What is probability?

Hi,

I am currently making a video for my youtube channel on probability. I would like to share the script with you as any comments/ideas are very welcome before I do all the recording & editing.

It is pretty basic stuff (for everyone who has looked into the subject), but things I'm acutally thinking about. I'm planning to do more on the subject in further videos.

So here it is:

Let’s think of a lottery. What is the probability that you get a prize? Of course you don’t know because you don’t know how many lottery tickets are marked as prizes. But from the perspective of the Flying Spaghetti Monster we would know because the omniscient Flying Spaghetti Monster does know how many lottery tickets are marked as prices. Let’s say it is 10%. If we now pick a ticket, is it then correct to say that this one, this particular ticket has a 10% chance to be a price? It has already decided beforehand if it is a price or not. It either is a price or it isn’t, we just don’t know. We could of course restate our statement from saying the lottery ticket has a 10% chance of being a price to our chance of getting a price. That being an event in the future, it might seem less determent. But for everyone who holds a deterministic worldview, the same problem occurs. (And for everybody else as well, if the future is indeed determined. They just don’t have to worry about it.) It is already determined if we get a prize or not.

The way school book statistics – or frequentist statistics - deals with that is that they interpret probability as relative frequency. For example, the relative frequency of a coin landing heads up is about ½ or the relative frequency of rolling a 6 with a regular dice is about 1/6 in the long run.
The opposing – or Bayesian - way to look at probability would be to express your belief that a coin is landing heads up or you are rolling a 6.

Obviously we need some prior experience or experiments to have a belief about the probability a coin is landing heads up. When asked to estimate how many blue balls are in a bucket of 10 balls we might not know and think that every number of balls from 0 to 10 is equally likely.

Let’s go back to the lottery example. When we look at it from a school book statistic viewpoint – of frequentist viewpoint – we do not know what the probability of getting a prize is unless we draw a lot of lottery tickets (with replacement) and calculate the relative frequency of getting a prize. Each one of the lottery tickets itself either wins or it doesn’t.

This might not be feasible, though, because our monetary means might be limited. So from the Bayesian point of view we could include our prior knowledge about winning a lottery into the estimate. If it says “Every ticket wins”, it should be ~100%, though we can doubt the value of the prize. If you can win only 3 cars (nothing else) and it is unknown how many tickets are given out, the probability is probably pretty low. If you set up the lottery and know that 10% of the tickets are marked as prizes you know the probability is 10%.

The important distinction is: From the frequentist viewpoint we can only know the relative frequency of getting a prize. From the Bayesian viewpoint we only know our degree of belief in getting a prize. Both probabilities are updated as more knowledge is gained – for example by experiments – but the updating is done in different ways. But that is beyond the scope of this video.

The question for this video is: What is probability? Is the objective frequentist view the right one or the subjective Bayesian one? Or are both correct at the same time or in different situations?

Let’s look at another example: A doctor tells a patient he has a 50% chance of surviving the next 12 month. But in the end, the only thing we know for sure is that he’ll either die within one year of not. He can’t survive 50%. Of course we can say that 50% of people with the disease die within one year, but that is a statement about the population of people with the disease and not the individual. The individual or does or does not die. (Within one year.)

Relative frequencies can only be obtained for the population of patients and not for the individual case. Repeated measurements are not possible unless the individual dead patient is able to arise of the dead.

So another possibility to say, that the patient has a 50% chance of surviving would be to say that the degree of belief (of the doctor) that the patient survives one year in 50%.  

Just a matter of terminology or a really fundamental difference? I would like to discuss that with you. Post in the comments.


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What do you think? Appropriate for a youtube video in length and content? Any further comments?

Just comment below or write me on twitter @Amoral_Atheist or at Google+.
I appreciate your opinion.

Decision making...

I work at a research institute as a research assistant while I'm (trying to) do(ing) my dissertation at the same time. A few month ago, probably about last October or November the person responsible for "research strategies" and such stuff gave a talk where she explained our chances to "survive" in science and what other job alternatives we might have.

In her talk she had one figure where she said the chances to get a untermed job in research IF you have a Phd are less than 0.1%. Again, IF you have a Phd, I don't have one yet. (To be fair, she also said, that we have plenty of other alternatives to get jobs... but that might not be what I'm interested in. And it seemed not too convincing for me.) 

In Germany, where I live, the problem is also that you are only allowed to hold termed jobs for 12 years (6 years after the Phd), so to live on termed jobs is no real possibility either. You have to get one of the rare untermend job sooner or not too much later or you are out.

Being unemployed with nearly 40 (after those 12 years in termed jobs) might not be too much fun, especially if you don't have any other working experience outside of research/science you can build upon.

Well, so that was the information I got. And while it is not completely new, the 0.1% figure was. I don't think it is necessary really that bad, but reality might be still quite devastating. And then, if you look who are the X% who ended up getting permanent jobs, you ask yourself if you want to be like they are. At least I ask myself if I want to be like them. (Of course there are nice ppl as well. But I still think that there is a pattern, like everywhere. Of course this isn't specific to science; it's just that in other jobs you can get a untermed job more easy.)

But that is not really what I wanted to tell... The point is, that she told us, that we really, really, really need a plan B, for the case we belong to the 99.9%. (Don't ask me why the institue employs her to tell us this, bc, when we all would focus on a plan B we obviously would have less time available to focus on the scientific work we are doing.)

I'm sure I neither belong to the best 0.1% nor to the boldest 0.1% so I looked after a plan B.

Because I studied Psychology (working in Neuroscience) I thought about doing the Cognitive Behavioral Therapy Education. I have to say, that this is something I NEVER wanted to do. I wanted to work in research. I think learning about the human mind (in the Therapy Education) might be interesting, but that is about all positive I can think and say about it. Everything else is just very frightening for me. Or in other words, I really don't want to do it, I know I can't, I know I'm not the right person for this. I was a very stupid idea to even consider this. However, I managed to sign the contract for the therapy education... why? I don't know. I mean, it is nothing you do in 5 minutes; you have to apply for it and pass the test and everything.

I convinced myself that I would be interesting to learn these things (and it probably is, but it is a very expensive way to learn this) and then I was - no I am - very dissapointed by the way science/research works (publication biases, problems to publish negative results, statistical methods, lots of underpowered studies, replications not valued in some fields, etc.) and of course scared by the prospect of my possible future (unemployed by 40 if not earlier). And I was/am surrounded by ppl how were/are judging pain patients because they felt bothered by them. I'm sure I wouldn't feel the same way, cause I understand pain sucks and then I'm not bothered very easily (I think at least).

But now, that the start of the education comes sooner and sooner, I just know that I CAN'T give advice to patients. Hell, I don't even know what to say in normal conversations, how I would know what to say to a patient. Most things are very complicated and there are lots of possible ways to look at them... I would only confuse the patients. And would myself never be sure if I understood what the patient meant, just because there are so many different ways of understanding everything...

And then, I don't know if I have the standard opinion on everything. I.E. I'm really unjudgmental (I think, compared to others) and you might think that is good, but it might not always be, because sometimes patients might need advice in that direction just to feel better (and that is the goal of therapy, right? Of course not on the cost of others, but that they feel better.). But I wouldn't be able to do that (it's confusing enough for me).

So now... what do I do? Do I try to get out of that contract (might or might not be possible, but maybe I should figure out). (It might be that someone else who really likes to have that place would get it then, but I don't know.) Or do I spend 5 years of my life (and most of the money I earn) in that education? Of course I have to keep in mind, that jobs in research are and will be very unsave. But I think I wouldn't be a good therapist. So that might answer the question.

Can it be right to make decisions for other people?

On Saturday, as I was walking home on busy streets and busy places... when I was seeing an homeless person* resting on the balustrade to a little artificial pond. This might sound strange, but it actually isn't. The balustrade is low and you can sit on it quite comfortably. He was lying on it. Besides him were standing a couple bottles of beer. I couldn't see if they were all empty but some were. So... I didn't know if he was just resting or if he was in serious danger from alcohol intoxication or if he was about to fall into the pond. I stood there and watched to see if he was breathing or not, while a lot of people were walking by. He was breathing, but he was also moving towards the pond (shifting his weight in this direction).
So I went to him and asked him if he was ok. At first he didn't answer, so I repeated my question and he finally hummed something, but I couldn't understand. I told him, that this was dangerous, but obviously he was not interested in my concerns.
A man stopped his bike, starred, not exactly in that direction, but somewhere and after a few minutes (or maybe less, I don't know) he continued his ride. 
I could have asked him for help, but what else could he have done? Well, I hadn't had my mobile phone with me, so I couldn't call the ambulance. But there was another woman, about 60 to 70 years old, who was sitting in a restaurant nearby and was watching the situation. I went to her. She asked me, if it was his beer. I said, that I don't know and she went with me. She then screamed at him louder than I did before (well, I didn't, I just tried to talk to him) and after that she slapped him in the face a few times. He woke up and she told him to get up. Then a man went by. He called the ambulance then, although the man (the probably homeless one) said he didn't want one.
So I thanked them and went home.

There are some people who think that it is ALWAYS, and defiantly ALWAYS false to lie, to slap someone, to hit someone, to kill, to ... (fill in with things which are mostly seen as not ok), i.e. some things are just categorically false. I do not think so! But why didn't I slap him in the face? Maybe I'm just a scaredy-cat, that is totally possibly. And he had a jack knife in his hand. But it was closed and it was quite fast clear that he was no real danger. Maybe I don't like to decide over people. It was quite clear, he just wanted to lie there and rest, maybe sleep out the alcohol and not be bothered by anyone. Just because he might not have a home, why shouldn't he have a right to be not bothered? He didn't do any harm. So why did I bother then? I could have gone along like all the other people did? And I thought about it, but I would have felt bad if he had died BECAUSE OF ME. Of course there would have been a great chance that he would not have died but I might not find out.

This is, of course, extremely egoistic: that I only cared about his death because I would have felt bad if he died because of me. (I'm not even sure if I did, so I should say: I might feel bad, because...). I wanted to avoid being sleepless thinking about weather he is dead or alive. I'm very clear about this, as I was thinking in that situation "Oh shit, I will not be able to sleep... if..." (this is shorted but in essence what I thought). And now, unfortunately, I'm sleepless, thinking... this.

Obviously, the other people, who just went by, were not as concerned about their well being as I was. That was the reason I decided to interfere. What bothers me is, that I obviously have no idea if it was good for him or not, I simply can't know. That might be a philosophical question (too)?


* I assume. Maybe he wasn't. I don't know.

P.S.: I had to look I few words up, (it is difficult to decide which are the words used in "real language" if you don't know them), I hope this makes some sense.

Some people spend tremendous energy merely to be normal - 

and some people spend tremendous energy merely to exist.

What kind of studies should be done?

Should questions be answered that are already be "common sense" but have not been scientifically validated yet or should the focus be on new discoveries?

In the following video I try to explore this question:

Additional information:

Their study design was basically the following. In a training phase the dogs were shown pictures with either happy or angry human expressions on it and rewarded to touch it (either the happy or the angry one) on a touch screen monitor. The trick is that they were only shown either the upper or the lower half of the picture. In the test phase the dogs where then shown either the same part of the picture (upper or lower) or just the left half of faces. (If dogs were shown the same half, it was always novel, if dogs were shown the other half, it could be either novel or from the same faces as in the training phase. The left-half faces were the same the dogs already saw in the training phase but only the left half.) So what is the hypothesis then? The hypothesis is, that if dogs only learn to discriminate the faces based on local cues in the training phase then they should be able to do the discrimination in the test phase if shown novel faces of the same half but not if shown “old” or novel faces of the other half, because there the local cues are not present. To discriminate between faces of which the other half was shown in the test phase the dogs had to learn more general/global cues present in the picture, i.e. emotion.

However, they have four test conditions (novel face same half, training face other half, novel face other half, training face left half) with 11 dogs and 10 trails per dog and condition. So their standard errors are huge and therefore it would but difficult to detect any difference between the conditions, if present. (One could assume that the dogs in the novel face same half and training face left half are better than in the novel face other half condition, because there more cues remain the same.) They shown, that there is no difference, but of course there isn’t. The variation is too big. (Pause my video at 1:50 to see the related figure.)

How did they show that the dogs really decode the emotion and not some other more general/global cue? Well, they rewarded some dogs for touching the happy and some dogs for touch the angry face (problem here: it doesn’t seem to be randomized, the first 9 dogs were in the happy-condition, the next 9 dogs were in the angry condition… unlikely to get that by chance) and their finding was, that in the test phase, the dogs responded slower to the angry face. However, shouldn’t the dogs show the same reaction the in training phase? Another explanation might be, that angry faces are more difficult to decode than happy faces because the cues in happy faces are more prominent (or dogs these dogs had more experience with them).

I don’t argue against the ability of dogs to discriminate human emotions. However, based on the data of their study I wouldn’t bet on their ability to discriminate human emotions from halved pictures of human faces. But it is difficult to argue against that; because not a lot of data are presented (the data are not very detailed at all). (It is just a “report” not an “original study”).
To the problem with the pet-psychics (or pseudo-science in general): Of course scientific findings can’t be hidden just because they might be used by someone in a false way. But uncertainties in the findings need to be expressed and (in general) findings shouldn’t be misrepresented by people reporting them. In this case I think we don’t know much more than before, other than that they developed a innovative paradigm, what is great but what is not what is reported about.

What is your opinion on this topic?