Session will be 11:00 am to 12:30 pm.    More Information to follow soon.

Flexible multivariate statistical dependence models are needed for many 
data structures. While the popular multivariate normal distribution is 
very restrictive and cannot account for features like asymmetry and 
heavy tails, copulas can be used to build more flexible models. 
Exploiting the famous theorem by Sklar which allows to separate the 
dependence structure from the marginal distributions many successful 
models have been developed in recent years. Much of this research 
however is limited to the bivariate case, where numerous copulas are 
available. This is unlike the multivariate case, where standard 
multivariate copulas are rather restrictive in their structure. Vine 
copulas do not suffer from such shortcomings and can be conveniently 
constructed using only bivariate copulas as building blocks. In this 
talk I introduce the concept of vine copulas and discuss appropriate 
statistical inference techniques. This in particular includes issues of 
model selection, which may be challenging in higher dimensions. As an 
application I consider weather measurements of different variables like 
temperature, humidity and pressure observed at Hohenpeissenberg, the 
oldest mountain weather station in the world. Finally, I give an outlook 
how such models may be extended to data from multiple stations using a 
hierarchical copula construction.

Joint work with Michael Pachali, Claudia Czado, and Christian Zang.

From the extant statistical data, this paper reconstructs several episodes in the history of the Royal Mint during Isaac Newton’s tenure. We discuss four types of uncertainty embedded in the production of coins, extending S. Stigler’s work (1977) back in time. The thirteen Jury Verdicts in Trials of the Pyx for 1696-1727 allow judgment on the impartiality of the Jury at the trials. The Verdicts, together with several remarks by Newton in his correspondence with the Treasury, allow us to estimate the standard deviation σ in weights of individual guineas coined before and during Newton’s Mastership. This parameter, in turn, permits us to estimate the amount of money Newton saved Britain after he put a stop to the illegal practice by goldsmiths and bankers of culling heavy guineas and recoining them to their advantage; a conservative estimate for savings to the Crown is £41,510, and possibly three times as much. The procedure with which he likely improved coinage gives historical insight on how important statistical notions – standard deviation and sampling -- came to the forefront in practical matters: the former as a measure of variation of weights of coins, and the latter as a test of several coins to evaluate the quality of the entire population. Newton can be credited with the formal introduction of testing a small sample of coins, a pound in weight, in the trials of the Pyx from 1707 onwards, effectively reducing the size of admissible error. Even Newton’s “Cooling Law” could have been contrived for the purpose of reducing variation in the weight of coins during initial stages of the minting process.  Three open questions are posed in the Summary.
 
Key words: Isaac Newton, Royal Mint, Trial of the Pyx, Jury Verdicts, guinea, remedy, margin in weight, Gaussian distribution, mean and standard deviation, small samples
 

If the last century in Science belongs to Physical Sciences then this century must belong to Life Sciences with many breakthroughs arising from DNA and proteins! The proteins are biological macromolecules that are of primary importance to all living organisms and there are various open problems including the Nobel-Prize-type problem related to protein folding. All these questions mainly depend on shape of the protein in 3-D which can be summarized in terms of either the configuration of points (landmarks) or more compactly by conformational angles. Thus it has led to new non- Euclidean statistical methods in shape analysis and directional data analysis. We will discuss the following topics with appropriate motivation:- 

 

- Protein alignment and Bayesian methods (Green and Mardia,2006; Green, Mardia Vysaul and Ruffieux 2010, Mardia et al, 2011) 

 

- Statistical distribution of conformational angles and Ramachandran plots (Mardia, Taylor and Subramaniam, 2007) 

 

- Prediction and simulation of protein structure (Boomsma, W., Mardia, K.V., Taylor, C.C., Ferkinghoff-Borg, J., Krogh A. and Hamelryck, T. ,2008 .).