README.md

Examples

This page contains a number of examples showing how to use Pints.

Each example was created as a Jupyter notebook (http://jupyter.org/). These notebooks can be downloaded and used, or you can simply copy/paste the relevant code.

Before you get started

• Using Python
• Installing PINTS
• An introduction to Bayesian inference and optimisation

Getting started

• Optimisation: First example
• Sampling: First example
• Writing a model
• Writing a custom LogPDF
• Writing a custom LogPrior

Digging deeper

• Full control with the ask-and-tell interface
• Optimisation in a transformed parameter space - using a Transform object
• Optimisation in a transformed parameter space - writing a model wrapper
• Sampling in a transformed parameter space - using a Transform object
• Sampling in a transformed parameter space - with or without Jacobian adjustment

Optimisation

Particle-based methods

• CMA-ES
• CMA-ES (bare bones version)
• Gradient descent
• PSO
• SNES
• XNES

Local optimisers

• Nelder-Mead

Further optimisation

• Convenience methods fmin() and curve_fit()
• Maximum loglikelihood
• Multiple objectives
• Spotting unidentifiable parameters with MCMC
• Visualising a 2d error surface

Sampling

MCMC without gradients

• Differential Evolution MCMC
• DRAM ACMC
• DREAM MCMC
• Emcee Hammer
• Haario Adaptive Covariance MCMC
• Haario-Bardenet Adaptive Covariance MCMC
• Metropolis Random Walk MCMC
• Population MCMC
• Rao-Blackwell Adaptive Covariance MCMC
• Slice Sampling: Doubling MCMC
• Slice Sampling: Overrelaxation MCMC
• Slice Sampling: Stepout MCMC

MCMC with gradients

• Hamiltonian MCMC
• MALA MCMC
• Monomial-Gamma HMC MCMC
• No-U-Turn MCMC
• Relativistic MCMC
• Slice Sampling: Rank Shrinking MCMC

Nested sampling

• Ellipsoidal nested sampling
• Rejection nested sampling

Analysing sampling results

• Autocorrelation
• Customise analysis plots
• Effective sample size
• Evaluating noise models using autocorrelation plots of the residuals
• Histogram plots
• Noise model diagnostic plots (correlation)
• Noise model diagnostic plots (magnitude)
• Pairwise scatterplots
• Predicted time series
• Trace plots

Statistical modelling

• Autoregressive moving average errors
• Cauchy sampling error
• Constant and multiplicative Gaussian error
• Integrated noise model
• Log priors
• Multiplicative Gaussian noise
• Pooling parameters
• Student-t noise model

Toy problems

Models

• Beeler-Reuter action potential model
• Constant model
• Fitzhugh-Nagumo model
• Goodwin oscillator model
• HES1 Michaelis-Menten model
• Hodgkin-Huxley Potassium current model
• Logistic growth model
• Lotka-Volterra predator-prey model
• Repressilator model
• Simple Harmonic Oscillator model
• SIR Epidemiology model
• Stochastic Degradation model
• Stochastic Logistic model

Distributions

• Annulus
• Cone
• Eight schools distribution
• German credit hierarchical logistic model
• German credit logistic model
• High dimensional gaussian
• Multimodal gaussian distribution
• Neals Funnel
• Rosenbrock function
• Simple Egg Box
• Twisted Gaussian Banana

Interfaces

• Statsmodels ARIMA
• Statsmodels state space

Miscellaneous

• Automatic differentiation using autograd
• The example shown on the landing page