# The LiU Seminar Series in Statistics and Mathematical Statistics

Fall 2012

### Tuesday, September 11, 3.15 pm, 2012. Seminar in Statistics

**A study of multilevel models with block circular symmetric covariance structures**

Yuli Liang, Statistics, Stockholm University.

Yuli Liang

*Abstract*: Our work concerns the study of multilevel models with specific patterned covariance structures and addresses the issues of maximum likelihood estimation. In particular, circular symmetric hierarchical data structures are considered. Models which covariance structures reflect both circularity and exchangeability present in the data can be widely used in different applications, with early examples from psychometric and medical research. Two derived patterns of the covariance matrices which characterizes models under consideration. The relationship between these two patterned covariance ma- trices was investigated and it has been verified they are similar matrices. New expressions for the eigenvalues of block circular symmetric matrices are obtained which take into account the block structure. Maximum likelihood estimation of balanced multilevel models with block circular symmetric covariance matrices is discussed. We show that explicit maximum likelihood estimators of variance com- ponents exist under certain restrictions on the parameter space.

Location: Alan Turing

### Tuesday, September 18, 3.15 pm, 2012. Seminar in Mathematical Statistics

**Efficient calculation of financial Greeks**

Patrik Andersson, Mathematical Statistics, Stockholm University

Patrik Andersson

*Abstract*: In finance a Greek is the sensitivity of the price of a derivative, e.g. a European call option, with respect to some parameter in the model, e.g. the current price of the underlying asset. The Greeks are important both for hedging purposes and from a risk-management perspective. In realistic models of asset prices, e.g. with stochastic volatility, there are no known formulas for these and one solution is to resort to simulation; however, calculating a Greek involves differentiating an expectation and this can be computationally difficult. A number of methods have been proposed, one of which is the so-called Malliavin calculus integration by parts. This method allows one to write the expectation of a differentiated function as the expectation of the function itself times a stochastic weight. These stochastic weights are however not unique and so there is a freedom to choose them in an efficient way, i.e. in a way that gives a low variance.

Location: Kompakta rummet, MAI.

### Tuesday, September 25, 3.15 pm, 2012. Seminar in Mathematical Statistics

**Long-range percolation on the hierarchical lattice**

Pieter Trapman, Mathematical Statistics, Stockholm University

Pieter Trapman

*Abstract*: The hierarchical lattice of order N, may be seen as the leaves of an infinite regular N-tree, in which the distance between two vertices is the distance to their most recent common ancestor in the tree. We create a random graph by independent long-range percolation on the hierarchical lattice of order N: The probability that a pair of vertices/nodes at (hierarchical) distance R share an edge/bond depends only on R and is exponentially decaying in R, furthermore the presence or absence of different edges are independent. We give criteria for percolation (the presence of an infinite cluster) and we show that in the supercritical parameter domain, the infinite component is unique. Furthermore, we show that the percolation probability (the density of the infinite cluster) is continuous in the model parameters. In particular, there is no percolation at criticality.

Location: Kompakta rummet, MAI.

### Tuesday, October 16, 3.15 pm, 2012. Seminar in Statistics

**Minimax Optimal Designs of Contingent Valuation Experiments: Willingness to Pay for Environmentally Friendly Clothes**

Linda Wänström, Statistics, Linköping University

Linda Wänström

*Abstract*: Contingent valuation experiments (CVEs) are commonly used to estimate the value of non-market goods or services. Design of the experiments involves choosing the design points and the proportion of respondents to assign to each point. For example, the question "Would you be willing to pay A SEK extra for an environmentally friendly produced top?" can be used when the interest is in assessing the willingness to pay (WTP) for environmentally friendly produced clothes. Here, there is a need to specify the values of A and the proportion of respondents who will be asked about these specific values. If, in addition, ALL respondents are asked if they are willing to pay ANYTHING extra at all, the trinomial spike model can be used to model the responses. This model is basically a truncated version of the logistic model with support only for positive values, and with a spike at zero that models the probability that an individual has zero WTP. Optimal design for this model depends on values of unknown parameters. In practice we therefore need information about the parameters in order to design the experiment. The purpose of this paper is to demonstrate how to use pilot data to optimally design a CVE about the value of environmentally friendly produced clothes. In particular, a method of how to find minimax designs, using a relationship between optimum in the average designs and minimax designs, is demonstrated.

Location: Alan Turing

### Tuesday, October 23, 3.15 pm, 2012. Seminar in Statistics

**Applying the wavelet method to deal with irregular data in statistical analysis**

Yushu Li, Economics, Lund University

Yushu Li

*Abstract*: The seminar will present how wavelet method can be combined with statistical analysis to deal with irregular data with unit root, different cyclical combination, structure breaks, outliers, long memory or measurement error. The analysis can be carried out in different areas such as Panel model, Causality model, Hidden Markov model, Statistical surveillance and Support Vector machines. Traditional methodology in pure time or frequency domain could not fully recover the underlying non-stationarity of the irregular data. Wavelet method, which can give out resolutions in both time and frequency domain, can be a powerful tool to deal with irregularity. This method has a sophisticated developed mathematical background as well as widely application in signal and image processing. The application in economics and finances is not fully explored but has great potential for further investigation.

Location: Alan Turing

### Tuesday, November 6, 3.15 pm, 2012. Seminar in Statistics

**Efficient Estimation of Covariance Matrices using Posterior Mode Multiple Shrinkage**

Paolo Giordani, Research Division, Sveriges Riksbank

Paolo Giordani

*Abstract*: We propose an approach to the regularization of covariance matrices that can be applied to any model for which the likelihood is available in closed form. The approach is based on using mixtures of double exponential or normal distributions as priors for correlation parameters, and on maximizing the resulting log-posterior (or penalized likelihood) using a stochastic optimization algorithm. The mixture priors are capable of clustering the correlations in several groups, each with separate mean and variance, and can therefore capture a large variety of structures besides sparsity. We apply this approach to the normal linear multivariate regression model as well as several other models that are popular in the literature but have not been previously studied for the purpose of regularization, including multivariate t, normal and t copulas, and mixture of normal distributions. Simulation experiments show the potential for large efficiency gains in estimating the density of the observations in all these models. Sizable gains are also obtained in four real applications.

Location: Alan Turing

### Tuesday, November 20, 3.15 pm, 2012. Seminar in Mathematical Statistics

**On the BK inequality**

Johan Jonasson, Mathematical Sciences, Chalmers

Johan Jonasson

*Abstract*: A family of binary random variables is said to have the BK property if, loosely speaking, for any two events that are increasing in the random variables, the probability that they occur disjointly is at most the product of the probabilities of the two events. The classical BK inequality states that this holds if the random variables are independent. Since the BK property is stronger than negative association, it is a form of negative dependence property and one would expect other negatively dependent families to have the BK property. This has turned out to be quite a challenge and until very recently, no substantial example beside the independent case were known. In this talk I will give two of these examples, the k-out-of-n measure and pivotal sampling, and sketch how to prove the BK inequality for these. I will also mention a few seemingly "simple questions" and how solutions to these would be profoundly important.

Location: Kompakta rummet, MAI.

### Tuesday, December 4, 3.15 pm, 2012. Seminar in Mathematical Statistics

**Conditioned branching processes and the evolution of species**

Krzysztof Bartoszek, Mathematical Sciences, Chalmers

Krzysztof Bartoszek

*Abstract*: Conditioned branching processes have recently received a lot of attention in the biomathematical literature. They are useful for modelling and developing software in the field of phylogenetic tree inference. However on top of this they can also be combined with continuous stochastic processes to describe the evolution of character traits without the need to use a fixed phylogeny. This makes them an appealing tool for the field of phylogenetic comparative methods where often there can be great uncertainty attached to the underlying evolutionary relationships. By using them we can predict how much we expect species to diverge (in the trait of interest) and include uncertainty due to phylogeny in our conclusions. Morphological characteristics are an important factor in the field of systematics, for example for the delimitation of species, and therefore the framework of phylogenetic comparative models on top of branching processes offers an attractive application of stochastics in biology.

Location: Kompakta rummet, MAI.

Page responsible: Mattias Villani

Last updated: 2012-11-29