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 run a Welch two-sample t-test in SciPy (with Code)
Call scipy.stats.ttest_ind with equal_var=False to compare the means of two independent samples without assuming equal population variances.
The Best Statistics AI Solver Tools in 2026: Honest Rankings After 40+ Hours of Testing
Best statistics AI solvers: Wolfram Alpha (symbolic computation), TutorBin (student homework), Julius AI (dataset analysis), Mathway (routine problems), ChatGPT Advanced Data Analysis (Python-powered analysis). Match the tool to your task — symbolic computation vs. dataset analysis are fundamentally different use cases.
How to display prediction intervals around a line in Plotly (with Code)
Draw lower and upper Scatter traces in increasing x order, then set fill="tonexty" on the upper trace to shade the interval between them.
How to create a heatmap with fixed color limits in Plotly (with Code)
Pass range_color=(lower, upper) to px.imshow for a numeric two-dimensional heatmap.
How to plot multiple time series with a range slider in Plotly (with Code)
Create one line trace per series on a shared date axis and enable xaxis_rangeslider_visible=True.
How to export an interactive chart to a standalone HTML file in Plotly (with Code)
Use fig.write_html with include_plotlyjs=True and full_html=True to create a complete Plotly HTML document with its chart library included.
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