Welcome to bayesloop’s documentation!

Probabilistic programming framework that facilitates objective model selection for time-varying parameter models.

The tutorials and examples in this documentation can be run directly in the browser. Selecting the run button on a code cell starts a Python session in which the code of that page can be executed and freely modified, without a local installation.

See also

If you want to contribute to the project or just browse the source code, visit the Github repository of bayesloop.

Contents

• Installation
  • Development version
  • Dependencies
• Migrating from bayesloop 1.x
• Tutorials
  • First steps with bayesloop
    • Study class
    • Data import
    • Observation model
    • Transition model
    • Model fit
    • Plotting
    • Saving studies
  • Model Selection
    • Bayes factors
    • Combined transition models
    • Serial transition model
  • Optimization of hyper-parameters
    • Global optimization
    • Conditional optimization in nested transition models
  • Hyper-study
  • Change-point study
    • Analyzing abrupt changes of parameter values
    • Analyzing structural breaks in time series models
  • Online study
  • Prior distributions
    • Parameter prior
    • Hyper-parameter priors
  • Custom observation models
    • SymPy.stats random variables
    • SciPy.stats probability distributions
    • NumPy likelihood functions
  • Multiprocessing
• Examples
  • Anomalous diffusion
    • Diffusion gradient
    • Regime-switch diffusion process
  • Stock market fluctuations
    • Persistent random walk model
    • Online study
    • Volatility spikes
    • Islands of stability
    • Automatic tuning
    • Real-time model selection
  • Measles in the United States: abrupt break or gradual decline
    • The data
    • A time-varying transmission level
    • Letting the evidence choose between abrupt and gradual change
    • The post-elimination era: a custom Poisson observation model
    • What this example showed
  • The rate of great earthquakes over time
    • The data
    • Model comparison: constant versus time-varying Poisson rate
    • A change-point scan around 2004
    • What this example showed
  • Atlantic hurricanes: a shift in activity in the 1990s
    • The data
    • A time-varying rate over the aircraft era
    • Constant, gradual, or a single break?
    • What this example showed
  • The Great Moderation: dating a fall in US growth volatility
    • The data
    • A Gaussian model with a time-varying mean and volatility
    • Comparing static, drifting and single-break models
    • Dating the break and scoring the models
    • The joint posterior of the two smoothness hyper-parameters
    • What this example showed
  • A century of baseball: dating the home-run regime shifts
    • The data
    • Modelling the rate: a Gaussian with inferred scatter
    • A smooth time-varying rate over the full history
    • Letting the evidence choose: constant, gradual, or one break
    • Isolating the steroid-era onset
    • Quantifying the regimes from the raw series
    • The home run as one time-varying parameter
    • The two dated breaks
    • What this example showed
  • Sunspots: the 20th-century “Grand Maximum”
    • The data
    • A Gaussian model with a time-varying envelope
    • Comparing an envelope with a constant mean
    • Reading off the eras
    • Visualising the record and the envelope
    • The scientific conclusion
    • What this example showed
  • Real-time seizure detection from EEG
    • The data
    • Offline reconstruction of the time-varying parameters
    • Online detection with model selection
    • Average detection latency
    • What this example showed
  • Online COVID-19 forecasting with a time-varying growth rate
    • The data
    • The observation model
    • The adaptive model
    • The static baseline
    • One-step-ahead point forecasts
    • Real-time wave detection
    • The forecast, the growth rate, and the wave indicator
    • Probabilistic prediction
    • What this example showed
  • Real-time S&P 500 volatility: bayesloop versus GARCH
    • The data
    • The observation model: zero-mean white noise with time-varying volatility
    • The online model: real-time selection between calm and turbulent dynamics
    • The constant-volatility baseline
    • The benchmark: GARCH(1,1)
    • Validation: forecasts, realized volatility, and shock dates
    • The scoreboard
    • Figure 1: the regime signal in context
    • Figure 2: the out-of-sample race and the volatility paths
    • What this example showed
  • Weather-adjusted electricity demand and the COVID shock
    • The data
    • Static and rolling OLS
    • A time-varying baseline with bayesloop
    • Comparison by model evidence
    • Comparison by out-of-sample prediction
    • Dating the COVID baseline drop
    • What this example showed
  • Animal movement: a continuum the HMM cannot represent
    • The data
    • A time-varying Rayleigh scale, and letting the evidence choose the dynamics
    • Comparison with a Gaussian HMM
    • Reading the result
    • What this example showed
• API Reference
  • Study types
    • ChangepointStudy
    • HyperStudy
    • OnlineStudy
    • Study
  • Observation models
    • AR1
    • Bernoulli
    • Gaussian
    • GaussianMean
    • Laplace
    • NumPy
    • ObservationModel
    • Poisson
    • ScaledAR1
    • SciPy
    • SymPy
    • WhiteNoise
  • Transition models
    • AlphaStableRandomWalk
    • BivariateRandomWalk
    • BreakPoint
    • ChangePoint
    • CombinedTransitionModel
    • Deterministic
    • GaussianRandomWalk
    • Independent
    • NotEqual
    • RegimeSwitch
    • SerialTransitionModel
    • Static
    • TransitionModel
    • gaussian_kernel_1d()
  • File I/O
    • load()
    • save()

Indices and tables

• Index

• Module Index

• Search Page