them learn Bayesian techniques just like the above resources helped me. I'd welcome any corrections/comments/contributions from the community.

Throughout this tutorial, we will use a dataset containing all of my Google Hangout chat messages. I've removed the messages content and anonymized my friends' names; the rest of the dataset is unaltered.

If you'd like to use your Hangout chat data whilst working through this tutorial, you can download your Google Hangout data from Google Takeout. The Hangout data is downloadable in JSON format. After downloading, you can replace the hangouts.json file in the data folder.

The json file is heavily nested and contains a lot of redundant information. Some of the key fields are summarized below:

Field Description Example
conversation_id Conversation id representing the chat thread Ugw5Xrm3ZO5mzAfKB7V4AaABAQ
participants List of participants in the chat thread [Mark, Peter, John]
event_id Id representing an event such as chat message or video hangout 7-H0Z7-FkyB7-H0au2avdw
timestamp Timestamp 2014-08-15 01:54:12
message Content of the message sent Went to the local wedding photographer today
sender Sender of the message Mark Regan
In [1]:
import json
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn.apionly as sns

from datetime import datetime

%matplotlib inline
plt.style.use('bmh')
colors = ['#348ABD', '#A60628', '#7A68A6', '#467821', '#D55E00',
'#CC79A7', '#56B4E9', '#009E73', '#F0E442', '#0072B2']


The below code loads the json data and parses each message into a single row in a pandas DataFrame.

Note: the data/ directory is missing the hangouts.json file. You must download and add your own JSON file as described above. Alternatively, you can skip to the next section where I import an anonymized dataset.

In [2]:
# Import json data
with open('data/Hangouts.json') as json_file:

# Generate map from gaia_id to real name
def user_name_mapping(data):
user_map = {'gaia_id': ''}
for state in data['conversation_state']:
participants = state['conversation_state']['conversation']['participant_data']
for participant in participants:
if 'fallback_name' in participant:
user_map[participant['id']['gaia_id']] = participant['fallback_name']

return user_map

user_dict = user_name_mapping(json_data)

# Parse data into flat list
def fetch_messages(data):
messages = []
for state in data['conversation_state']:
conversation_state = state['conversation_state']
conversation = conversation_state['conversation']
conversation_id = conversation_state['conversation']['id']['id']
participants = conversation['participant_data']

all_participants = []
for participant in participants:
if 'fallback_name' in participant:
user = participant['fallback_name']
else:
# Scope to call G+ API to get name
user = participant['id']['gaia_id']
all_participants.append(user)
num_participants = len(all_participants)

for event in conversation_state['event']:
try:
sender = user_dict[event['sender_id']['gaia_id']]
except:
sender = event['sender_id']['gaia_id']

timestamp = datetime.fromtimestamp(float(float(event['timestamp'])/10**6.))
event_id = event['event_id']

if 'chat_message' in event:
content = event['chat_message']['message_content']
if 'segment' in content:
segments = content['segment']
for segment in segments:
if 'text' in segment:
message = segment['text']
message_length = len(message)
message_type = segment['type']
if len(message) > 0:
messages.append((conversation_id,
event_id,
timestamp,
sender,
message,
message_length,
all_participants,
', '.join(all_participants),
num_participants,
message_type))

messages.sort(key=lambda x: x[0])
return messages

# Parse data into data frame
cols = ['conversation_id', 'event_id', 'timestamp', 'sender',
'message', 'message_length', 'participants', 'participants_str',
'num_participants', 'message_type']

messages = pd.DataFrame(fetch_messages(json_data), columns=cols).sort(['conversation_id', 'timestamp'])

/Users/mregan/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:75: FutureWarning: sort(columns=....) is deprecated, use sort_values(by=.....)

In [3]:
# Engineer features
messages['prev_timestamp'] = messages.groupby(['conversation_id'])['timestamp'].shift(1)
messages['prev_sender'] = messages.groupby(['conversation_id'])['sender'].shift(1)

# Exclude messages are are replies to oneself (not first reply)
messages = messages[messages['sender'] != messages['prev_sender']]

# Time delay
messages['time_delay_seconds'] = (messages['timestamp'] - messages['prev_timestamp']).astype('timedelta64[s]')
messages = messages[messages['time_delay_seconds'].notnull()]
messages['time_delay_mins'] = np.ceil(messages['time_delay_seconds'].astype(int)/60.0)

# Time attributes
messages['day_of_week'] = messages['timestamp'].apply(lambda x: x.dayofweek)
messages['year_month'] = messages['timestamp'].apply(lambda x: x.strftime("%Y-%m"))
messages['is_weekend'] = messages['day_of_week'].isin([5,6]).apply(lambda x: 1 if x == True else 0)

# Limit to messages sent by me and exclude all messages between me and Alison
messages = messages[(messages['sender'] == 'Mark Regan') & (messages['participants_str'] != 'Alison Darcy, Mark Regan')]

# Remove messages not responded within 60 seconds
messages = messages[messages['time_delay_seconds'] < 60]


Out[3]:
conversation_id event_id timestamp sender message message_length participants participants_str num_participants message_type prev_timestamp prev_sender time_delay_seconds time_delay_mins day_of_week year_month is_weekend
10 Ugw5Xrm3ZO5mzAfKB7V4AaABAQ 7-H0Z7-FkyB7-HDBYj4KKh 2014-08-15 03:44:12.840015 Mark Regan Thanks guys!!! 14 [Keir Alexander, Louise Alexander Regan, Mark ... Keir Alexander, Louise Alexander Regan, Mark R... 3 TEXT 2014-08-15 03:44:00.781653 Keir Alexander 12.0 1.0 4 2014-08 0

We now have a data model that we can work with more easily. The above table shows a single row in the pandas DataFrame. I'm interested in how long it takes me to respond to messages. Let's create some plots that describe my typical response times.

In [4]:
fig = plt.figure(figsize=(10,7))

order = np.sort(messages['year_month'].unique())
sns.boxplot(x=messages['year_month'], y=messages['time_delay_seconds'], order=order, orient="v", color=colors[5], linewidth=1, ax=ax)
_ = ax.set_title('Response time distribution by month')
_ = ax.set_xlabel('Month-Year')
_ = ax.set_ylabel('Response time')
_ = plt.xticks(rotation=30)

plt.hist(messages['time_delay_seconds'].values, range=[0, 60], bins=60, histtype='stepfilled', color=colors[0])
_ = ax.set_title('Response time distribution')
_ = ax.set_xlabel('Response time (seconds)')
_ = ax.set_ylabel('Number of messages')

plt.tight_layout()


The above plots give a monthly and an overall perspective of the length of time (in seconds) that it takes me to respond to messages. At this point I have a lot of questions that I want to ask of the data. For example:

1. Is my response time affected by who I am talking to?
2. Are there environmental factors that affect my response time (day of week, location, etc.)?
3. What is the best and worst day to get in touch with me?

Before we try and answer some of these questions, lets take some baby steps by estimating some parameters of a model that describes the above data. That'll make it easier for us to understand the data and inquire further.

In the next section, we'll estimate parameters that describe the above distribution.

### Export data for usage throughout tutorial¶

In [5]:
# excluded some colums from csv output
messages.drop(['participants', 'message', 'participants_str'], axis=1, inplace=True)

# Save csv to data folder
messages.to_csv('data/hangout_chat_data.csv', index=False)


### References¶

1. Hangout reader by Fabian Mueller
In [6]:
# Apply pretty styles
from IPython.core.display import HTML

def css_styling():