# Probability and time series

1. Feb 25, 2014

### sthoriginal

hi

I'm a physician and really need help from somebody who is good at probability. I calculated time series of tidal stresses. It turned out that the probability of having positive tidal stress is 0.45 and negative - 0.55 (I counted up number of hours when the stress was positive/negative and divided by the total number of hours). Usually you would expect to have 0.5 for positive stress and 0.5 for negative. So now, if we assume that an earthquake occurs at random, does it mean that there is 0.45 chance that it happens when the stress is positive? if yes, what is the probability that this earthquake occurs within some one particular hour when the stress is positive (e.g. within one hour centred on a max tidal stress)? Is it also 0.45?

I'd be really grateful if somebody can help me with it. Thanks a lot

2. Feb 25, 2014

### Stephen Tashi

The meaning of that question isn't clear. I suggest you give an example of your question using a table of data or a graph.

3. Feb 25, 2014

### sthoriginal

thanks for your replay. please have a look at the image file i attached. you can see that for 4 h the tidal stress was positive and for 6h negative. So the probability of an earthquake happening when the stress was positive was 0.4 and when the stress was negative - 0.6. does it mean that the probability of the earthquake randomly happened at the exact tidal maximum (red on a pic) is 0.4 and tidal min - 0.6)?

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4. Feb 25, 2014

### Stephen Tashi

The probability of an earthquake happening exactly at hour 2 is 1/10 if the hour is selected with equal probability from the hours 1,2...10.

If you analyze this to introduce the conditions of positive and negative stress, you get the same answer.

pr( quake happens at hr = 2) = pr( quake happens at hr of positive stress) pr(quake happens at hr = 2 given hr has positive stress) = (4/10) ( 1/4) = 1/10.

5. Feb 25, 2014

### sthoriginal

What if we only know that the probability that an earthquake occurs when stress is positive is 0.4 and 0.6 when stress is negative and we have 1000 recorded during 1 h when the stress was positive and during one hour when stress was negative. can we assume then (using the probability values) that 400 events happened during the hour of the positive stress and 600 when the stress was negative? thanks again for your effort!

6. Feb 25, 2014

### Stephen Tashi

You can't assume that unless the 1000 records were the data used to estimate the probability values. The probability of an event and the observed frequency of an event in a given experiment and not the same thing.

For example, a typical sort of textbook question is "If a fair coin is thrown 10 times, what is the probability of 3 heads?". An outcome of 3 heads is a fraction of 3/10. It is a possible outcome of an experiment where the coin has a probability of 1/2 of landing heads on each toss.

7. Feb 25, 2014

### sthoriginal

what if these 1000 events are a sample taken from population that was used to estimate the probability 0.4 to 0.6?

8. Feb 25, 2014

### Stephen Tashi

If the probability of a randomly selected hr. having positive stress was estimated from the sample in the straightforward way then the sample had exactly 400 hours with positive stress and 600 with negative stress.

9. Feb 26, 2014