Yes , says this blog : Sour Grapes: Seven Reasons Why “That” Twitter Prediction Model is Cooked
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Yes , says this blog : Sour Grapes: Seven Reasons Why “That” Twitter Prediction Model is Cooked
Posted at 09:54 PM in Statistics | Permalink | Comments (0) | TrackBack (0)
This book is an awesome resource for understanding finite Markov chains. The book is written in Pre-Latex era and hence one has to struggle to follow the notation. Is the Struggle worth it? IT IS, if you are looking at developing a Matrix perspective towards “Discrete Stochastic Process”. IT IS NOT, if you are looking at quick and dirty formulae. The first version of the book appeared in 1960 and second version in 1976. I wasn’t even born when these books came out –:) . However like many things in life, things that age have their own charm. The book serves as a precursor to understanding Markov chain Monte Carlo method which is an essential tool for any quant.
Chapter 1: Pre-requisites:
Most of the stuff can be quick read in this chapter. What I found interesting was the mention of set theory concepts such as equivalence relation, weak ordering relation, minimal elements etc. One must patiently go over these stuff as they find immense application in classifying Markov chains. An attempt is made to describe a simple stochastic process and readers might find this example appealing before venturing in to complicated stochastic processes. I understood Cesaro-Summability and Euler Summability clearly in this context , even though I had quick read them in “Understanding Analysis”- Abbott.
Chapter 2: Basic Concepts of Markov Chains
The chapter starts off by defining a Markov process which essentially is a process where essentially previous outcome is all that is needed to predict the probability of future outcome. Markov chain is a finite Markov process where the transition probability from step i to step j does not depend on the trail number. One of the equivalent ways to state a Markov chain is that , given the present, the past and future are completely independent of each other. To deviate in to philosophy here a bit, I think we should lead our lives also like a Markov process. Whatever be the past, given the present, we must work in the present, be in the NOW so that future becomes independent of the past. Ok, enough of this philosophy crap J , Let me get back to the contents of the chapter.
What’s the difference between Markov Process and Markov Chain ?
Well, Markov chain is a type of Markov process. Apart from that, one of the biggest differences arises from the fact that a Reverse Markov process is also Markov process but a reverse Markov chain need not be a Markov chain. The transition probability matrix of a reversed Markov chain may well depend on the trail number and hence does not qualify to be a Markov chain. This nifty difference is sometimes not highlighted clearly most of the times in other books.
The author gives a set of examples representing Markov chains to get an idea of various finite Markov chains one can come across. One of the reasons I got interested in Markov chains is that they are an excellent computational tool for classic probability problems. At the same time, they serve as an ideal platform to understand stochastic processes. I used to struggle to work with problems involving absorbing barriers, reflecting barriers in a simple random walk. Setting up a recurrence relation and solving using PDE approach or some tricky method never gave me a tool to understand the stuff. Markov chains on the other hand actually give a fantastic way to compute these using matrices. I love when any problem is formulated using matrices. It makes everything so pleasant for a problem solver.
Classification of states in a Markov Chain:
The author uses set theory concepts such as partial ordering, equivalence classes induced by partial ordering, minimal elements of the partial ordering of equivalence classes etc to classify the states of a Markov Chain. Well, I was aware that “Relation” can be used to define equivalence classes that partition a set. But beyond that, my understanding of “Partial Ordering”, “Minimal Elements” etc was shallow. Hence I took a detour for a few hours and went through “Naive Set Theory” – Paul Halmos. I managed just enough to understand stuff about Markov Chain.
You start off with a relation – iRj, you can reach state i from state j, meaning it is a type of relation and you can then extend this to another relation ( iRj and jRi ) meaning you can reach i from j and j from i . So, you start with a weak ordering relation, and extend it form equivalence classes. When I first came across these concepts, I found some resistance in understanding these ideas. Why should I care if you start with a weak relation and you can extend that weak relation so that you can form equivalence classes?
Well, all these concepts make tremendous sense when you look at a Markov Chain. Firstly,the weak ordering relation can be extended to”communication” relation to first classify the states in to equivalence classes. Subsequently, you can order these states and the minimal elements of these ordered states form ergodic states. Cutting the fancy stuff around the word ,”minimal”, all it means is that if you take any element x of a set U, if iRx holds then xRi holds too. All those elements i form an ergodic set. One must understand the reason for this ordering and the rationale behind ordering. Once you order stuff , you have the transition matrix as follows
This pattern emerges once you order the states accordingly. The first thing that strikes you about the above matrix is that you can higher powers of this matrix retains the individual transition matrices on the diagonal and thus one can individually analyze these matrices without worrying about the entire chain.
The chapter then goes in to giving labels to various kinds of Finite Markov Chains. There are two broad categories of Markov Chain. Firstly the chains which do not have transition states. Secondly, the states have transition states.
Chains without Transition States are also called chains with single ergodic set (ergodic chain). They can be further divided in to:
Chains with transition states can be further divided in to
As can be seen from the above illustration, almost all the categories can be expressed using simple random walk. Given various states, what are the kinds of questions that one would be interested in?
Regular Markov Chain Questions
Transient States Questions
The book is sequenced in a way that the above questions are answered systematically. Absorbing Chains, Regular Markov Chains and Ergodic Chains are covered as specific chapters.
Chapter 3: Absorbing Markov Chains
The book looks at Absorbing Markov chain by segregating transient states from Persistent states. It then analyzes Transient State matrix and derives basic formulae in terms of matrix operations. The highlight of this book is “Fundamental Matrix Approach”. For any Markov chain, the book tries to zero on to a specific matrix which is fundamental to all the calculations relating to the Markov chain
Fundamental Matrix for Absorbing Markov Chains is derived: . The reason it is called Fundamental is because it is used in formulating solutions for most of the interesting questions about Absorbing Markov Chains
Solutions in Matrix form are furnished for the following:
From the examples give, all of them have high variance for the mean estimates. Is this a general case ? I mean are all the estimates of Markov chain characterized by high variance? I don’t know. Will find out someday.
Chapter 4: Regular Markov Chains
Regular Markov Chains are explored in this chapter using Matrices. The limiting properties of Regular Markov chain are explored where the chain settles down in to a constant row matrix after n iterations. This limiting markov chain is then used to state “Law of Large Numbers” . Most of us would have heard of “Law of Large Numbers” for independent trials where the statements become weak law or strong law based on whether the convergence is almost sure or convergence is in probability. This law from a Markov chain is radically different as it removes , “iid” clause from the law of large numbers and thus massively expanding its scope. This form of law was worked out by A.A.Markov in 1907. In the 100 odd years that have passed since then, Markov chains are now practically used in tons of applications.
The chapter then talks about Central Limit theorems for Markov chains. It merely states the theorem and defers proving the same. CLT for Markov chains connects the (average number of visits to a particular state, its limiting value) WITH Standard Normal Distribution.
The preface in the book mentions one of the reasons for the second edition. In the above formulae, Fixed weight vector was used to obtain the Fundamental Matrix. However there is an alternative method where any constant row vector can be used to obtain Z. The appendix of the book mentions the paper where pseudo-inverses are used.
Chapter 5: Ergodic Markov Chains
What if there is cyclicality in chains with transient states ? This chapter delves in to the math behind such chains. Condition for a markov chain to be considered as reversible is also mentioned. A Markov chain being reversible or not, has a great impact from a simulation perspective.The book then talks about further extensions to the above mentioned chains. Basically it involves stuff where a transient chain is made in to an persistent chain forcefully to compute some interesting stuff and vice versa.
In the concluding chapter, the book shows various application of Markov chains like
By no means these examples should make you think that Markov chain is used as Toy examples. The research and amount of stuff that has been done on Markov chains for the last 100 years is so massive that it has found applications in a wide variety of fields from sports betting to
Persi Diaconis (the iconoclastic Stanford Professor) remarks “To someone working in my part of the world, asking about applications of Markov chain Monte Carlo (MCMC) is a little like asking about applications of the quadratic formula. The results are really used in every aspect of scientific inquiry.”
Indeed, Markov Chain Monte Carlo methods have revolutionized the field of statistics. My takeaway from the book is not so much so about simulation as it is about understanding Martingale Objects. While formulating a Martingale, If you are able to visualize vaguely the discreet Markov Chain in the background, I bet your understanding will be much better.
Posted at 04:40 PM in Books, Math, Statistics | Permalink | Comments (0) | TrackBack (0)
For some unknown reason we got in to a wrangle about – of all things! – best sellers. All aspiring writers say these things : “ I will not compromise and write a best seller! “ – as if they could!. There may be a few totally faked-up books that sell, but on the whole I believe every writer writes as well as he can. It takes a good story teller to write a best seller, and a good craftsman. The professional will never brush the best seller aside as something he could do if he were willing to compromise. No, it is all a matter of kinds of perception, and of kinds of writing. Very great writers – Dickens, Joyce, Trollope, Hemingway – have been best sellers. And very great writers – Virginia Woolf, for example have not, or only by chance.
We do the best we can and hope for the best knowing that “the best” so far as selling goes, is a matter of chance. The only thing that is not chance is what one asks of oneself and how well or how hardly one meets one’s own standards.
- May Sarton
Posted at 12:26 PM in Reflections | Permalink | Comments (0) | TrackBack (0)
It seems that two qualities are necessary if a great artist is to remain creative to the end of a long life; he must on the one hand retain an abnormally keen awareness of life, he must never grow complacent, never be content with life, must always demand the impossible, and when he cannot have it, must despair. The burden of the mystery must be with him day and night. He must be shaken by the naked truths that will not be comforted. This divine discontent, this disequilibrium, this state of inner tension is the source of creative energy. Many lesser poets have it only in their youth; some even of the greatest lose it in middle life. Wordsworth lost his courage to despair and with it his poetic power. But more often, the dynamic tensions are so powerful that they destroy the man before he reaches maturity.
- Humphrey Trevelyan
Posted at 12:09 AM in Reflections | Permalink | Comments (0) | TrackBack (0)
1. THOU SHALT NOT DRINK, SMOKE OR TAKE DRUGS
To be a writer you need all the brains you've got.
2. THOU SHALT NOT HAVE EXPENSIVE HABITS
A writer is born from talent and time – time to observe, to study, to think. So you can't afford to waste a single hour earning money for non-essentials. Unless you were lucky enough to he born rich, you had better be prepared to live without too many worldly goods. True, Balzac got special inspiration from running up huge debts and buying things, but most people who have expensive habits tend to fail as writers.
At the age of 24 after the defeat of the Hungarian Revolution I found myself in Canada with about fifty words of English. When it got through to me that I was now a writer without a language, I took an elevator to the top of a high building on Dorchester Street in Montreal, intending to jump. Looking down from the roof, terrified of dying but even more afraid of breaking my spine and spending the rest of my life in a wheelchair, I decided to try to become an English writer instead. In the end, learning to write in another language was less difficult than writing something good, and I lived on the edge of destitution for six years before I was ready to write In Praise of Older Women.
I couldn't have done it if I had cared about clothes or cars – indeed, if the only alternative I saw had not been the top of that skyscraper. Some immigrant writers I knew took jobs as waiters or salesmen to save money and create a 'financial base' for themselves before trying to make a living by writing; one of them now owns a whole chain of restaurants and is richer than I could ever be, but neither he nor the others returned to writing. You've got to decide what is more important to you: to live well or to write well. Don't torment yourself with contrary ambitions.
3. THOU SHALT DREAM AND WRITE AND DREAM AND REWRITE
Don't let anybody tell you you're wasting your time when you're gazing into space. There is no other way to conceive an imaginary world.
I never sit down in front of a bare page to invent something. I daydream about my characters, their lives and their struggles, and when a scene has been played out in my imagination and I think l know what my characters felt, said and did, I take pen and paper and try to report what I've witnessed.
When I've written and typed my report I read it over and find that most of what I've written is (a) unclear or (b) inexact or (c) ponderous or (d) simply could not be true. Thus the typed draft serves as a kind of critical report on what I imagined, and I go back to dream the whole thing better.
It was this way of working that made me realize, when I was learning English, that my chief problem wasn't the language but, as always, getting things right in my head.
4. THOU SHALT NOT BE VAIN
Most bad books get that way because their authors are engaged in trying to justify themselves. If a vain author is an alcoholic, then the most sympathetically portrayed character in his book will be an alcoholic. This sort of thing. is very boring for outsiders. If you think you're wise, rational, good, a boon to the opposite sex, a victim of circumstances, then you don't know yourself well enough to write.
I stopped taking myself seriously at the age of 27 and since then I've regarded myself simply as raw material. I use myself the same way as an actor uses himself: all my characters – men and women, good and bad – are made up from myself plus observation.
5. THOU SHALT NOT BE MODEST
Modesty is an excuse for sloppiness, laziness, self-indulgence; small ambitions evoke small efforts. I never knew a good writer who wasn't trying to be a great one.
6. THOU SHALT THINK CONTINUALLY OF THOSE WHO ARE TRULY GREAT
‘The works of genius are watered with its tears,' wrote Balzac in Lost Illusions. Rejection, derision, poverty, failure, the constant struggle against one's own limitations – these are the chief events in the lives of most great artists, and if you aspire to share their fate you should fortify yourself by learning about them.
I've often taken heart from re-reading the first volume of Graham Greene's autobiography, A Sort of Life, which is about his early struggles. I've also had the chance to visit him in Antibes, where he lives in a small two-room flat (a tiny place for such a tall man) with the luxuries of benign air and a view of the sea but few possessions apart from books. He seems to have few material needs, and I'm sure this has something to do with the inner freedom which radiates from his works. Though he claims to have written his 'entertainments' for money, he is a writer who is directed by his obsessions without regard to changing fashions and popular ideologies, and this freedom is communicated to his readers. He liberates you from the weight of your own compromises, at least while you read him. This kind of achievement is possible only for a writer of Spartan habits.
None of us has a chance to meet many great men in person, but we can be in their company if we read their memoirs, journals and letters. Avoid biographies, though – especially dramatized biographies in the form of films or television series. Almost everything that comes to you about artists through the media is sheer bunk, written by lazy hacks who don't have the faintest notion of either art or hard work. The most recent example is Amadeus, which tries to convince you that it is easy to be a genius like Mozart and very hard to be a mediocrity like Salicri.
Read Mozart's letters instead. As for specific literature on the writing life I'd recommend Virginia Woolf's A Room of My Own, Shaw's preface to The Dark Lady of the Sonnets, Jack London's Martin Eden and, above all, Balzac's Lost Illusions.
7. THOU SHALT NOT LET A DAY PASS WITHOUT RE-READING SOMETHING GREAT
In my teens I studied to be a conductor, and from my musical training I picked up a habit which I think is essential also for writers: the constant, daily study of masterworks. Most professional musicians of any standing know hundreds of scores by heart; most writers, on the other hand, have only the vaguest recollections of the classics – which is one reason why there are more skilled musicians than skilled writers. A violinist who had the technical proficiency of most published novelists would never find an orchestra to play in. The truth is that only by absorbing perfect works, the specific ways great masters have invented to develop a theme, to construct a sentence, a paragraph, a chapter, can you possibly learn all there is to be learned about technique.
Nothing that has already been done can tell you how to do something new, but if you understand the masters' techniques, you have a better chance to develop your own. To put it in terms of chess: there hasn't yet been a grandmaster who didn't know his predecessors' championship games by heart.
Don't commit the common mistake of trying to read everything in order to be well-informed. Being well-informed will allow you to shine at parties but is absolutely no use to you as a writer. Reading a book so you can chat about it is not the same thing as understanding it. It is far more useful to read a few great novels over and over again until you see what makes them work and how the writers constructed them. You have to read a novel about five times before you can perceive its structure, what makes it dramatic, what gives it pace and momentum. Its variations in tempo and time-scale, for instance: the author describes a minute in two pages then covers two years in one sentence – why? When you've figured this out you really know something.
Every writer will pick his own favorites from whom he thinks he can learn the most, but I strongly advise against reading Victorian novels, which are riddled with hypocrisy and bloated with redundant words. Even George Eliot wrote too much about too little.
When you are tempted to overwrite, read the short stories of Heinrich von Kleist, who said more with fewer words than any other writer in the history of Western literature. I read him constantly, along with Swift and Sterne, Shakespeare and Mark Twain. At least once a year I reread some of the works of Pushkin, Gogol, Tolstoy, Dostoevsky, Stendhal and Balzac. To my mind Kleist and these 19th-century French and Russian novelists were the greatest masters of prose, a constellation of unsurpassed geniuses such as we find in music from Bach to Beethoven, and I try to learn something from them every day. This is my 'technique'.
8. THOU SHALT NOT WORSHIP LONDON/NEW YORK/PARIS
I often meet aspiring writers from out of the way places who believe that people who live in the media capitals have some special inside information about art which they do not possess. They read the review pages, watch arts programs on television, to find out what is important, what art really is, what intellectuals should e concerned about. The provincial is often an intelligent, gifted person who ends up following some glib journalist's or academic's notion of what constitutes literary excellence and betrays his talent by aping morons whose only talent is for getting on.
Even if you live at Land's End, there is no reason for you to feel out of touch. If you have a good paperback library of great writers, and if you keep re-reading them, you will have access to more secrets of literature than all the culture phonies who set the tone in the big cities. I know a leading New York critic who has never read Tolstoy and is proud of it too. So don't waste time worrying about what is the declared fashion, the right subject or the right style or what sort of things win prizes. Anybody who ever succeeded in literature did so on his own terms.
9. THOU SHALT WRITE TO PLEASE THYSELF
No writer has ever managed to please readers who were not on approximately his own level of general intelligence, who did not share his basic attitude to life, death, sex, politics, money. Playwrights are lucky: with the help of actors, they can broaden their appeal beyond the circle of kindred spirits. Yet only a couple of years ago I read the most condescending reviews in the American papers for Measure for Measure – the play itself, not the production! If Shakespeare can't please everyone, why should you even try?
This means there is no point in forcing yourself to be interested in something that bores you. When I was young I wasted a lot of time trying to describe clothes and furniture. I didn't have the slightest interest in clothes or furniture but Balzac had a passionate interest in them which he managed to communicate even to me while I was reading him, so I thought I had to master the art of writing exciting paragraphs about cupboards if I was ever to become a good novelist. My efforts were doomed and used up all my enthusiasm for what I had been trying to write about in the first place.
Now I only write about what interests me. I don't look for subjects: whatever it is that I can't stop thinking about – that is my subject. Stendhal said that literature is the art of leaving out, and I leave out everything that doesn't strike me as important. I describe people only in terms of their actions, statements, thoughts, feelings, which have shocked/mystified/amused/ delighted me in myself or others.
It isn't easy, of course, to stick to what you really care about; we would all like to be thought of as people who are curious about everything. Who ever attended a party without faking interest in something? But when you write you have to resist the temptation, and when you read over what you have written, you must always ask yourself, 'Does this really interest me?'
If you please yourself— your real self, not some fanciful notion of yourself as the noblest of persons who cares only about the starving children of Africa – then you have a chance to write a book that will please millions. This is so because no matter who you are, there are millions of people in the world who are more or less like you. But no one wants to read a novelist who doesn't really mean what he writes. The trashiest bestseller has one thing in common with a great novel: they are both authentic.
10. THOU SHALT BE HARD TO PLEASE
Most new books that I read seem to me half-finished. The writer was satisfied to get things more or less right, and then moved on to something new. For me writing becomes really exciting when I go back to a chapter a couple of months after I've done with it. At that stage I look at it not so much as the author but as a reader – and no matter how often I rewrote the chapter originally, I can still find sentences which are vague, adjectives which are inexact or redundant. Indeed I find whole scenes which though true add nothing to my understanding of the characters or the story, and so can be deleted.
It is at that stage that I ponder the chapter long enough to learn it by heart – recite it word-for-word to anyone who is willing to listen – and if I cannot remember something, I usually find that it wasn't right. Memory is a good critic.
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This is a free Kindle book that I stumbled upon. This book is basically designed to coach you through a piece of work be it writing a book / developing a software / creating a model / new venture / new product/ new service etc. This book is not so much about “what you should do”, but more about “how you should you do it”. In any creative endeavor, most of us would agree that the biggest obstacle is “internal”. You can name the internal struggle in umpteen ways, here the author chooses to call it “Resistance”. He starts off saying that three big forces against us doing creative work are Resistance (i.e., fear, self-doubt, procrastination, addiction, distraction, timidity, ego and narcissism, self-loathing, perfectionism, etc.), Rational thought , Friends and family. Out of the above three mentioned forces, the author dwells upon the beast (Resistance) in us which we do not recognize sometimes. The beast has the following characteristics :
Resistance Is Invisible , Insidious , Impersonal , Infallible , Universal Never Sleeps , Plays for Keeps
Our Allies in our creative efforts are Stupidity, Stubbornness, Blind faith, Passion, Assistance (the opposite of Resistance) Friends and family. One must invoke these allies from time to time so that one can fight against this dragon called resistance.
I guess everyone can relate to this book based on the nature of work they are up to. In my case where my work is to build math/stat models, there are some nice takeaways from this book that one can relate to any model building exercise
Start before you are ready : If you are building let’s say a volatility based model, don’t over prepare. Look at the data, do some diagnostics, fit a basic model and back test it. Once you know it really sucks you can improvise.
A Research Diet : You cannot read LOT of books and assume that at the end of it, the model will magically become crystal clear. You need to cut down the literature to a few important books and then start building a prototype of the model. However the books you shortlist should be read cover to cover. You got to forget everything else and go over the books so that you don’t miss any vital point from those shortlisted set of books. So, in one sense, what you include in your research diet becomes crucial. Again this is a process. First time you have no clue what to read. Second time, you become a little better in choosing the relevant to stuff to read, third time you get a decent idea and so on and so forth. Utopian state according to me would be,“You see a problem ---- You immediately know the kind of model that would work for that specific problem ---- If you have the skill sets well and good ---- else you kind of know precisely the books, the academic papers, the software, the people whom you must connect so that you can build a useful model”. Any modeler should strive towards this utopian world.
Stay Primitive : All you need is pen & paper, a programming language and a database to do your research work. Nothing fancy is needed. The advantage of using open source is that you can customize to your requirements, meaning you can decide what is needed and what is not. Most often than not, it is the pruning that is critical. Like a garden that becomes beautiful after pruning, most open source software from my experience work like a charm, once you know what to prune and how to prune.
Swing for the seats : Don’t be taken aback by the complexity of the model if you know that it has a potential to work. After all, most often than not, you might end up using only a SINGLE component of the model but that which works perfectly for the situation.
Three Act Structure : Like the artists, painters, movie makers, create a three act structure for your model. What are the three major components that your model has/model will accomplish by the time you ship it. These three acts should be the basis of everything that you do.
Fill in the gaps : Once you have the three act structure ready, work furiously to fill in the gaps. Do research. You must remember that ideas don’t come linearly. Some tangential direction from some footnote in some random paper could be just the thing that you want to implement.
The Process : Build a prototype / Back test / Do research / Build a prototype / Back test / Do research – Basically it boils down to ACT-REFLECT loop a zillion times till you are ready with the model
Obviously any process will hit roadblocks and this is where the book explains two tests where you will win over resistance based on your attitude.
Test Number One : How badly do you want it?
The scale below will help you answer. Mark the selection that corresponds to how you feel about your book/movie/ballet/new business/whatever.
Dabbling • Interested • Intrigued but Uncertain • Passionate • Totally Committed
If your answer is not the last one in the options list, then Resistance will eventually triumph.
Test Number Two : “Why do you want it?”
If you checked 8 or 9, you will beat the beast/Resistance. If you have checked any one of from 1 to 7 Resistance will win the war, even though you might win a few battles here and there.The book ends with saying that, @ the end, you have to ship it. You do the research/ math/back test and you don’t ship it, you have failed.
This book made me curious to read the expanded version of the same content “The War of Art”, a nifty play of words from the title of a famous book “The Art of War”.
This book explains the same points with many more examples and anecdotes. If you feel resistance in doing your work at any point in time, be it at the beginning/ middle/ towards the end of your project, these two books will jolt you out of your sloth.
The book makes one realize the beast in all of us, “Resistance”. By exposing its various manifestations, its allies, its weapons, one can be prepared to overcome it in our daily lives. We cannot remove it completely .We need to fight with it every day. However we can get better at it, day after day, if we are committed.
Posted at 04:08 PM in Books, Management, Reflections | Permalink | Comments (0) | TrackBack (0)
It is profoundly important to read around the area that you are working on; more so in mathematics. Theorems that you see in the texts are usually a result of ardous efforts / long drawn fights between mathematicians / result of being in extreme hysteria(Cantor for example)/ family duels(Bernoulli)/ Open air competitions(Solution to cubic & quartic polynomial ).
It is important for any person building stochastic models to have a thorough understanding of Markov chains as they typically lead to random walks and Brownian motion concepts .Typically one comes across some form of limit theorem in elementary courses on probability or statistics. In a crude form, one has an intuitive understanding that “You take a large collection of numbers and you take an average, it converges to some number.” It is tucked away in most books under some title which has the words,” law of large numbers” in it. However you miss the entire action if you miss the historical development to this concept and more importantly, the application of this law to dependent variables. Almost all the forms of weak law that one usually comes across has “independent and identically distributed” statement in it. This is where Markov’s work becomes important. Almost 100 years back he generalized the weak law to dependent variables. Sometimes historical developments such as these are not highlighted in math books and one needs to resort to reading around the material to get an idea of the immense contributions of the mathematicians.
This brief on the life of Markov is elegantly written. The takeaways from this note are :
The note concludes saying
Markov proved that the independence of random variables was not a necessary condition for the validity of the weak law of large numbers and the central limit theorem. He introduced a new sequence of dependent variable, called a chain, as well as a few basic concepts of chains such as transition probabilities, irreducibility and stationarity. His ideas were taken up and developed further by scientists around the world and now the theory of Markov Chains is one of the most powerful theories for analyzing various phenomena of the world.
Once you read this note I am certain that you will start looking at Markov chains with awe and admiration. The very essence of simulating random variables has undergone profound changes with the application of Markov chains.
Posted at 10:45 PM in Math | Permalink | Comments (0) | TrackBack (0)
It has been a really long time since I have read any of the Seth Godin books , so picked up his latest book – “Poke the Box”. Books from Seth are usually filled with nuggets of wisdom culled out from marketers / entrepreneurs/purple cows that he comes across. To me, I love the way he writes; Straight to the point, no bullshitting, no nonsense and blends his message with anecdotes and interesting insights.
Firstly something about the man on the cover; Seth says
“The man in a hurry is an archetype, first discovered in the hieroglyphs of ancient Egypt. He’s you, the excited, optimistic experimenter who understands that risk is misunderstood and that forward motion is the key to success. “
The phrase “Poke the box”, represents hacking or action. In author’s words,
“How do computer programmers learn their art? Is there a step-by-step process that guarantees you’ll get good? All great programmers learn the same way. They poke the box. They code something and see what the computer does. They change it and see what the computer does. They repeat the process again and again until they figure out how the box works. The box might be a computer or it might be a market or it might be a customer or it might be your boss. It’s a puzzle, one that can be solved in only one way—by poking.”
The book’s central message is “Start Often and Ship Often”. This applies to ideas/books/ventures/products and it means that creativity has to crisscross with the marketplace often. There is no use writing a novel and perfecting it endlessly instead of shipping the rough draft. There is no use in building the perfect product instead of shipping the product in versions and making it better as time goes. This does not mean that you ship something half-baked. It only means that you have to ship often , to fail often , and to finally succeed. Shipping entails the risk of failure and unless a company/an individual/team is not prepared to fail, it will be in an endless loop of perfecting the product and living in an utopian world, thus missing the critical component required for any success- “Failing too often”.
To be an initiator/shipper you don’t need to have some grandiose context. Seth puts in beautifully
Outsized entrepreneurs are lionized daily. We’ve heard their names again and again—people (too often men) who started a business, started an organization, started a revolution. Good for them. But you don’t have to be Howard Schultz to be an initiator. People have come to the erroneous conclusion that if they’re not willing to start something separate, world-changing, and risky, they have no business starting anything. Somehow, we’ve fooled ourselves into believing that the project has to have a name, a building, and a stock ticker symbol to matter. In fact, people within organizations are perfectly situated to start something. The third person in the four-person inbound customer service team can do it. The receptionist can do it. The assistant foreman can do it. The spark I’m talking about is simple to describe, but easy to avoid.
There is another aspect to starting/poking the box, which is “finishing”. If you don’t ship the idea/product/art/whatever that you are doing to find the reaction from the market place, then you have failed.
“Starting as a way of life” is probably the only way to ensure that you fail often, you ship often , and in the process succeed.
Posted at 01:57 PM in Books, Management | Permalink | Comments (1) | TrackBack (0)
Via Razblint :
Posted at 03:26 PM in Wierd | Permalink | Comments (0) | TrackBack (0)
If we are to speak well, our words must pass three gates.
At the first gate we ask: Are these words true?
At the second: Are they necessary?
At the third: Are they kind?
- A Sufi Saying
Posted at 12:08 PM in Reflections | Permalink | Comments (0) | TrackBack (0)
Do not go where the path may lead,
go instead where there is no path and leave a trail.
- Ralph Waldo Emerson
Posted at 03:56 AM in Reflections | Permalink | Comments (0) | TrackBack (0)