## Why is the topic of interest, why should it be discussed?

Monte Carlo methods have been the dominant form of approximate inference for Bayesian statistics over the last couple of decades. Monte Carlo methods are interesting as a technical topic of research in themselves, as well as enjoying widespread practical use. In a diverse number of application areas Monte Carlo methods have enabled Bayesian inference over classes of statistical models which previously would have been infeasible. Despite this broad and sustained attention, it is often still far from clear how best to set up a Monte Carlo method for a given problem, how to diagnose if it is working well, and how to improve under-performing methods. The impact of these issues is even more pronounced with new emerging applications.

## What does the workshop address and accomplish?

Identifying features of applications of Monte Carlo methods: This workshop is aimed equally at practitioners and core Monte Carlo researchers. For practitioners we hope to identify what properties of applications are important for selecting, running and checking a Monte Carlo algorithm. Monte Carlo methods are applied to a broad variety of problems. The workshop aims to identify and explore what properties of these disparate areas are important to think about when applying Monte Carlo methods. Areas we anticipate the workshop will explore in this regard are:

- How important is the dimensionality of the problem?
- What methods would be appropriate for discrete, continuous and hybrid distributions with varying properties such as: log-concavity, uni-modality, multi-modality and mega-modality, highly skewed regions and poor or unknown dimensional scaling?
- For continuous variables, is the target density such that gradients and the Hessian can be efficiently calculated analytically or numerically?
- How accurate an answer is actually needed for the problem at hand? For example, estimation of a physical constant may demand great accuracy, while many MCMC-based learning methods (e.g., contrastive divergence) only require approximate gradients.
- Normalizing constants (partition functions or the Bayesian evidence / integrated likelihood / marginal likelihood / prior predictive likelihood) are often important for model comparison and selection. What is the best way to estimate these quantities?
- Are estimates of probabilities for very rare events needed and how could these be estimated.
- Combining deterministic methods with Monte Carlo.
- How to deal with missing data in posterior inference via Monte Carlo?
- Dealing with changing dimensionality (structure learning, non-parametrics, reversible jump).

We also hope that the workshop will help to direct future Monte Carlo research in the ways that will be most useful for the current spectrum of practical applications such as:

- Large scale applications such as climate modelling, inference in dynamic system, emulation.
- Classical hierarchical statistical models, perhaps smaller scale but with strong coupling and structure.
- Real-time applications such as robotics and HCI.
- Large scale physics experiments with huge datasets of many events, each of which can be modelled in detail (e.g., in astronomy and particle physics).
- Large-scale undirected graphical models such as MRFs, Markov logic networks or Boltzmann machines and related models from statistical physics.
- Biological applications especially systems biology.
- Language modelling and Natural language processing tasks.

Identifying features of algorithms: the classes of Monte Carlo methods, such as simple importance sampling, MCMC, SMC and ABC vary significantly in their applicability and failure modes. We can also consider:

- Various meta-methods such as annealing/bridging/nesting that sit on top of MCMC. How should we choose amongst these given the features of an application?
- When should we use deterministic methods instead?
- Parallelization: how to utilize multiple cores and GPUs.
- Trade-offs: issues to consider regarding ease-of-use and performance.
- Setting things up: what choices should be made, how are things tuned and what are the most important “tricks of the trade”? Post-mortems: what diagnostics should we all be doing? Are there any (useful) guarantees?

## What is the targeted group of participants?

While the workshop will be as inclusive as possible, time is short and we cannot assume zero knowledge. Knowledge of basic Monte Carlo algorithms will be assumed, but specified well in advance in the form of recommended reading in widely-available textbooks or tutorials.