# Statistics, Probability, Analysis and Applied Mathematics

SPAAM student seminar series

*Organised by the Warwick SIAM-IMA Student Chapter
Committee members: Hanson Bharth, Connah Johnson, Jaromir Sant and Jack Thomas*

#### Term 3:

In light of the coronavirus outbreak, we are following university advice and suspending all SPAAM talks for term 3. If and when we learn more, we will be in touch.

- Last updated: 17 March 20

#### Term 2: *Tuesdays 2-3pm, B3.01*

#### Dr. Alice Corbella | Towards automatic Zig Zag sapling and its use for epidemic inference

*Abstract*: Zig-Zag sampling, introduced by Bierkens et al. 2019, is based on the simulation of a piecewise deterministic Markov process (PDMP) whose switching rate $\lambda(t)$ is governed by the derivative of the log-target density. To our knowledge, Zig-Zag sampling has been used mainly on simple targets for which derivatives can be computed manually in a reasonable time.

To expand the applicability of this method, we incorporate Automatic Differentiation (AD) tools in the Zig-Zag algorithm, computing $ \lambda(t) $ automatically from the functional form of the log-target density. Moreover, to allow the simulation of the PDMP via thinning, we use standard optimization routines to find a local upper bound for the rate.

We present several implementations of our automatic Zig-Zag sampling and we measure the potential loss in computational time caused by AD and optimization routines. Among the examples, we consider the case of data arising from an epidemic which can be approximated by a deterministic system of equations; here manual derivation of the posterior density is practically infeasible due to the recursive relationships contained the likelihood function. Automatic Zig-Zag sampling successfully explores the parameter space and samples efficiently from the posterior distribution.

(Joint work with Gareth O. Roberts and Simon E. F. Spencer)

#### Term 1:* Tuesdays 3-4pm, MS.03*

#### Phil Herbert | *MASDOC* | The membrane mediated force on point attachments with application to a near spherical biomembrane

*Abstract:* We consider a hybrid model of a biomembrane with attached particles. The membrane is represented by a near spherical continuous surface, attached proteins are described by rigid bodies which are free to move tangentially and rotate in the axis normal to a reference point. As the standard energy for a membrane is highly non-linear, we consider a quadratic energy which may be shown to be an approximation of the Canham-Helfrich energy with a volume constraint and the deformations due to the attached proteins are imposed by point Dirichlet constraints. We show differentiability of the membrane energy with respect to parameterisation of these embedded particles and provide illustrative numerical examples.

#### Dom Brockington | *MASDOC* | Sticky Flows and KPZ Universality

*Abstract:* We shall introduce stochastic flows, and stochastic flows of kernels, before moving to the special case of sticky flows and their fluctuations. On the large deviation scale these fluctuations turn out to be Tracey-Widom GUE distributed, thus the sticky flows lie in the KPZ universality class.