Prometheus

The maths i was thinking is stuff like stochastic calculus, statistical inference and measure theory - pretty rigorous stuff. I'm not sure about the stuff in that link you provided, i haven't heard of any of it, like M-waves. From your description it does look like BS though. It may be that some places offer decent courses while others do not.

If the maths is thorough i've no problem with it being taught for credit, but any model stands or falls on how well it holds up to the assumptions it makes: i think this is where financial modelling falls. It's future might be brighter though: you could think of financial modelling as just an application of quantitative social science. Now we have data sets kindly provided by Facebook and co to anyone an their mother, and with developing machine learning techniques, we are starting to see rigorous mathematical applications in social sciences.

I guess you must be using some kind of time series analysis, an ARIMA model perhaps, which assumes past information is sufficient to predict the future. This can work if the assumption is reasonable - if you are running an airline company and have observed a seasonality in the data (i.e. more people fly in summer), that can be usefully modelled. But this simple model can't take into account events like shooting down a plane (unless it happens regularly) which shocks the market. A better model might be something like the Black-Scholes equation which models market ups and downs as a Brownian motion (i think it makes the assumption that time is independent). As i understand it the important parameter is the variance (or market volatility) as it makes the likely range of predictions (under monte carlo simulations) broader. I'm not sure how useful it is in practice though, people in the business must already know more unpredictability means more risk. Horoscopes might work just as well for these decisions, i wouldn't call it a science. Interestingly, i came across a particular MSc course called Financial Engineering which costs £20,000, which with the selection of certain modules was identical to an Applied Statistics MSc which cost £8,000. People were willing to pay just for the name of the MSc.

The conundrum comes when supporting one person may adversely effect another person. Lets take a silly example that some treatment to sustain your life for possibly 6 more months costs a million pounds. There are 60 people waiting for a hip operation who will have to wait years longer in pain and disability if your treatment is approved. This is a caricature, but health providers do have to make these sorts of decisions at some point. Any one individual cannot be given primacy in the system because the system is comprised of a great many individuals. I assume you are American? I only ask because i have noticed it is usually Americans who balk the most at the idea that the needs of an individual may be over-ridden by the needs of society. What works in the UK and other parts of the world would not be accepted in the US.

Thanks. I can understand why molecules will most likely start in the ground state - although the proportion of molecules in this state must follow some kind of Boltzmann distribution dependent on temperature. But in Raman scattering we see stokes and anti-stokes scattering, energy lost and gained, so i'm not sure how the starting state influences the type of scattering. The latter part of that statement suggests return to the ground state is most probable - i assume this has something to do with selection rules and quantum numbers so i'm slowly reading up on these (probably the former part too). What i really want is a mathematical description of these: i will likely need to revise my physics a bit to understand it, but until i do i won't understand. Any hints or resources on the maths i should be reading up on would be greatly appreciated.

This is the best answer i have yet received on this topic, but my understanding is lacking. I will revise quantum numbers and come back - i think they cropped up during the solutions to solving SE due to the imposition of certain constraints.

I don't really understand what point you are trying to make. If patients want information about their condition and input into their care i absolutely agree it should be accomodated. It generally is.

Trouble shooting is one of the most important aspects of programming. I would recommend you go through your code line by line and check it does what you think it does. First instance what do you think rand(0,1) is doing? If you run just this line do you get a value of x you expect or something else? Type help rand into your command window to see why it might not be doing what you expect and some suggested alternatives.

I often hear that Rayleigh scattering is several orders of magnitude more common than Raman scattering; for instance here is one description. However, i have not come across any explanations as to why this is so. I presume it has something to do with Raman being an inelastic process. Does anyone know of any quantum or classical derivations showing why Rayleigh is so much more common than Raman scattering?

So you want flip a coin d times and plot the outcomes for different parameters of that coin? Or do you want to run a monte carlo simulation to check the probability of getting n heads from d flips? What have you tried so far?

Yep. CPR isn't assessed by NICE though. If they did that US study i linked to earlier suggests they wouldn't offer it to octogenarians at current thresholds.

But the doctor isn't just concerned with THE patient: they will have many patients. Any decision regarding one patient will likely have an impact on another patient, including financial decisions. Doctors will already sometimes triage patients in extreme situations, choosing not to save one person in order to focus on someone else more likely to survive. Financial limits exist and they force these life and death decisions. Yes each person has paid into the pot, but it's not an infinite pot and paying in shouldn't mean you can take out so much it's to the detriment of others. If you want to pay into your own pot we have private healthcare insurance too.

The counter argument is that sustaining a life will cost the healthcare provider money. This money is not an infinite resource; by spending money on keeping one person alive necessarily impacts upon the care, and even the life or death, of another person. At some point it will become unreasonable to sustain one life at considerable cost: the money would do more good and save more lives spent elsewhere. These things are already considered in the UK when deciding whether to licence the use of certain drugs. The question is whether to extend it to DNR decisions. There is always a case that resources can be diverted away from, say, military spending (a common argument in the UK) to avoid such problems but i think that's just kicking the can down the road. I'm not sure it would save much money. Many signing DNR go on to die relatively soon anyway (can't remember the figures right now) and i would hope we divert resources into good end of life care (currently lacking in the UK) which might up eating up any financial savings. However, if it improves end of life care i think this would be preferential.

Try this link. It's an extract from a book (seems OK); you should be able to find the details of it for a full reference. I googled 'equation for fourth standardised moment'.

We create meaning because the human brain is an organ that constructs meaning: presumably it benefits us as a species. It's just another thing the universe does when the conditions are right for it: another swirl in a mote of dust , no more or less real than the formation of spiral arms in galaxies. We could attempt to deconstruct it and ask what is going on, but i think it would be a mistake to treat it as an illusion. At some point though you just got to try to enjoy the ride.

You can find moment generating functions in just about any book on fundamental statistics, something like A First Course in Probability by Sheldon Ross. I'm not sure of a specific book with the specific equations you want. There are plenty of books on google you can check - they'de be under moment generating functions or MGFs section (or maybe under a thorough chapter on expectation).

Yes. This is essentially the same as working out the first four terms in a moment generating function. -3 from the last one if you want the excess kurtosis rather than vanilla kurtosis for some reason. This page might be helpful.

By develop the pdf do you mean you have developed a closed form for it? If so, calculating the moment generating function would be the best (most precise) way. It's not too hard to calculate assuming the pdf isn't some beast of a function - it's an integral of the pdf exponentiated. Post it here, i'm sure a few people would have a go. If you have an empirical distribution rather than the closed form there are estimators for skew/kurtosis - something like R should have a function, or at least a package, to do this. If you have a closed form and really don't fancy the integral you could build an empirical distribution by taking samples from your distribution and then use an estimator for skew/kurtosis. Should converge to the true values for a sufficient number of samples, assuming the estimators aren't biased.

Do you know about moment generating functions?

This paper explores some of the mood-changing organisms, might be a good place to start.

Yep. Except you could divide sci-fi authors into two camps: those who actually try to extrapolate the future based on current scientific progress and those who just want to tell a story within the context of some future, fanciful or otherwise. But in an attempt to keep this on-topic i'd be interested to know about any sci-fi stories which utilise the microbiome. Maybe plants influencing humans by introducing some organisms into the human gut flora.

And everyone forgets all the sci-fi that unsuccessfully predicted the future: aka most sci-fi.

Digitise poetry? William Blake must be spinning like a neutron star in his grave.

Not sure i get your point. That document refers to actual in-hospital do not attempt resus orders. By non-medically indicated attempts you mean out of hospital attempts by by-standers?

That would be part of the awareness campaign. Even in hospital CPR has a very low 'success' rate - success being simply to get the heart beating again. I think it's something like 3% of CPR survivors will return to a near normal life. Check out point 10 of this document: Should be noted this is far from the norm. But ultimately healthcare professionals can choose not to resuscitate.