Comments on: Recent advances in directional statistics
Kanti V. Mardia · Test · 2021
I should first like to congratulate the authors on giving a very comprehensive review of what has happened since (Mardia and Jupp 1999) (we are grateful for making our book as its base) in directional statistics (DS); the task is not an easy one as the field has grown dramatically since then.In my discussion I will take a complimentary approach-a broad historical perspective starting from the beginning of the field.More so, 2020 was the Florence Nightingale's Bicentenary Year as she was born on 12 May 1820, and indeed, on the 1 December 2020 there was the "Florence Nightingale Bicentenary Celebration" in Oxford with an Exhibition.As expected, Florence Nightingale's rose diagrams to visualize data on a torus (trivariate) were highlighted in the talks and in the exhibition.In fact, about 160 years ago (1858) she gave us these visualizations to make the subject accessible to policy makers namely, Crimean War deaths through Rose Diagrams and others (see also Hedley 2020).Visualization of data on a torus (bivariate) has also appeared in Biochemistry-the celebrated Ramachandran plots which appeared in 1963; see, for example, Mardia (2013).I have extended its visualization (Mardia 2012) by opening the torus on a repeated 3 × 3 grid so that modes and antimodes can easily be seen.