Airline Passenger Data
Trend, evolving seasonality and long-term growth
Since 2014 · Automated statistical modelling
Artificial intelligence for data science.
Automated data analysis, interpretable models and human-readable statistical reports for the modern data stack.
Explore how machines can discover structure in data, compare models, explain patterns and turn complex analysis into understandable reports.
Airline Passenger Analysis
OBSERVED
TREND
FORECAST · 95% CI
Long-term trend
Annual periodic structure
Increasing seasonal amplitude
Residual variation
TREND DETECTED
+2.7% / year
PERIODIC COMPONENT
12 month cycle
CHANGE POINT
Detected: 2008
MODEL CONFIDENCE · HIGH
The method
From raw data to an understandable model
DATAMODEL DISCOVERYEVALUATIONEXPLANATIONREPORT
01
Explore
Inspect structure, missingness, distributions and relationships.
02
Discover
Search across candidate statistical models and structural explanations.
03
Evaluate
Compare fit, complexity, predictive performance and uncertainty.
04
Explain
Turn discovered patterns into charts, predictions and readable descriptions.
Example reports
See what automated analysis can uncover
Solar Irradiance
Long-term structure, variation and periodic behaviour
Unemployment
Structural change, trends and uncertainty over time
Topics
Automated data science has evolved
Automated Statistical Analysis
Discover patterns and choose appropriate analytical methods automatically.
AutoML
Automated model selection, tuning and evaluation.
Explainable AI
Make machine-generated conclusions understandable and auditable.
Gaussian Processes
Probabilistic modelling with interpretable uncertainty.
Time-Series Intelligence
Detect trends, seasonality, change points and anomalies.
AI Analytics
Modern AI systems that help analysts explore and understand data.
Origins
The idea behind the Automatic Statistician
The original Automatic Statistician research investigated whether parts of statistical modelling could be automated without giving up interpretability. Rather than fitting a single fixed model, the system searched a compositional space of Gaussian process kernels, building structure out of smooth trends, periodic components, changepoints and noise.
Candidate models were compared using Bayesian reasoning, which balances fit against complexity. The discovered structure was then translated into natural-language descriptions and charts, together with model criticism that flagged where the model disagreed with the data. The result was a report a statistician could read, check and argue with.
Explore the Research
SE × PER
+ SE × LIN
+ CP(2008) × SE
+ WN
+ SE × LIN
+ CP(2008) × SE
+ WN
SE — smooth trend
PER — periodicity
LIN — linear growth
CP — changepoint
WN — noise
BIC — model score
Guides
Learn automated data analysis
How to parse dates with an explicit format in Pandas (with Code)
Pass the documented date order to pandas.to_datetime through format, and choose errors="raise" or errors="coerce" deliberately.
How to calculate a time-based rolling mean in Pandas (with Code)
Use rolling with a fixed time span such as "2h" on a sorted DatetimeIndex to average observations in a trailing interval.
How to resample a time series to daily intervals in Pandas (with Code)
Convert timestamps to the intended reporting timezone and use resample("D") with explicit left-closed, left-labelled bins.
How to pivot a table with duplicate key pairs in Pandas (with Code)
Use pivot_table with an explicit aggregation function when repeated row-key and column-key pairs represent legitimate repeated measurements.
How to reshape wide data to long format in Pandas (with Code)
Use melt with explicit identifier and measurement columns to turn each selected wide cell into one long-format row.
How to validate a many-to-one merge in Pandas (with Code)
Use validate="many_to_one" in a left merge to require unique join keys in the right-hand lookup table.
Software
Tools for automated data science
Reviews and comparisons of the platforms that automate parts of the analytical workflow, evaluated against the methodology we publish.
Explore Data Science Tools