## Department of Statistics

# Seminars

**The C3 depletion design: Population estimation and gear calibration using Catches from Concentric Circles.**

Speaker: Liese Carleton

Affiliation: Virginia Institute of Marine Science, College of William & Mary

When: Monday, 28 May 2018, 1:00 pm to 2:00 pm

Where: 303-310

Depletion studies are often used in closed systems to estimate population size and catchability coefficient. Application of depletion methods to open water systems is hindered by the uncertain size of the defined domain due to the attraction of fish from the outside into the study area. In this novel design approach, the study area is comprised of two concentric circles. The diameter of the outer circle is specified by the length of a bottom longline, which is set repeatedly in a star pattern to serially deplete the circle. Catches are recorded as either within the smaller inner circle or in the outer ring. This design allows us to include an immigration component into the depletion model so that initial abundance, catchability, and net movement can be estimated. Gear efficiency can be derived from the estimated catchability, and could then be used to convert a survey index of abundance into an estimate of absolute population size. The method is illustrated with bottom longline sets for Atlantic sharpnose shark in the Gulf of Mexico.

**Combinatorial Inference**

Speaker: Junwei Lu

Affiliation: Department of Operations Research and Financial Engineering Princeton University

When: Monday, 14 May 2018, 1:00 pm to 2:00 pm

Where: 303-310

We propose the combinatorial inference to explore the topologicl structures of graphical models. The combinatorial inference can conduct the hypothesis tests on many graph properties including connectivity, hub detection, perfect matching, etc. On the other side, we also develop a generic minimax lower bound which shows the optimality of the proposed method for a large family of graph properties. Our methods are applied to the neuroscience by discovering hub voxels contributing to visual memories.

**Bayesian nonparametric analysis of multivariate time series**

Speaker: Alexander Meier

Affiliation: Otto-von-Guericke University Magdeburg

When: Wednesday, 9 May 2018, 3:00 pm to 4:00 pm

Where: 303.310

While there is an increasing amount of literature about Bayesian time series analysis, only few nonparametric approaches to multivariate time series exist. Many methods rely on Whittle's likelihood, involving the second order structure of a stationary time series by means of its spectral density matrix f. The latter is often modeled in terms of the Cholesky decomposition to ensure positive definiteness. However, asymptotic properties under these priors such as posterior consistency or posterior contraction rates are not known.

A different idea is to model f by means of random measures. This is in line with (1), who model the normalized spectral density of a univariate time series with a Dirichlet process mixture of beta densities. We use a similar approach, with matrix-valued mixture weights induced by a completely random matrix-valued measure (2,3). We use a class of infinitely divisible matrix Gamma distributions (4) for this purpose. While the procedure performs well in practice, we also establish posterior consistency and derive posterior contraction rates.

(1) N. Choudhuri, S. Ghosal and A. Roy (2004). Bayesian estimation of the spectral density of a time series. Journal of the American Statistical Association 99(468), 1050–1059

(2) A. Lijoi and I. Pruenster (2010). Models beyond the Dirichlet process. Bayesian nonparametrics, 28:80

(3) J. B. Robertson, M. Rosenberg, et al. (1968). The decomposition of matrix-valued measures. The Michigan Mathematical Journal, 15(3), 353-368

(4) V. Perez-Abreu and R. Stelzer (2014). Infinitely divisible multivariate and matrix Gamma distributions. Journal of Multivariate Analysis, 130, 155–175

Authors:

Alexander Meier, Otto-von-Guericke University Magdeburg

Claudia Kirch, Otto-von-Guericke University Magdeburg

Renate Meyer, The University of Auckland

**Modelling spatial-temporal processes with applications to hydrology and wildfires**

Speaker: Professor Valerie Isham

Affiliation: University College London

When: Friday, 4 May 2018, 11:00 am to 12:00 pm

Where: 303-610

Mechanistic stochastic models aim to represent an underlying physical process (albeit in highly idealised form, and using stochastic components to reflect uncertainty) via analytically tractable models, in which interpretable parameters relate directly to physical phenomena. Such models can be used to gain understanding of the process dynamics and thereby to develop control strategies.

In this talk, I will review some stochastic point process-based models constructed in continuous time and continuous space using spatial-temporal examples from hydrology such as rainfall (where flood control is a particular application) and soil moisture. By working with continuous spaces, consistent properties can be obtained analytically at any spatial and temporal resolutions, as required for fitting and applications. I will briefly cover basic model components and properties, and then go on to discuss model construction, fitting and validation, including ways to incorporate nonstationarity and climate change scenarios. I will also describe some thoughts about using similar models for wildfires.

**Dirichlet and Poisson-Dirichlet approximations**

Speaker: Han Liang Gan

Affiliation: Northwestern University

When: Thursday, 26 April 2018, 1:00 pm to 2:00 pm

Where: 303-257

The Dirichlet and Poisson-Dirichlet distributions are multi-dimensional distributions that can be used to model proportions. In this talk, we will give explicit error bounds when applying Dirichlet and Poisson-Dirichlet approximations in a variety of applications that include urn models and stationary distributions of genetic drift models. The results are derived using new developments in Stein's method.

This is joint work with Adrian Rollin (National University of Singapore) and Nathan Ross (University of Melbourne).

**Weakly informative prior for mixture models**

Speaker: Kate Lee

Affiliation: Auckland University of Technology

When: Thursday, 19 April 2018, 1:00 pm to 2:00 pm

Where: 303-310

A mixture model is a probability model for presenting the presence of subpopulation within an overall population. It comprises a finite or infinite number of components, possibly of different distributions, that can describe different features of data. They thus facilitate much more careful description of complex systems and they have been adopted in diverse areas. While mixture models have been studied for more than a century, the construction of a reference Bayesian analysis of those models remains unsolved due to the ill-posed nature of such statistical objects. In this talk, a new parameterisation centred on the mean and possibly the variance of the mixture distribution is suggested and based on the reparameterisation, a weakly informative prior for a wide class of mixtures is proposed. I will demonstrate that under some generous conditions, the resulting posterior distributions are proper and illustrate MCMC implementations.

**Statistics of forensic lineage DNA markers**

Speaker: Mikkel Meyer Andersen

Affiliation: Associate professor, Department of Mathematical Sciences, Aalborg University, Denmark

When: Wednesday, 18 April 2018, 11:00 am to 12:00 pm

Where: 303-310

Genetic information from biological material is often used in forensic casework such as in criminal cases. The biological material collected from the crime scene (assumed to originate from the culprit) is used to obtain a so-called DNA profile.

When a suspect is detained, a reference DNA profile can be taken from the suspect and compared to the crime scene profile. If the profiles do not match, the suspect can be released. If the profiles match, the evidential value of this match must be assessed because a DNA profile is only a part of the entire genome. There are many different kinds of DNA profiles and calculation of an evidential value depends on the type of DNA profile. The most common kind of DNA profiles is called autosomal DNA profiles (and are based on the non-sex chromosomes), and there is a wide consensus on how to calculate the evidential value of matching autosomal DNA profiles (I will not spend much time on these).

Another type of DNA profiles are lineage DNA markers as they are based on the paternal lineage using the paternally inherited Y-chromosome and the maternal lineage using the maternally inherited mitochondrial. Y-chromosome profiles are valuable when there is a mixture of male-source and female-source DNA, and interest centres on the identity of the male source of the DNA. This happens for example in sexual assault cases. Mitochondrial profiles are used for example when the biological material obtained from the crime scene is heavily degraded (e.g. by weather or time). Traditional DNA profiles are based on the nuclear DNA, and if the nuclei of the cells are too damaged then such profiles cannot be obtained. Instead, DNA profiles based on the mitochondria are made because mitochondria are more robust than the nuclei of the cells and are often present even in heavily degraded samples.

DNA profiles based on lineage markers pose a challenging statistical problem as the markers are not statistically independent (as markers used in autosomal DNA profiles are). Thus, the joint probability distribution must be modelled instead of just the marginal distributions.

In this talk, I will discuss methods for calculating the evidential value of lineage DNA markers. This includes both a statistical model based on a finite mixture of generalised linear models (GLMs) and a simulation model. I will discuss computational aspects of both these models.

**Visual trumpery: How charts lie**

Speaker: Alberto Cairo

Affiliation: University of Miami

When: Wednesday, 21 March 2018, 6:30 pm to 7:30 pm

Where: 6.30pm, Large Chemistry Lecture Theatre, Ground Floor, Building 301, 23 Symonds Street, City Campus, Auckland Central.

In our final 2018 Ihaka lecture, Alberto Cairo (Knight Chair in Visual Journalism at the University of Miami) will deliver the following:

Visual trumpery: How charts lie -- and how they make us smarter

With facts and truth increasingly under assault, many interest groups have enlisted charts -- graphs, maps, diagrams, etc. -- to support all manner of spin. Because digital images are inherently shareable and can quickly amplify messages, sifting through the visual information and misinformation is an important skill for any citizen.

The use of graphs, charts, maps and infographics to explore data and communicate science to the public has become more and more popular. However, this rise in popularity has not been accompanied by an increasing awareness of the rules that should guide the design of these visualisations.

This talk teaches normal citizens principles to become a more critical and better informed readers of charts.

Lecture commences at 6.30pm, Large Chemistry Lecture Theatre, Ground Floor, Building 301, 23 Symonds Street, City Campus, Auckland Central.

Please join us for refreshments from 6pm in the foyer area outside the lecture theatre.

Biography

Alberto Cairo is the Knight Chair in Visual Journalism at the University of Miami. He's also the director of the visualisation programme at UM's Center for Computational Science. Cairo has been a director of infographics and multimedia at news publications in Spain (El Mundo, 2000-2005) and Brazil (Editora Globo, 2010-2012,) and a professor at the University of North Carolina-Chapel Hill. Besides teaching at UM, he works as a freelancer and consultant for companies such as Google and Microsoft. He's the author of the books The Functional Art: An Introduction to Information Graphics and Visualization (2012) and The Truthful Art: Data, Charts, and Maps for Communication (2016).

[ihaka Series Link: https://www.stat.auckland.ac.nz/ihaka-lectures

Map: https://goo.gl/maps/fNuHvmNWPru ]

https://www.stat.auckland.ac.nz/ihaka-lectures

**On the distribution of the ratio for the components of a bivariate normal random vector**

Speaker: Francois Perron

Affiliation: University of Montreal

When: Wednesday, 21 March 2018, 11:00 am to 12:00 pm

Where: 303-310

Let X be a bivariate normal random vector and R=X_1/X_2. We show that the distribution of R can be represented as a Poisson mixture of some new distributions extending the family of Student distributions. We give some of the properties related to this new family. We also show that the distribution of R can be approximated by a normal distribution. We give more precision on how good are the approximations.

**Making colour accessible**

Speaker: Paul Murrell

Affiliation: The University of Auckland

When: Wednesday, 14 March 2018, 6:30 pm to 7:30 pm

Where: 6.30pm, Large Chemistry Lecture Theatre(LgeChem/301-G050), Ground Floor, UoA Building 301 at 23 Symonds Street, City Campus, Auckland Central.

In the second of the 2018 Ihaka lecture series, Associate Professor Paul Murrell (The University of Auckland) will deliver the following lecture:

Making colour accessible

The 'BrailleR' package for R generates text descriptions of R plots.

When combined with screen reader software, this provides information for blind and visually-impaired R users about the contents of an R plot. A minor difficulty that arises in the generation of these text descriptions involves the information about colours within a plot. As far as R is concerned, colours are described as six-digit hexadecimal strings, e.g. "#123456", but that is not very helpful for a human audience. It would be more useful to report colour names like "red" or "blue".

This talk will make a mountain out of that molehill and embark on a daring Statistical Graphics journey featuring colour spaces, high-performance computing, Te Reo, and XKCD. The only disappointment will be the ending.

Lecture commences at 6.30pm, Large Chemistry Lecture Theatre, Ground Floor, Building 301, 23 Symonds Street, City Campus, Auckland Central.

Please join us for refreshments from 6pm in the foyer area outside the lecture theatre.

Biography

Paul Murrell is an Associate Professor in the Department of Statistics at The University of Auckland. He is a member of the core development team for R, with primary responsibility for the graphics system.