## Calculating Probabilities

Complex mathematical models are commonly used to describe naturally occurring processes in the sciences, and also to make predictions. These descriptions and predictions are often presented in the language of probability theory, since measurements are very often noisy and there may therefore be multiple answers that plausibly describe the data. The main challenge with such approaches often lies in calculating the complex probability distributions that result. This image shows one such probability distribution – note how it is quite a bit more complex than a standard Gaussian distribution!

Our ongoing research involves developing statistical methods for exploring and sampling from such complex probability distributions as efficiently as possible, involving ideas from physics, statistics and mathematics (in particular differential geometry). For more information on this work have a look at the following research papers:

- Girolami M. and Calderhead B. (2011) Riemann manifold Langevin and Hamiltonian Monte Carlo methods. J. R. Statist. Soc. B. (with discussion). 73, Part 2. pp 1-37.
- Calderhead B. and Girolami M. (2009) Estimating Bayes factors via thermodynamic Integration and Population MCMC. Computational Statistics and Data Analysis, 48. pp 4028 - 4045.

This work is funded via the following research grants:

- Inference-based Modelling in Population and Systems Biology - BBSRC BB/G006997/1 - 2010 to 2013
- Computational Statistics and Cognitive Neuroscience - EPSRC EP/H024875/1 - 2009 – 2011
- The Molecular Nose - EPSRC EP/E032745/1 2007 to 2011
- The Synthesis of Probabilistic Prediction and Mechanistic Modelling within a Systems Biology Context - EPSRC EP/E052029/1 - 2007 to 2012
- Bayesian Inference in Systems Biology: Modelling Organ Specificity of Circadian Control in Plants - Microsoft Research - 2007 to 2011