# Algorithms & Computationally Intensive Inference seminars

Terms 1-3, Location MB2.23, Fridays 12:15-14:00 (12:15-12:45 is an informal sandwich lunch).

Reminder emails are not sent to participants unless there is a change to the scheduled programme at short notice. If you would like to speak, or you want to be included in any emails, please contact one of the organisers.

Current Organisers: Dootika Vats,

• If you would like to talk, or have ideas for possible speakers, then please email one of the organisers above.

Website URL: www.warwick.ac.uk/compstat

Mailing List Sign-Up: http://mailman1.csv.warwick.ac.uk/mailman/listinfo/algorithmseminar

Mailing List: algorithmseminar@listserv.csv.warwick.ac.uk (NB - only approved members can post)

## 2018/19 Term 1:

• Week 1 - 5th October - Cancelled
• Week 2 - 12th October - Summary of research short talks:
• Week 3 - 19th October - Summary of research short talks:
• Week 4 - 26th October - Giulio Morina (Warwick) - "From the Bernoulli Factory to a Dice Enterprise via Perfect Sampling of Markov Chains"
• Abstract: Given a p-coin that lands heads with unknown probability p, we wish to construct an algorithm that produces an f(p)-coin for a given function f:(0, 1)→(0, 1). This problem is commonly known as the Bernoulli
Factory and generic ways to design a practical algorithm for a given function f exist only in a few special cases. We present a constructive way to build an efficient Bernoulli Factory when f(p) is a rational function. Moreover, we extend the original problem to a more general setting where we have access to an m-sided
die and we wish to roll a v-sided one, where the probability of rolling each face is a fixed function of the original probabilties. We achieve this by perfectly simulating from the stationary distribution of a
certain class of Markov chains.
• Week 5 - 2nd November - Cancelled. CoSInES Launch Day.
• Week 6 - 9th November - Iker Perez (Nottingham) - "Novel approaches to efficiently augment a Markov Jump process for exact Bayesian Inference"
• Abstract: In this talk we will discuss foundational statistical challenges associated with families of Markovian jump models, which often find applications in domains such as genetics, epidemiology, mathematical biology or queueing theory. We will first review Markov jump processes, and by means of common accessible examples, illustrate the computational impediments posed by real-world application scenarios to inverse uncertainty quantification tasks. Then, we will give an overview of the recent advances linked to structured jump systems. Our work is concerned with building on uniformization procedures and we propose a novel efficient auxiliary-variable algorithm for data augmentation, which yields computationally tractable distributions suited for exact (in Monte Carlo sense) Bayesian inference in often large, infinite or multivariate population systems. We demonstrate the capabilities of the presented methods by drawing Bayesian inference for partially observed stochastic epidemics and show that it overcomes the limitations of existing vanilla approaches. This is joint work (in progress) with Theo Kypraios.
• Week 7 - 16th November - Ritabrata Dutta (Warwick) - "Well-Tempered Hamiltonian Monte Carlo on Active-Space"
• Abstract: When the gradient of the log-target distribution is available, Hamiltonian Monte
Carlo (HMC) has been proved to be an efficient simulation algorithm. However,
HMC performs poorly when the target is high-dimensional and has multiple isolated
modes. To alleviate these problems we propose to perform HMC on a locally and
continuously tempered target distribution. This tempering is based on an efficient
approach to simulate molecular dynamics in high-dimensional space, known as well-
tempered meta-dynamics. The tempering we suggest is performed locally and only
along the directions of the maximum changes in the target which we identify as
the active space of the target. The active space is the span of the eigenfunctions
corresponding to the dominant eigenvalues of the expected Hessian matrix of the
log-target. To capture the state dependent non-linearity of the target, we iteratively
estimate the active space from the most recent batch of samples obtained from the
simulation. Finally, we suggest a re-weighting scheme based on path-sampling to
provide importance weights for the samples drawn from the continuously-tempered
distribution. We illustrate the performance of this scheme for target distributions
with complex geometry and multiple modes on high-dimensional spaces in comparison
• Week 8 - 23rd November - Stephen Connor (York) - "Omnithermal Perfect Simulation for Multi-server Queues"
• Abstract: The last few years have seen much progress in the area of perfect simulation algorithms for multi-server queueing systems, allowing us to sample from the exact equilibrium distribution of the Kiefer-Wolfowitz workload vector. This talk will describe an “omnithermal" variant of one such algorithm for M/G/c queues, which permits simultaneous sampling from the equilibrium distributions for a range of c (the number of servers) at relatively little additional cost.
• Week 9 - 30th November - Emilia Pompe (Oxford) - "Adaptive MCMC for Multimodal Distributions"
• Abstract: We propose a new Monte Carlo method for sampling from multimodal distributions (Jumping Adaptive Multimodal Sampler). The idea of this technique is based on splitting the task into two: finding the modes of the target distribution and sampling, given the knowledge of the locations of the modes. The sampling algorithm is based on steps of two types: local ones, preserving the mode, and jumps to a region associated with a different mode. Besides, the method learns the optimal parameters while it runs, without requiring user intervention. The main properties of our algorithm will be discussed and its performance will be illustrated with several examples of multimodal target distributions. Some ergodic results that we proved for this method will also be presented. This is joint work with Chris Holmes and Krys Latuszynski.
• Week 10 - 7th December - Flávio Gonçalves (UFMG) - "Exact Bayesian inference for Level-Set Cox Processes"
• Abstract: We consider a Level-Set spatial Cox process which assumes the intensity function to be piece-wise constant. The Level-Set approach considers the levels of a latent Gaussian Process to define the IF contours in a continuous and flexible way. This is an infinite dimensional model for which existing inference solutions rely on discrete approximations. This introduces a significant bias to the estimation procedure and, often, model decharacterisation. Attempts to mitigate the approximation problems inevitably lead to impractical computational costs. We propose a novel pseudo-marginal MCMC algorithm that has the exact posterior distribution as the target. The likelihood function estimator for the pseudo-marginal algorithm is devised through a Poisson estimator in which a non-centred parametrisation plays an important roll.

## 2018/19 Term 2:

• Week 1 - 11th January- Neil Chada (NUS) - "Title: Posterior convergence analysis of $\alpha$-stable processes: applications in Bayesian inversion"
• Abstract: This talk is concerned with the theoretical understanding of $\alpha$-stable sheets ${X}$. Our motivation for this is in the context of Bayesian inverse problems, where we consider the treatment of these processes as prior forms for parameter estimation. We derive various convergence results of these processes. In doing so we use a number of variants which these sheets can take, such as a stochastic integral representation, but also random series expansions through Poisson processes. Our convergence analysis will rely on the fact of whether ${X}$ omits $L^p$ sample paths, and if so how regular the paths are.
• Week 2 - 18th January - James Flegal (UC Riverside) (in room MB2.22) - "Weighted batch means estimators in Markov chain Monte Carlo"
• Abstract: We propose a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo simulations and estimation of the asymptotic covariance matrix in the Markov chain central limit theorem, where conditions ensuring strong consistency are provided. Finite sample performance is evaluated through auto-regressive, Bayesian spatial-temporal, and Bayesian logistic regression examples, where the new estimators show significant computational gains with a minor sacrifice in variance compared with existing methods.
• Week 3 - 25th January - Joint Session (Short Talks)
• Week 4 - 1st February - Mateusz Majka (Warwick) - Title / Abstract TBA
• Week 5 - 8th February - Ioannis Kosmidis (Warwick) - Title / Abstract TBA
• Week 6 - 15th February - Matthew Ludkin (Lancaster) - Title / Abstract TBA
• Week 7 - 22nd February - Patrick Rebeschini (Oxford) - Title / Abstract TBA
• Week 8 - 1st March - Susana Gomes (Warwick) - Title / Abstract TBA
• Week 9 - 8th March - Available
• Week 10 - 15th March - Jake Carson (Warwick) - Title / Abstract TBA

## 2018/19 Term 3:

• Week 1 - 26th April - Toni Karvonen (Aalto University) - Title / Abstract TBA
• Week 2 - 3rd May - Dootika Vats (Warwick) - Title / Abstract TBA
• Week 3 - 10th May - Jonathan Harrison (Warwick) - Title / Abstract TBA
• Week 4 - 17th May - Available
• Week 5 - 24th May - Available
• Week 6 - 31st May - Available
• Week 7 - 7th June - Available
• Week 8 - 14th June - Available
• Week 9 - 21st June - Available
• Week 10 - 28th June - Available

## Previous Years:

2017/2018

2016/2017

2015/2016

2014/2015

2013/2014

2012/2013

2010/2011

Some key phrases:

- Sampling and inference for diffusions
- Exact algorithms
- Intractable likelihood
- Pseudo-marginal algorithms
- Particle filters
- Importance sampling
- MCMC