ARogueTrader wrote: But this is why QRNGs are chosen over PRNGs. Would one laugh at random bits from http://www.fourmilab.ch/hotbits/generate.html ? Nature has the last laugh.
I was just trying to point out that you cannot possibly define randomness or anything else to the point of certainty.
"Your definition consists of terms,": no that's the point . Walter Shewart says that currently randomness cannot be defined with terms but rather implicitly by refering to an existing physical process that we qualify as random . The purpose of science is to know the "true" nature of thing - at least to approach it as far as possible - that is to say to define it. Even if a definition is not clear yet, it doesn't prevent that the concept is needed in everyday life. One obvious example is the concept of temperature. Even before the invention of intruments to mesure temperature, people refer to degree of hot or cold. When these instrument appear they were not very precise not only because of lack of technology but above all because the true nature or cause of temperature wasn't known. For long people thought it was due to a "hot" substance with so called "phlogistic theory" - Phlogiston was defined as "the matter and principle of fire, contained in all metals and combustible bodies, and given up in burning or calcination" - whereas today science knows that it is due to atoms moving ... RANDOMLY so that it is not so far from our subject - and so the link made later in science between the two concepts: Randomness and Entropy. Don't forget that words are just proxies to reality. In fact words are sort of models of the world because behind each word lies an interpretation, this interpretation changes from period to period with scientific knowledge and even from individual to individual when it is not defined clearly yet. So when something has no clear definition it means that progress has still to be done in the field.
Now once that one realises that randomness cannot be defined explicitly but only implictly by refering to a physical process, we can find criterias that allows us to say that something is probably NOT random. For example if you flip a coin and get 1111111111111110000000000000, by using the MATHEMATICAL probability axioms (founded by Kolmogorov) you CANNOT conclude that it is not random because within these axioms this sequence has the same weight than any other sequence, whereas if we refer to the PHYSICAL process of coin flipping, ORDER COUNTS so that we know that this sequence should most probably be a clue that the underlying process is not random. That's why IN PRACTICE - for example using so called "run test" in non-parametric statistics - thanks to this reference to a physical process, there is now ways to detect NON Randomness - although one sequence is not enough repetition is also necessary which is also a very important characteristic but I don't discuss it at the moment. Now although there is way to detect NON Randomness, there is no way to detect the opposite Randomness. And it is very important to understand this ASSYMETRY in reasoning because it is the foundation of SCIENTIFIC APPROACH. If you find indice of NON Randomness you can say that the process is not random whereas if you find NO indice of NON randomness you CANNOT conclude that the thing is random ! For example I mentionned above that using "run-test" could detect non-randomness. But if you detects nothing with it you CANNOT conclude that the process is random ! This is the core of Hypothesis testing in inferential statistics, the core of proof in law (for example you can suspect somebody of being the murder in a crime because of its psychology, even if you can't find any proof yet it doesn't imply that you conclude that he is innocent it is the same spirit in inferential statistics), and as said above the core of scientific reasoning . This seems evident in concept but if you look at reality, some people don't apply it although they claim to use scientific approach: the EMH propagandists for example claimed for long that the market was random just because there was no proof of non randomness by not taking order into account. Today there are so many clues of non-randomness that they have to capitulate but they manage to change the definition of EMH so that it doesn't mean Randomness any more but so called Martingale - so I will have to talk about martingale later but this thread will make understand how they switch from Randomness argument to Martingale argument .
Since I have just answered a question about martingale can see here: http://www.elitetrader.com/vb/showthread.php?s=&postid=401943#post401943
harrytrader wrote: While EMH random processes satisify the Martingale property, non-EMH random processes (with application to Technical Analysis) are typically formulated to satisfy the Markov property (albeit may be a multidimensional process): EMH = Martingale random process TA = Markov random process
Martingale is not incompatible with Markov Property, the trivial example being that a brownian motion satifies both. So it is not a criteria to distinguish EMH from TA. The very reason why martingale has been introduced in financial theory by Samuelson - who receives the Nobel Prize for that - is that it imposes no autocorrelation (independancy) condition on the residuals which was too restrictive in RMH (Random Market Hypothesis).
Quote from FireWalker: Something is either random or it's not. There is no such thing as partially random. Of course there is. The absence of a deterministic component is in some sense the definition of a martingale. Imagine two drunk traders by a bar in downtown Manhattan. A slightly drunk guy going home has a random component to his motions, but eventually drifts to his high-priced condo. His motion (or more scientifically, change of position) is not a martingale. A completely shit-faced fellows motion is a martingale â you can expect to find him by the bar next morning. For a somewhat drunk trader, however, a Moore transform is possible â you can give him a bit more to drink (and then some, if he is Russian or Italian), thus removing his deterministic component. After that his motion is a true martingale, as he vomits and remains by the bar until next morning.
sle wrote: Your drunks would typically be modeled as Markov random processes, in either case (depends on what the recurrent and absorbing states are).
There is no contradiction between the two models. However, one can think of non-markovian martingales, just to make life even more misarable. For example, the way rates are specified in the HJM family of interest rate models makes their processes non-markovian, causing a lot of headache for the traders and quants (life is soo hard without trees).