Search This Blog

Sunday, 24 May 2020


      They are lots of articles in the literature about using stochastic processes e,g.Markov Chains to compose music. I don't know whether the following suggestion is original.

                 A log-Gaussian Cox Process driven by an Ornstein-Uhlenbeck Process.

   This process was first proposed by Tom Leonard (Journal of the Royal Society, Series B, 1978) . It is a special case of the Doubly Stochastic Poisson Process described by my undergraduate mentor David Cox in the same journal in 1955 

          Suppose you wish  to compose a piece of music on the time interval (0,T) and assume that each note may assume one of M different characteristics, Then the times of occurrences of any particular characteristic in the tune may be represented by points in the interval (0,T), These could be specified by the composer  (see above diagram) . If repeated for each of the N characteristics, then the N sets of points (when superimposed with different labels on the same interval) defines the entire composition.

         For any particular characteristic, it would instead be possible to simulate the points from a random point process on the interval (0,T). If a different point process is used to generate the points for each characteristic, then the entire composition can be simulated.

         A log-Gaussian Cox Process can  be parameterised using a mean value function M(t) for t assuming values in the interval (0,T),  See, for example, the smoother curve in the above diagram.

         If the Cox Process is driven by an Ornstein-Uhlenbeck process. then a variance V and a correlation parameter R also need to be specified.

         It is left to the composer to come up with an imaginative choice of the continuous function M. He may then use a standard computer package to simulate the points of occurrence of that particular characteristic, for specified V and R (which could of course be fiddled with to improve the quality of the tune).

         If the composer can devise a different choice of continuous function M for each of the N characteristics, then his entire composition can be simulated from the N thus defined Cox Processes, keeping V and R fixed and specified across all simulations.

          This suggests to me to suggest a whole neball park, where the ingenuity of the composer is still an essential ingredient.


Friday, 1 May 2020


                                                               SAMPLE SPACE



Welcome to our first edition of Sample Space, a newsletter that aims to keep our community of past and present students and staff in touch with what’s happening in Statistical Science at UCL. I hope you find the contents interesting: we plan to do more of this kind of thing in the future, to keep you all updated with the latest news from the department. UCL Statistical Science is currently undergoing a period of significant expansion: this is part of a strategic investment in mathematics, statistics and operational research that will lead to the establishment of a UCL Institute for Mathematical and Statistical Sciences, or IMSS for short. We plan for the Statistical Science and Mathematics departments to be re-housed next to each other on a single site, in a purposedesigned facility that will put UCL on the map as one of the ‘go-to’ places for the mathematical sciences in London – and that will also provide our students with a much greater sense of community than is currently possible. Bringing this idea to fruition has already taken considerable effort, and will continue to do so in the coming months and years, although I strongly believe that the rewards will be well worth it. Apart from anything else, being bigger gives us additional resources to do things like producing Sample Space! The department has also recently established a new master’s programme in Data Science, which has proven very popular with students. A recent graduate, Mete Veyisoglu, has kindly taken the time to share his experiences of the programme in this issue. Further curriculum developments are being undertaken at the moment to ensure that we continue to equip our students with the tools to be statistically literate, perhaps a more desirable skill than ever in today's world. On the research side, the recent announcement of a large increase in UK government funding for the mathematical sciences is very welcome, and particularly timely in view of our IMSS expansion plans. Final preparations are underway for REF 2021, the latest iteration of the UK’s ‘Research Excellence Framework’. The department’s performance in this exercise will also contribute to the level of government funding we receive for the next few years. We have excellent staff doing exciting and incredibly diverse research, some of which is making a real impact outside academia: this issue highlights work being done by Serge Guillas and his team on understanding tsunami risk around the world. As always, there are external challenges: as I write, UK universities are grappling with the uncertainties posed by Brexit and, more urgently, by the worldwide Covid-19 outbreak. UCL Statistical Science is such a thoroughly international community that these issues will certainly affect us to some extent. I very much hope, however, that the effects will be minimal for all of us. Finally, I would like to extend my very sincere thanks to everyone who contributed to this first issue of Sample Space, and in particular to Samuel Livingstone for coordinating and editing it. If any readers have feedback, or potential contributions to future issues, or suggestions for material that they’d like to see, please contact him at I think he and all the contributors have done a fantastic job: I hope you do too. 

Wednesday, 29 April 2020



                                                                 Thomas Leonard 

                                                    Retired  Bayesian Statistician


                                                                A logistic  model


                                                               An exponential model

If a pandemic is well-controlled e.g. by safe spacing, then the total numbers of deaths, and the total numbers of cases, will hopefully increase in time according to a logistic curve, in which case the curve will eventually flatten out. However, if the pandemic is badly controlled, then the numbers of deaths, and the numbers of cases, can instead follow an exponential curve, in which case vast swathes of the population will perish.

          Despite the bad start in Britain (because of the herd mentality and parsimonious attitudes of our crass political advisors) there is some hope that the numbers of deaths in hospitals (excluding mental hospitals) will follow a logistic curve, and eventually flatten out. However, for the spiralling deaths in nursing homes, an exponential curve at the moment seems to be more appropriate. Moreover, extra, non-covid deaths in nursing homes are likely to be enormous. I am also very concerned about covid and extra non-covid deaths in our mental hospitals and prisons.

        If we start moving more elderly covid-patients from nursing homes into hospitals, then that could well prevent the curve for hospital patients from flattening out. If we don't then we will face mass disaster in our nursing homes, with many patients left abandoned and dying.

       Finally, the continuation of the lock-down, which seems absolutely necessary, is likely to lead to numerous extra deaths in our vulnerable and impoverished populations, for a whole variety of reasons,

       I find it hard to believe that less than 200000 extra UK residents will perish during the course of this pandemic (the rate is currently about 12000 a week), and it is possible that 200000 could die from the coronavirus alone (including at least 50000 in hospitals). While it is impossible, given the quality of the data, to make valid quantitative conclusions at this moment, the number 500000 does come fearfully into my mind.

      This could all lead to even worse civilian disaster scenarios e.g. in deprived, shopping, or downtown areas. If the people come onto the streets, then the reaction of the authorities is unpredictable. If there is a partial press blackout, then we might not know how many thousands have died,

      Today (30th April) our crass Prime Minister painted a totally more optimistic picture. I think that Bojo's trying, as always, to  brainwash his electorate. The U.K. is ranked worst per capita in the world.

Sunday, 26 April 2020

Jo Clifford, Writer, Performer, and Trans Rights Leader


I met Jo Clifford at the Candlelight vigil for trans people outside the Scottish Parliament during December 2019. I talked to her e.g. about the Gender Recognition Act, and she then gave an inspiring speech. She has since been pro-active in Brazil.

                                                                  SALTIRE SOCIETY

Jo Clifford was born in North Staffordshire in 1951 where she was raised as a boy.
This entailed an enforced separation from her mother at the age of 7 when she was sent to boarding school; the resulting trauma was intensified at the sudden death of her mother when she was 12.
She discovered her vocation for theatre when she played women’s roles in school plays. That was when it became clear to her she was not male. The terror, shame and confusion of this realisation in a completely ignorant, hostile, and prejudiced environment unfortunately  became  associated  with  the  theatre.  It  took  her twenty years to recover enough to find her voice as a theatre writer (with “Losing Venice” in 1985) and another twenty years after that to re-discover her vocation as an actress and performer (with “The Gospel According To Jesus Queen of Heaven” in 2009)

                                                                       PLAYWRIGHT'S STUDIO

Jo Clifford

Jo has written over 70 performed scripts which encompass every dramatic form, and her work has been performed all over the world.
                                                                SCOTTISH BOOK TRUST
Jo loves running writer’s workshops, and is hugely experienced at doing it. She has led writer’s workshops with the Traverse, the Festival Hub, Playwrights’ Workshop, in secondary schools; in Valencia, in Singapore, in Mumbai, and has designed and led Masters’ courses in Playwriting at Queen Margaret University. Besides playwriting, she can teach workshops that focus on radio writing, on gender, on bereavement. In fact, on anything you care to mention
                               TEATRO DO  MUNDO
Jo is a writer, performer, poet and teacher based in Edinburgh.
She is the author of about 80 plays, many of which have been translated into various languages and performed all over the world.
Her original plays include: Losing VeniceLucy’s PlayPlaying With FireInes de CastroLight In The VillageWar in America, The Tree Of Life, The Tree of Knowledge, God’s New FrockThe Gospel According to Jesus Queen of HeavenAn Apple a Day, Sex, Chips and the Holy Ghost and Every One.
Libretti include: Ines de Castro (music: James McMillan), Anna (music: Craig Armstrong), The Magic Flute (adapted from Mozart), Hansel and Gretel (adapted from Humperdinck).
She is an Associate Artist of Chris Goode and Company.
Her transition from John to Jo has enabled her to become an actor and performer. Performances include “God’s New Frock”, “Sex, Chips and the Holy Ghost”, “The Gospel According to Jesus Queen of Heaven”, “High Heels Aren’t Compulsory”.
Work in 2015 includes the opening of a new dramatisation of “Dr. Jekyll and Mr. Hyde” (Sell A Door theatre Company); revivals of “Great Expectations” (Studio Life, Tokyo, and Dundee Rep); “Anna Karenina” (Manchester Royal Exchange and West Yorkshire Playhouse), “Ines de Castro The Opera” (Scottish Opera), and “The Gospel According To Jesus, Queen Of Heaven” (Edinburgh festival fringe at Summerhall).
In 2016 Jo will be performing a new play she has co-written with Chris Goode for the National Theatre of Scotland. She will be perfuming her “Jesus Queen of Heaven” at Queer Contact in Manchester and Outburst Arts Festival in Belfast.
Chris Goode and Company are mounting a new production of "Every One" in March 2016 in Battersea Arts Centre.

                                         Nick Hern Books



Almost a decade after it was first performed Jo Clifford says her play The Gospel According to Jesus, Queen of Heaven is still provoking "extraordinary violence and hatred but at the same time very intense love".
The one-woman play which portrays a transgender Christ has most recently toured Brazil, where it has become the "most talked-about" show there sparking both strong protests and devotion.
Clifford says everyone involved in the Brazilian production has "really suffered".

                                              IN MEMORIUM SYVIA RIVERA



Monday, 13 April 2020

Capital. A Critique of Political Economy (Karl Marx)


Many of the recent cataclysmic events can be blamed on Capitalism. While we're looking for something different, it would be a good idea to consider Marx's Das Kapital again.

                                                  VOLUME 1: PDF


Das Kapital, (German: Capital) one of the major works of the 19th-century economist and philosopher Karl Marx (1818–83), in which he expounded his theory of the capitalist system, its dynamism, and its tendencies toward self-destruction. He described his purpose as to lay bare “the economic law of motion of modern society.” The first volume was published in Berlin in 1867; the second and third volumes, edited by his collaborator Friedrich Engels (1820–95), were published posthumously in 1885 and 1894, respectively.

                Karl Marx  (Stanford Encyclopedia of Philosophy)

Karl Marx (1818–1883) is best known not as a philosopher but as a revolutionary, whose works inspired the foundation of many communist regimes in the twentieth century. It is hard to think of many who have had as much influence in the creation of the modern world. Trained as a philosopher, Marx turned away from philosophy in his mid-twenties, towards economics and politics. However, in addition to his overtly philosophical early work, his later writings have many points of contact with contemporary philosophical debates, especially in the philosophy of history and the social sciences, and in moral and political philosophy. Historical materialism — Marx’s theory of history — is centered around the idea that forms of society rise and fall as they further and then impede the development of human productive power. Marx sees the historical process as proceeding through a necessary series of modes of production, characterized by class struggle, culminating in communism. Marx’s economic analysis of capitalism is based on his version of the labour theory of value, and includes the analysis of capitalist profit as the extraction of surplus value from the exploited proletariat. The analysis of history and economics come together in Marx’s prediction of the inevitable economic breakdown of capitalism, to be replaced by communism. However Marx refused to speculate in detail about the nature of communism, arguing that it would arise through historical processes, and was not the realisation of a pre-determined moral ideal.


                                                    KARL MARX : Wikipedia

                                                    DAS KAPITAL: Wikipedia

Das Kapital, also called Capital. A Critique of Political Economy (GermanDas Kapital. Kritik der politischen Ökonomiepronounced [das kapiˈtaːl kʁɪˈtiːk deːɐ poˈliːtɪʃən økonomˈiː]; 1867–1883), is a foundational theoretical text in materialist philosophyeconomics and politics by Karl Marx.[1][2][3] Marx aimed to reveal the economic patterns underpinning the capitalist mode of production in contrast to classical political economists such as Adam SmithJean-Baptiste SayDavid Ricardo and John Stuart Mill. While Marx did not live to publish the planned second and third parts, they were both completed from his notes and published after his death by his colleague Friedrich EngelsDas Kapital is the most cited book in the social sciences published before 1950.[4]

 In Das Kapital (1867), Marx proposes that the motivating force of capitalism is in the exploitation of labor, whose unpaid work is the ultimate source of surplus value. The owner of the means of production is able to claim the right to this surplus value because he or she is legally protected by the ruling regime through property rights and the legally established distribution of shares which are by law only to be distributed to company owners and their board members. The historical section shows how these rights were acquired in the first place chiefly through plunder and conquest and the activity of the merchant and "middle-man". In producing capital (produced goods), the workers continually reproduce the economic conditions by which they labour. Das Kapital proposes an explanation of the "laws of motion" of the capitalist economic system from its origins to its future by describing the dynamics of the accumulation of capital, the growth of wage labour, the transformation of the workplace, the concentration of capital, commercial competition, the banking system, the decline of the profit rate, land-rents, et cetera. The critique of the political economy of capitalism proposes:
  • Wage-labour is the basic "cell-form" (trade unit) of a capitalist society. Moreover, because commerce as a human activity implied no morality beyond that required to buy and sell goods and services, the growth of the market system made discrete entities of the economic, the moral and the legal spheres of human activity in society; hence, subjective moral value is separate from objective economic value. Subsequently, political economy—the just distribution of wealth and "political arithmetick" about taxes—became three discrete fields of human activity, namely economicslaw and ethics, politics and economics divorced.[citation needed]
  • "The economic formation of society [is] a process of natural history". Thus, it is possible for a political economist to objectively study the scientific laws of capitalism, given that its expansion of the market system of commerce had objectified human economic relations. The use of money (cash nexus) voided religious and political illusions about its economic value and replaced them with commodity fetishism, the belief that an object (commodity) has inherent economic value. Because societal economic formation is a historical process, no one person could control or direct it, thereby creating a global complex of social connections among capitalists.[citation needed] The economic formation (individual commerce) of a society thus precedes the human administration of an economy (organised commerce).
  • The structural contradictions of a capitalist economy (German: gegensätzliche Bewegung) describe the contradictory movement originating from the two-fold character of labour and so the class struggle between labour and capital, the wage labourer and the owner of the means of production. These capitalist economic contradictions operate "behind the backs" of the capitalists and the workers as a result of their activities and yet remain beyond their immediate perceptions as men and women and as social classes.[5]
  • The economic crises (recessiondepressionet cetera) that are rooted in the contradictory character of the economic value of the commodity (cell-unit) of a capitalist society are the conditions that propitiate proletarian revolution—which The Communist Manifesto (1848) collectively identified as a weapon forged by the capitalists which the working class "turned against the bourgeoisie itself".
  • In a capitalist economy, technological improvement and its consequent increased production augment the amount of material wealth (use value) in society while simultaneously diminishing the economic value of the same wealth, thereby diminishing the rate of profit—a paradox characteristic of economic crisis in a capitalist economy. "Poverty in the midst of plenty" consequent to over-production and under-consumption

Monday, 6 April 2020



         The seven Prime Ministers who died in office
NameYearCountryTitleCause of death
Spencer Compton, Earl of Wilmington1743 Great BritainPrime Minister
Henry Pelham1754 Great BritainPrime Minister
Charles Watson-Wentworth, Marquess of Rockingham1782 Great BritainPrime MinisterIllness – influenza
William Pitt the Younger1806 United KingdomPrime MinisterIllness
Spencer Perceval1812 United KingdomPrime MinisterAssassination – shooting
George Canning1827 United KingdomPrime MinisterIllness

                                                          SPENCER PERCEVAL  Wiki



At 5:15 pm, on the evening of 11 May 1812, Perceval was on his way to attend the inquiry into the Orders in Council. As he entered the lobby of the House of Commons, a man stepped forward, drew a pistol and shot him in the chest. Perceval fell to the floor, after uttering something that was variously heard as "murder" and "oh my God".[14] They were his last words. By the time he had been carried into an adjoining room and propped up on a table with his feet on two chairs, he was senseless, although there was still a faint pulse. When a surgeon arrived a few minutes later, the pulse had stopped, and Perceval was declared dead.[7]
At first it was feared that the shot might signal the start of an uprising, but it soon became apparent that the assassin – who had made no attempt to escape – was a man with an obsessive grievance against the Government and had acted alone. The assassin, John Bellingham, was a merchant who believed he had been unjustly imprisoned in Russia and was entitled to compensation from the government, but all his petitions had been rejected.[14] Perceval's body was laid on a sofa in the speaker's drawing room and removed to Number 10 in the early hours of 12 May. That same morning an inquest was held at the Cat and Bagpipes public house on the corner of Downing Street and a verdict of wilful murder was returned.[7]

One of Perceval's most noted critics, especially on the question of Catholic emancipation, was the cleric Sydney Smith. In Peter Plymley's Letters Smith writes:
If I lived at Hampstead upon stewed meats and claret; if I walked to church every Sunday before eleven young gentlemen of my own begetting, with their faces washed, and their hair pleasingly combed; if the Almighty had blessed me with every earthly comfort–how awfully would I pause before I sent forth the flame and the sword over the cabins of the poor, brave, generous, open-hearted peasants of Ireland

John Bellingham was tried on Friday 15 May 1812 at the Old Bailey, where he argued that he would have preferred to shoot the British Ambassador to Russia, but insisted as a wronged man he was justified in killing the representative of his oppressors.                           


He made a formal statement to the court, saying:[3]
Recollect, Gentlemen, what was my situation. Recollect that my family was ruined and myself destroyed, merely because it was Mr Perceval's pleasure that justice should not be granted; sheltering himself behind the imagined security of his station, and trampling upon law and right in the belief that no retribution could reach him. I demand only my right, and not a favour; I demand what is the birthright and privilege of every Englishman.
Gentlemen, when a minister sets himself above the laws, as Mr Perceval did, he does it as his own personal risk. If this were not so, the mere will of the minister would become the law, and what would then become of your liberties?
I trust that this serious lesson will operate as a warning to all future ministers, and that they will henceforth do the thing that is right, for if the upper ranks of society are permitted to act wrong with impunity, the inferior ramifications will soon become wholly corrupted.
Gentlemen, my life is in your hands, I rely confidently in your justice.
Evidence was presented that Bellingham was insane, but it was discounted by the trial judge, Sir James Mansfield. Bellingham was found guilty, and was sentenced to death.[3]
Bellingham was hanged in public three days later. René Martin Pillet, a Frenchman who wrote an account of his ten years in England, described the sentiment of the crowd at the execution:[4]
Farewell poor man, you owe satisfaction to the offended laws of your country, but God bless you! you have rendered an important service to your country, you have taught ministers that they should do justice, and grant audience when it is asked of them.
A subscription was raised for the widow and children of Bellingham, and "their fortune was ten times greater than they could ever have expected in any other circumstances".[4] His widow remarried the following year.
Bellingham's skull was preserved at Barts Pathology Museum.[5]
In September 2009 the St Neots Local History Society erected a plaque on Bellingham House in St Neots. The house, on the corner of Huntingdon Street and Cambridge Street, is said to be the birthplace of Bellingham.[6]