kristalris

Well I don't see that as the point of the thread. The thread title and OP must be placed in a scientific context. So the title in that context is correct as a start of an honest inference. The OP is incorrect in the idea that science at all can deal with truisms. It doesn't per definition.

Bayes can infer ALL relationships via a proof system. No-one as far as I know has ever disputed this. Do you? So all mathematics can be translated into a Bayesian proof. Like translating Dutch into English. Because Bayes does all relationships - what can't be said of all other mathematical languages - it doesn't work the other way round. For instance Bayes can solve more proofs (because it can do it all) than empirical statistics that can't handle n1. So there can't be any reason why Bayes can't handle GR and QM. No one will of done that because it would be in breach of Occam. Using Bayes would only make it more complicated without getting better results. So it would be silly attempting it. (Edit: or maybe not so silly come to think of it) Edit BTW this doesn't mean that if you put GR and QM to Bayes that you have married the two. Bayes will then say that they are in conflict. (Edit: and might show you where to start looking for a marriage of the two.) Logic is more than mathematics. All scientific logic can be put into mathematics. How can you say that taking in guesses doesn't matter? It rules out Gobel for his position doesn't cater for that. Bayes does and can thus handle all proofs. I guess Gobel forgot to take Bayes into account. His proof is I guess deterministic. The question should be the other way round: can you name one form of mathematical proof that can't be handled by Bayes? You are the mathematician. Whether or not Bayes can solve all logic I guess not for there is logic that is outside science. For instance religious logic given a priori contradictions to be taken as a fact. Bayes can't handle that other than rejecting it, what it is on religious grounds not allowed to do. Because science is about the furtherance of knowledge it doesn't per definition handle logical truisms. A Bayesian inference is the minimum. And Bayes also provides the maximum encompassing all of mathematics and scientific logic. In fact thus Bayes & Occam are the minimum requirements of science. The norm of science as condition sine qua non.

Gödel doesn't as far as I can see allow for guessing. So given that he's right it doesn't completely capture all logic. Bayes does for allowing you to guess. The only limitation Bayes prescribes is that you formally at least follow all the steps for it to be science. I.e. there is logic outside science. Yet Bayes also allows for informal logic via Occam. Science is the systematic i.e. logical enterprise to reach the ultimate truth as close as possible in the simplest way possible (=> honesty is prerequisite and speed an issue) So you get problem => probandum => hypothesis => prior odds => discovery => LR x LR etc. => posterior odds => norm => proof/ no proof Via this method you can even tackle the "this sentence is false". Bayes: as a short cut: what sentence? This actual one? Honest? No => non scientific problem. If you want to go further Bayes can do that as well dear Gobel. Because you can say honest? Yes. Then what probandum? Fill in here please.................

Most certainly. This is especially true if one believes in DSM V.

(No, this was easy leaving the quote box.) Logic is always logical as is (correct) mathematics. You are a mathematician. Logic (by language) only has a large bandwidth of inaccuracy and accuracy. The latter bandwidth is needed to quickly solve problems. Even - if not especially so - the most complex ones. It makes it possible to draw a quick sketch, showing where to start extremely accurate testing if required.

Yes Bayes can describe all logic. mathematics is the a tool of logic. => Bayes can describe all mathematics Bayes is mathematics => mathematics is the ultimate tool of all logic Bayes is the mathematics of intuitive common sense set in language => mathematics doesn't exclude language as first gear of science concerning any probandum

Suddenly the box split. This proves it's magic. Back to black then. (must of done something right that I can't replicate yet this digibeet will get there (possibly) Anyway there is no mathematical formula that can't be described via Bayes. So this mathematics you take can be done via Bayes as well, only I'm near certain that it will be more cumbersome. So Occam rules out Bayes. Yet Bayes can describe it just as accurate or even more accurate. The opposite isn't true. (Now don't think I can do this again split the quote box at will, anyway:) I'm puzzled where your problem is at? Bayes can describe anything mathematics can describe. So what is the problem? Mathematics is a tool. Don't expect the tool to build the building. You will have to do that yourself. Bayes sec will not solve Schrodinger (though I claim I have via Bayes using common sense = Bayes & Occam) (I think based on mounting testing of guesses that the trick is to click the left mouse and then enter. I.e. Bayes is getting me there.) In exactly the same way as I'm finding out how to split the quote box. Just mucking around and guessing and testing. You keep missing the point that Bayes points to non Bayes (that can be described by Bayes.) So any useful mathematics that you agree can be used can be replicated by Bayes. That doesn't mean you should use Bayes. Use the correct mathematics you need (= concurs with Bayes) No there aren't. Any and all questions can be dealt with using common sense. That is Bayes. It can help you go from lower level to higher level. You have no scientific logical basis to exclude these lower levels that Bayes allows for. And yes, that helps. It gets it going. It is first gear, second to third gear. Yet not fourth and higher gear (even though it can describe that if you like even though it's too much work) Current science only accepts overdrive and only slower and slower gets off the mark. That is illogical and impractical. Yet explainable: DNA and the distribution thereof / psychology. The lower gears need - probably the DNA / possibly only nurture - imagination. The higher gears need - the DNA / nurture - for hard conscientious work. Yes, by razoring it down as well. It is not only descriptive but also prescriptive.

I've been thinking how to explain Bayes further: It ranges from n absolutely 0 via n1 to n plus or minus infinite at infinitely every point infinitely accurate or infinitely inaccurate in any chosen bandwidth of accuracy. Ergo it can describe anything or nothing. Combined with Occam in a Yin and Yang with Bayes Occam maximum simple Bayes Integrally infinite striving to answer the question on ultimate truth being that God, magic or a fundamentally simple set of formulas and constants or whatever. It can describe an infinite amount of relationships or any limited amount. It ranges from common sense to the most complex mathematics conceivable. It catches all observations and makes it possible to fill in all that is perceived as missing via imaginative guesswork. It is both descriptive and prescriptive minimum norm on what science is and what it can possibly be.

Is there any mathematical model that already can do this provide the ground state energy of the hydrogen atom? If not then still Bayes and Occam can take a shot via guessing. And if there is, then certainly Bayes and Occam will point towards that same method. Indeed the friendly statistician will not reach for Bayes, but that is not the question then is it? The question is, can Bayes get then the same result. If so, it fits and proves you wrong. If no other form of mathematics can solve the problem then why should Bayes not be allowed on this probandum to fail as well? Bayes BTW doesn't fail we do with the garbage guess having too little data.

Now it can be that simple. The error in your thinking lies in the idea of a "best practise" at least in the idea that that is always something that can be mathematically shown to be that. When you know that you have too little data you can't claim that. (Bayes dixit) So then you are left with several possible scientifically valid "best practises" from which you indeed may choose indeed conforming to your taste. Bayes and Occam let you do that intuitively as long as you honestly state that that is what you've done and as long as you haven't skipped already present observations that are already present in science especially when these contradict. That is why it is called - intuitive statistics - remember? You may / are forced to guess in order to get an integral picture. Bayes and Occam will simply say: one of these three methods is probably best and there is at this moment no way to distinguish between them: you may choose one or all if you like. You whish to place R&D of science in a box. Yet Bayes doesn't know why you want to do that? The whole of Science isn't in a box, only the knowledge part of it, the research part is per definition out of the box. Bayes and Occam show (mathematically if need be) that you have your expectations and thus put your norms to high all across the board. The reason is probably that you don't accept the fact that there are far above average good guessers in the game of human nature. Who only need these simple starting points to get the show of science going. Compare it to a fractal. Simple beginning spinning into a complex system. I can't give you a full Bayesian mathematical proof myself, but it is evident that it is possible to do so. Now you show me one example of a scientific problem even in pure mathematics that Bayes and Occam can't solve. Then I'll put that forward to a real statistician and see if he agrees. Ok? Mind you that Bayes and Occam might solve that problem by stating: use empirical statistics. This because although a full blown! Bayes will render - exactly - the same result Occam will rule out Bayes for being to bloody complicated in comparison. So Bayes and Occam can claim to cover the results achieved by empirical statistics in being simple by ruling out themselves. Empirical statistics can't do it the other way round. It can only say: don't use me for this problem.

Well one shouldn’t mix up bollocks with buttocks like I seem to have done, in my Double Dutch way, because it can be a very painful mistake, complicating matters. Because both Bayes and Occam are thus infringed I have to say I’m sorry. The simplest explanation is per definition the shortest one. That is simply easy. The problem lies in the Yin and Yang of Bayes and Occam. The Bayesian machine is a cutting Razor that runs on high octane Occam gas. Occam in its simplest form is the algorithm keep it as short as possible. => the law to strive towards this & (what swansont clearly only thought: the probability that the hypothesis with the least assumptions is probably best. Putting this in the Bayes machine that covers everything OR any limited issue if you so choose. But then a full blown Bayes will require you to address or assume where the boundaries are of the limitation. Assuming thus that what is outside those chosen boundaries is irrelevant to the issue you ask Bayes to solve, will make it fit Bayes again. Ergo both GR & QM in their respective fields are the simplest ways of explaining at the most accurate way currently possible all that the assumed scope of GR & QM can be assumed to cover. Because GR is in conflict with QM in their respective fields you may not assume that both are valid all over the infinite universe as an estimate using fewest assumptions. (said in short hand). If you accept that Bayes covers it all and accept Occam in this context then you’ve not only got your equivalence but even surpassed it. Bayes also covers the bit you assumed irrelevant, and makes you state that. For the scientific method to be chosen Bayes and Occam dictate you strive to the simplest way (= Occam) dealing with the integral problem (=Bayes). Ergo the shortest quickest way doing that. Otherwise it can’t be made to fit these two fundamental mathematical algorithms of science. To answer your question which mathematical system is best: If both are equal then neither is best. Furthermore a serious misunderstanding of Bayes in science is the “best practice” dogma. Correct Bayes & Occam does nothing of the sort. Take DSM V as best practice. Doing that infringes on Bayes and Occam. If you know that you don’t know what it is to a sufficient degree (which is the case on diagnosing mental illnesses) then one should expect several “best practices” adjunct to each other. Only when you have sufficient data that you can prove that you outrun the best experienced guessers in the business, all across the appropriate board may you claim best practice in that sense. In short Bayes & Occam tell you when to use your common sense and when not to in the sense that that then is also common sense to use complicate mathematics. Ergo Bayes & Occam are the alpha and omega of science. It covers it from its smallest simplest short cut method to the all-encompassing full blown mathematical analysis of everything or anything. It even deals with the problem when not to use Bayes (because full blown Bayes is extremely complicated.) Again current neurology even finds probable that even a mathematician doing non-statistical mathematics first guesses intuitively unwittingly via the Bayes in the brain algorithm what to do and then doing it. Too many current scientific methods are too complicated, proof: they can be cut down too their essence by razor deleting the humbug. “If it ain’t Bayes & Occam it ain’t science” is thus the better adagium. Proving even I’m still learning Bayes. Always also include Occam. Otherwise its Yin without Yang. Edit: I seem to have had yet again a problem with the quote box for I thought I posted it underneath. I'm in part a digibeet yet fiercely proud of that. Though it does tend to give the John Cleese moments of man against the system. Last one I shouted at the bloody machine only to discover that it shouted back because I unwittingly was also recording what I was shouting. Great fun. Now just to put another important point to the Bayes razor machine it is of course the goal: the ultimate truth. => You must be honest. Ultimate truth via Bayes and Occam implies that it isn't magic because the Bayes machine runs on logic. Yet it even can deal with the extremely improbability of it all being magic as well. Ergo if we as a thought experiment see it as the scientific radar observing there is a dark side under the radar due to the curvature of the earth. Any plane (idea) that is based on magic like Krauss et all is more than a trillion to the trillionth miles away, any God more than a trillion and any integral idea that is simple and consistent with it all and testable concurs with Occam and Bayes with whatever tool has been used and is thus to be assumed the closest to the goal and thus scientifically most valid. Any scientific dogma that is based on ignoring part of the issue is not compatible with Bayes but only with Occam. So then you're out. Disqualified on the game of science but the mathematics of Bayes and the algorithm of Occam (asap)on the stated goal: the ultimate truth. This is NOT a democratic principle. It is the dictatorship of Bayes and Occam on the stated goal. Yet Bayes and Occam also show you why It is that democratic science believes that rigid systems like DSM V become more and more the winning best practise even though it is evidently wrong. The way in which the Bayes in the brain is distributed by MN / God as probably DNA in the population in order to have this population the best chance of surviving. The Big Five as simple model shines through in all cultures. In the highest level of quick thinkers you have but a few of the best Bayes guessers who keep it simple as best leaders in R&D breaking the rules; a lot of production leaders abiding by the authoritive rules for production guessing that that is best and thinking it isn't a guess, and a few emotionally intelligent sales men and woman. In an open culture many production minded persons dare to be creative. In an authoritive culture only the open minded emotionally dare to oppose. Only rationally putting the brake on. Only when everybody is honest about oneself and the strong and weak points by working together does the pareto optimum become possible. Say the collective algorithm / goal of having a long as possible happy life, with the least possible infringement to others. Seeing us as DNA driven robots with a Yin deterministic and Yang dice of chance "free will". Given this and the DNA division I can build you the entire legal system. And describe proven to work well societies. Such as successful R&D driven companies such as Apple Inc. And also why it is that in this internet age the emotionally intelligent leader will more and more become the boss. (The actor / salesman / great communicator.) No problem when advice is given from R&D what is to be taken in or out f production. On the long run or short run in a crises a bloody disaster, when that is not dealt with, by getting the team to conform the Bayes / Occam machine. (BTW whether it is ultimately nature or nurture is immaterial given the Big Five.) The Bayes in the brain machine (by MN/ God) creates the illusion of being broad minded due to the great volume of current science. Knowing a lot doesn't imply being open minded and thus a good Bayesian guesser. R&D needs to pass a new paradigm to sales in order to get it into production in time. The problem is that our current society changes faster than our social Bayes in the brain DNA limitations allow for to quickly accommodate. BTW the proof that we humans are good Bayesian machine guessers is that we haven't gone extinct yet. Yet we might still go extinct, if we don't get this in order. When R&D types are out of the loop the Bayes machine in our brains will go into an ever more ISO 2000 quality system like DSM V. Simple statistics.

I don't quite know why I can't get rid of the bold lettering but anyway. I just apologized for not doing as the Romans do on this Forum Romanum, and now I get treated by the senator of the site on a Freudian Bollocks. Well then senator you are in for a spanking: Empirical[edit] Occam's razor has gained strong empirical support as far as helping to converge on better theories (see "Applications" section below for some examples). In the related concept of overfitting, excessively complex models are affected by statistical noise (a problem also known as the bias-variance trade-off), whereas simpler models may capture the underlying structure better and may thus have better predictive performance. It is, however, often difficult to deduce which part of the data is noise (cf. model selection, test set, minimum description length, Bayesian inference, etc.). Now I know you love empirical. Care to edit the Wikipedia on Occam? Think you should or withdraw your bollocks. Occam is thus a very very widely held empirically based guideline, for probability, yet also a basic rule of science namely lex parsimoniae. Lex means law BTW in the Forum Romanum of Science mate. I know that there are quite a few physicists that think like lawyers and try to (unnecessarily) complicate the issue. Is that what you mean with bollocks BTW, no mate, not unbreakable? What do you mean then not unbreakable? Example please, for you are then in for a further spanking. Further more you clearly need to reread what I've explained on Bayes and the proper use thereof for you still don't get it even after simple explanation. If you can use empirical statistics because Occam sais so then Bayes sais you should, as I've pointed out several times. Bayes & Occam are probably wondering if the bollocks hurt now?

Well, yes and no. Bayes is to be seen as the first word of science, the second word is Occam. If what follows in science doesn't fit this - sufficiently - then one can indeed say that what is presented is not science or best scientific practise. I do agree with you in part, because that too is Bayes; namely that there is latitude to be given. This because being too strict concerning something where you know that you don't exactly know what the exact science is, requires this. Yet again it is then Bayes & Occam that only provide this latitude in the form of use of verbal logic, because normal language is nice and woolly. Because having any scientific method in any field that is strict all across the board, for instance demanding the exclusive use of mathematics concerning issues where you know you don't know the exact science is a contradiction. A contradiction Bayes doesn't allow for because then you are inherently claiming more than anyone can deliver and thus no-one may demand. Neither does Bayes via Occam allow anyone in science to use too difficult methods such as mathematics at least forbids demanding the use thereof in issues that can be and thus should be dealt with via the simplest method or tool available. I.e. normal language. Thus even in physics concerning issues where you know that you don't know all the relevant questions that Bayes forces you to address, should these questions if need be by guessing have been answered, prior to claiming correct / best scientific method. Not complying to this is per definition thus pseudo scientific. The ultimate irony is thus that it is the demanded mathematics in physics is provided by Bayes because that is mathematics the physicists demand, yet it forces them into verbal logic and answering questions their dogma prohibits on specific questions. Finally adhering to Bayes & Occam would speed up the furtherance of science enormously.

What if the investigation of the hypothesis shows an enormous / probably infinite amount of data? Well see there the problem then with the education of physicists, they have only just climbed out of the Rutherford tree a few years back by stopping opposition to empirical statistics. It leads to in fact the same sort of a discussion concerning the proper use of Bayes. Bayes spans the extremely simple to the infinitely complex. It can always be applied and is thus the ultimate arbiter of science. Now the problem is as soon as scientists / physicists don't contest that or even accept that, physicists immediately run into a wee problem.

Thank you. yet I don't quite catch your drift concerning the likelihood of any hypothesis only becoming infinitely small, because the opposite is also true dependent on the direction this enough evidence points. Further more only having hypotheses could one be more probable than the other. It is not the likelihood as such but the ratio of likelihood pro versus con that provides the probability. The latter is important the crux so to speak of Bayes. You should compare probabilities and not just likelihoods.

Although I wasn’t planning on a reaction, I will give one. Insofar apologies also are directed towards me, I accept them, though I don’t deserve them. If you push like I’ve pushed then one shouldn’t moan I believe, yet I accept that others might not, as I do, enjoy a stiff debate. For which I then should apologize, as one should do in Rome as the Romans do, being a guest as I am.

To keep my reaction to your question as short as possible and intelligible for those not following the other discussion part of my answer is in this thread as you know: http://www.scienceforums.net/topic/80193-the-bayesian-machine/?p=779504 In further answer to this specific question on relevance: everything you guess or know to be because many you know agree that it’s a scientifically accepted fact or that you deem it to be commonly held to be true that is larger or smaller than a LR of 1 is relevant. It is not circular because it’s testable: i.e. you can check whether others accept your guess, for instance that nurses hardly ever if at all kill patients against their will or in conflict with the rules. A guess presented as a guess is scientifically valid. An honest guess is possible reality.

In reaction to Gees and to Cap'n Refsmmat: Indeed Gees, and that is exactly what Bayes allows you to do: guess by using your imagination and see how your guess taken as a fact (= hypothesis = assumed to be absolutely true) fits all the other facts (= assumed to be absolutely true.) Logic is in fact an empty shell. You put garbage or non-garbage in and compare it to other garbage or non-garbage. Logic in general only tells you if it is consistent with each other. The same goes for all tools of logic such as language and all forms of mathematics. The only tool that covers it all is Bayes. The paradox ( seeming contradiction) is that you don’t practically use Bayes that often, even though current neurology is saying that we probably (= Bayes BTW) have the algorithm described by Bayes in our brains. In fact thus not only the algorithm covering all mathematics but also common sense. So indeed you can take the probandum “does God exist?”. Well, using the Bayesian what I’d call the enhanced common sense method it goes like this: The applicable norm here is absolute truth. Can I absolutely prove or disprove that he exists? No. Now Bayes lets you take it further than that: Okay let’s assume God exists (taken as an assumed absolute truth) Now I compare this absolute truth with the opposite I take the fact that God doesn’t exist. (In fact a very clever mathematical trick.) A priori I see no evidence that he exists or evidence that he doesn’t exist. So that is 1/1 = 1 or irrelevant. For my likelihood ratio (= on further evidence acquired by further investigation) I thus have no evidence either so I’ll have to guess: I guess the chance of God existing given that there is no evidence either way (extremely far, but he give or take a bit then) less than one in a trillion of being true in general. (For I a priori don’t believe that we can know the absolute truth) I.e. taking something extremely complex to be true in agreed absence (that is then challenged by religious people, but not by most scientists) I’ve already established the fact that I can’t prove it either way on an absolute norm so I’ll prove it for myself on my personal norm. Now I could immediately conclude thus he doesn’t exist, yet I can via Bayes go one further still: The further evidence I have is that I personally have the very strong feeling he doesn’t exist, at least as I wise old man with a beard or the like. This I can give a LR of 1/10 or infinite against because it closes for me the argument: I take as a fact (assumed absolute truth that God doesn’t exist.) Now I could of used the shortcut and simply state: “I don’t believe in God.” If need be my above argument can also be written down in a full blown Bayesian net, and forcing me to answer maybe via guessing certain facts that I’ve missed in the argument. This then via the rigors of mathematics. Like you Gees, I couldn’t cope immediately at least. Yet no problem: you go to your friendly experienced open minded statistician for this. He/she will probably tell you to sod off, because further mathematics won’t prove a thing further for those who don’t believe or disprove a thing for those who do, but anyway Cap’tn it can of course deal with any problem you like, in psychology or what not. Now when I die and indeed find myself standing before Peters Gate I will reconsider my position on this on the basis of the new evidence that has then presented itself. (In fact thus the scientific / Bayesian approach BTW) Now to go one further still: Nuclear physicist Krauss et all believing via mathematics that it all scientifically stems from nothing thus believes in a blatant contradiction. I.e. magic. That is worse than believing in a God because believing in God doesn’t conflict with anything. I.e. as a guess Krauss et all are less than 1 in a trillion to the trillionth of being correct. Now I could even go one further with God. If you guess (like I do BTW) that it fundamentally is something then even a thought is a material thing of fundamental parts bouncing around. So then the collective thought of God exerting a power (for good or bad) by religious people then does exist, as is consistent with what we observe in religion. Taken that way proves / can prove (= dependent on the norm you choose) then that God does exist. There you go: easy Bayes. Bayes is both extremely easy and extremely or even infinitely complex. I.e. you can make it as complex as you like yet keep an eye on Occam => keep it as simple as possible! => Bayes more often than not says: “don’t use me! But says for instance: “use empirical statistics on this problem for it is more simple!” So yes, in science you are allowed and even forced in the fields where you know that you don’t know the answer yet forced to act, or to find out what to test or not to test to use common sense. You may guess using your imagination. As long as you state that that is what you are doing! It then is a scientific fact that you are speculating. The forum thereof is thus correctly part of the science forums. What you’re not allowed to do, yet what happens a lot is claiming science or more science than can be had such as DSM V in psychology. Yet even these too rigid models are not so dangerous in the hands not just of the experienced knowledgeable exert, AS LONG AS HE OR SHE IS OPEN-MINDED! I.e. if it is someone who can make an adult guess because thus having sufficient imagination to fill in what Bayes requires you to fill in, in order to test. Sometimes in the test of actual life BTW. If the one doing the psychological diagnoses is not open-minded - as most are BTW (not open-minded that is) - then the simple observable statistics are that the rigid system like DSM V becomes more and more dominant. Leading to the hilarious consequence that they in fact state that nearly everybody, sometimes even including themselves are mad. Proving that they are Intergalactic Idiots when doing R&D i.e. making diagnoses or providing the "evidence based medicine" thereof like DSM). God / MN would a priori not have nearly everybody mad now would he/ she? (What they should be doing is leaving the R&D diagnoses to the open-minded ones and concentrate on what they are good at: production and / or sales: the therapy that requires conscientiously risk avoiding treatment via the book. If it doesn't work? back to R&D then to figure out what next? Or to provide schooling on what "the book" says. But please no R&D by too narrow minded people on issues where you know that you don't know a lot that needs to be known in order to take a decision!) I hope this clarifies Bayes for you.

Okay, YdoaP, we I guess are at odds on what "logic" should entail within a scientific context (i.e. the context of this site). We are running in circles otherwise in a Monty Python style. Now I've scanned this Wikipedia and it seems to me to be in order. Where do you stand in it? I'll scan it again to see where I stand. Beforehand I'd say logic per definition entails inference between assumed absolute truths. So, there is only one logic: logic sec. There further more are only different tools to reach the scientific goal. Science entails the trying to reach the absolute truth (= the goal) on everything as close as possible in the quickest easiest way via the systematic (i.e. logical) inference of observations (i.e. taken in as evidence). In short it's what Bayes given Occam is all about. .http://en.wikipedia.org/wiki/Logic#Philosophical_logic

No YdoaP, the prior is not only the previous posterior, yet can also be what you or any more or less larger body of people guess it is: such as the question do nurses or don’t they kill their patients? Within the framework of accepted risks and time you want to come up with a scientifically valid way of reasoning (time sometimes prohibiting taking in all possible evidence and thus the previous posterior known to man by checking all data of every hospital in the world and more. Is that what you think it means? Well yes in a way it does, but that is normless. Bayes requires you to define everything if you like, yet also allows you to cut it short. This by Occam. Bayes shows you the way. I don’t know what Bayes would probably of thought by what you think you mean by the very first prior? Adam and Eve? He was a reverend remember. The scope of Bayes is limitless mate. It can if you like start there but I guess it would be a bit too much work to serve any useful scientific purpose. Your repeated statement: "It's a fact that you cannot have evidence for whether or not that which did not happen could have actually happened." Get real. If I through a dice and get a six, then what did not happen could of actually happened namely that it became a 1,2,3,4, 5 or indeed again a six. The chance is 1/6. That remains the a priori even taken as absolute (assuming thus a pure chance and perfect die). The evidence for a die under these assumptions being 1/6 is overwhelming. What the hell are you talking about? And the blather you think is blather is blather about something that in practice goes horribly wrong a lot of times. Because there are people who simply can’t grasp its importance. Proof: the Lucia case. This also goes in a court of Law, when you've driven through the town at a 100 km/h. You will be punished more severely - and Justly so - not only for what you did but also for what could of happened yet didn't. Setting therewith the norm and reason for upholding that norm. Reasoning that BTW can be inferred via Bayes. And indeed you cannot make any inference whatsoever if you do not have any evidence. Even in pure mathematics within Bayes you take what you had prior on mathematics in as evidence thereof. The assumed situation of there being no evidence has never occurred to us humans at least anyway, so what do you mean? The situation of no relevant evidence being available is something to be inferred and can not and may not be taken for granted in science. Per bloody definition mate! In science you are not allowed to state "the world is flat as truism" You are not allowed to state any a priori truism whatsoever. This because it simply can't be made to fit the requirements of logic in its broadest sense as described by Bayes. Indeed frequentist and Bayesian approaches on the same problem do often come apart, as in the Lucia case because one or both (that wasn't the case in the Lucia case because Elfers came up against real statisticians whacking him silly.) of the statisticians doesn’t know his business. If they collide then there is something wrong that needs fixing. Both always should render exactly the same results if both are used correctly. This is a dictate of logic for there can only one logic: namely logic. (Now if you indeed don’t know what “logic” means we do then have finally found the problem. Logic always dictates the correct answer, otherwise it is illogical: logic, yet agree it is a pleonasm, used to stress this consequence of logic you keep on missing.) And ALL the correctly used tools of logic such as mathematics should on the same question render the same result. For instance you can use deterministic Rutherford reasoning on a question where most if not all mathematicians would use frequentist statistics. Then there is no conflict as long as you state to accept the larger error that deterministic reasoning then entails. The latter being in fact a Bayesian shortcut. Get it? Bayesian statistics is often called intuitive as opposed to empirical statistics because Bayes allows you contrary to empirical statistics to GUESS. That is also the reason why Bayes always applies ultimately yet not always practically. The latter even again dealt with by Bayes' probabilistic reasoning. And finally: no, Bayes does NOT allow you to start with the posterior other than taking that posterior as prior and subsequently seeing what further relevant evidence is available BEFORE INFERRING a conclusion based on matching the posterior with the NORM you choose, or what not. THAT IS SCIENCE: for if it ain't Bayes it ain't science! Science is always inherently about inferring old boy. By logical definition.

Hurray it finally works again the quote box. Thanks YodaP. Well we didn’t delve into it fully, but anyway it’s an answer to your question. Still on a different note than TOE it is thus not I guess then contested by you that Bayes is indeed the ultimate arbiter of science, or do I understand you have no position, or object to that? Because statistics doesn’t as such include - unless used as then as a stipulative definition - Bayesian probalistic reasoning. The latter has baring on everything that science does. Ergo if it doesn’t fit Bayesian probabilistic reasoning it isn’t science. Again, combined with Occam Bayesian probalistic reasoning shows you when to use simple verbal logic instead of say Bayesian nets. The latter is extremely slow and arduous process. Only ultimately in a nice market to be used as the ultimate arbiter on any scientific dispute. It even rules all mathematics, even pure mathematics because there shouldn’t be any conflict between them when used correctly. It is in fact Bayes that intuitively shows the mathematician when to use what sort of mathematics. The algorithm of Bayes is probably according to current science in all our brains as. Bayes describes this algorithm in our brain being thus the mathematics of common sense and all of science. On any scientific question Bayes dictates: take all relevant evidence a priori and subsequent evidence and weigh that becoming the posterior. It even shows you what norms to use on any stated goal. And it shows you what sort of logic or mathematical tools are in order. The fact that everybody always uses shortcuts in deciding what to use doesn’t mean it isn’t governed by Bayes in our brain.

TAR2 That must have been a horrendous experience for you. I was watching TV and saw the second plane strike real time. Indeed I felt that as an attack on us Dutch as well, so I wholeheartedly supported joining the attack on the Taliban in Afghanistan. BTW the Taliban came about due to the enormous chaos caused by the Mujahedeen after the Sowjets had left. Part of this Mujahedeen under Dostum held out and became our ally (like Bin Laden BTW). That said and I’ve stated earlier I don’t see why we don’t learn from history. I.e. the Romans. Go in hit hard and get out after having the tribes in Afghanistan become a NATO legion, whereby no tribesman serves in his own area yet is bonded in a band of brothers under NATO leadership and airpower. Providing them and their families a secured financial and medical future via a pension. When having fulfilled the service loyally. Following what the Loya Jirga wants as long as within International Law. The US choose not to do this because it clearly hadn’t heeded the warning of president Eisenhower to watch out for the industrial military complex. A guided bomb provides more profit and a stronger US military than an Afghan soldier with a pension, the latter at a fraction of the cost and absolutely effective. Yet guided bombs create more terrorists than they kill, and the US / NATO military have lost more lives in the process than in 911. (Especially when you include the attack on Iraq that was not wise at all.) Like a magnet NATO soldiers draw in would be martyrs from all over the world to take potshots at the infidels. A xenophobe afghan legion wouldn’t have this. Apart from that what you thought before 911 that we were on track to world brotherhood was I guess seen wrong with hindsight. Like in 1914 people thought the same. Yet with an enormous and growing world overpopulation we are in for a big bang if we don’t get things in balance asap. 911 IMO is at its deepest level a group of fearless Muslim leaders filling in the need of the Muslim have-nots, who take pride in their religion and history, for that is all they have. Most often providing some sort of social support for political and religious indoctrination. The same struggle BTW in Turkey and Egypt at the moment between the haves and have-nots under Muslims themselves. Only if we humans can get it organized in a globally Just way, will the danger of international terrorism be kept at bay to the maximum possible IMO. The route we in the west are following more and more is one of polarization. This needs immediate reorganization possible via having the right personalities and intelligence put in power of advice via use of the power of the cloud. Q In this, it is important to me to stay away from ideas one might have, that would only be true, if everybody else knew your secret. EQ ? Here you lost me. K

I agree we should try. But not to the degree of wanting to resort to either rigidly enforcing via drugs and what not the idea that this is possible, if - I'd say even: when - it shows that most people simply can't think independently for it scares them. They want to follow the authority. Only a well balanced Just legal system within a parliamentary democratic society can in the long run, I'm convinced - protect the weak against the strong, the minority against the majority rule. At the moment in the Netherlands as in the States it is unbalanced.

I fully agree with you. Examples where Bayesian statistics is correctly used is with expert evidence in legal cases concerning DNA matching a swipe of the suspect with a sample found at the crime scene. A case where Bayes shows that Bayesian probabilistic reasoning (=/= exactly the same as Bayesian statistics) had scientifically best not be used is concerning areas where so little or no data is available concerning the probandum especially when time is of the essence: i.e. in courts of law (if you want as you should strive to remain within scientific boundaries). In many daily life problems, in a great part of philosophy (within the realm of science that is.) A case that shows incorrect use of empirical statistics and correct use of Bayesian statistics is the Lucia de B case. http://en.wikipedia.org/wiki/Lucia_de_Berk#Statistical_arguments In this case there was a long and heated debate between scientists prior to Lucia’s release whether to use Bayes or empirical statistics. It is/ was a nonsensical debate. Correctly used both methods should render the same result (= logical dictate). Why then prefer in this case Bayes before empirical? As a rule of thumb: too little data => use Bayes! In casu had mathematician professor Elfers (teaches statistics to psychologists) used Bayes it would of put him on the right track via the a priori question: in the world you live in do you believe that nurses often, not often or ever kill patients against the rules? (euthanasia (BTW only allowed to be done by doctors if at all in the Netherlands)) I guess most people will assume / be convinced that this if at all will be very unlikely. => Bayes dictates a lot of extra evidence to the contrary on a given norm of proof. => All the more reason to check the data that the police provided, which Elfers didn’t do. Now if we were to run into an Monty Python style argument that in fact my a priori is wrong and there is a Roald Dale scenario in which nurses are in fact witches that regularly kill off patients, based on the evidence on hand and in order to prove that you would have to nearly even resort to a degree of investigation and requiring data via secret camera’s and the such that you indeed better even use frequentist statistics. Another nice area where you shouldn’t even use Bayes or any other form of mathematics is when trying to solve a TOE. You simply don’t have the data needed to solve the – essential and unavoidable question – whether or not the universe is infinite or not. It either is or isn’t a relevant question, and it either is or isn’t infinite. Bayesian probabilistic reasoning as does simple logic will show the use of verbal logic to be the best quickest and most safe way to deal with that problem. And it forbids the only use of mathematics in order to tackle that problem. You get your Escher Institute honoree degree if you don’t grasp that. Ultimately I agree with you in all cases Bayesian mathematics is at the deepest level the thus ultimate arbiter, for clenching any Monty Python style course on argument on ANY scientific problem. Yet, few if any arguments well dealt with using proper verbal argument have to resort to that. Usually the reason not even Bayes or full logical argument will clench the Monty Python issue lies in psychology. Usually a paradigm (or simple bad faith) prevents this and the argument will even go towards a held mathematical truth that is even agreed extremely improbable yet because it has mathematics is widely considered probably best. Which is totally illogical because Bayes shows you’ve gone into a simple or full blown prosecutors or defense attorneys fallacy respectively. Albeit at the heart of it probably DNA talking in the given DNA environment or if you like psychology nurture scenario.