Re: probability definition
This is a multi-part message in MIME format. --FF841A0334127EDA335D19E4 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit I'm glad to hear that somebody has his eye on the ball. Unfortunately, a designation of a region like "western Puerto Rico" means so many different things to so many different people, that I disbelieve its utility. With the definition you quote, we should have a 100% chance of precipitation almost every day. --FF841A0334127EDA335D19E4 Content-Type: text/x-vcard; charset=us-ascii; name="rabeldin.vcf" Content-Transfer-Encoding: 7bit Content-Description: Card for Richard A. Beldin Content-Disposition: attachment; filename="rabeldin.vcf" begin:vcard n:Beldin;Richard tel;home:787-255-2142 x-mozilla-html:TRUE url:netdial.caribe.net/~rabeldin/Home.html org:BELDIN Consulting Services version:2.1 email;internet:[EMAIL PROTECTED] title:Professional Statistician (retired) adr;quoted-printable:;;PO Box 716=0D=0A;Boquerón;PR;00622; fn:Richard A. Beldin end:vcard --FF841A0334127EDA335D19E4-- = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: probability definition
This is a multi-part message in MIME format. --3C6331B8C260BF767681A8B3 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit The "definition" via axioms provides a mathematical structure that we interpret either as "relative frequency" or as "degrees of belief". Indeed, I think that any phenomenon which satisfies the axioms can serve as an "interpretation". As they say, "If it walks like a duck, ...". As far as the probability of rain tomorrow, I always explained to my students that the language is so imprecise that the numerical value has only rhetorical utility. We need to know: 1) How much rain in cm. ? 2) In which locations? 3) During what time span? Does 70% probability mean that it rains in 70% of the locations or 70% of the time or what? Your instincts are correct. That example is severely flawed because we have not made the experiment clear. Continue to question the simple examples. You will learn from it. --3C6331B8C260BF767681A8B3 Content-Type: text/x-vcard; charset=us-ascii; name="rabeldin.vcf" Content-Transfer-Encoding: 7bit Content-Description: Card for Richard A. Beldin Content-Disposition: attachment; filename="rabeldin.vcf" begin:vcard n:Beldin;Richard tel;home:787-255-2142 x-mozilla-html:TRUE url:netdial.caribe.net/~rabeldin/Home.html org:BELDIN Consulting Services version:2.1 email;internet:[EMAIL PROTECTED] title:Professional Statistician (retired) adr;quoted-printable:;;PO Box 716=0D=0A;Boquerón;PR;00622; fn:Richard A. Beldin end:vcard --3C6331B8C260BF767681A8B3-- = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: probability definition
In article [EMAIL PROTECTED], "Richard A. Beldin" [EMAIL PROTECTED] wrote: This is a multi-part message in MIME format. --3C6331B8C260BF767681A8B3 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit The "definition" via axioms provides a mathematical structure that we interpret either as "relative frequency" or as "degrees of belief". Indeed, I think that any phenomenon which satisfies the axioms can serve as an "interpretation". As they say, "If it walks like a duck, ...". As far as the probability of rain tomorrow, I always explained to my students that the language is so imprecise that the numerical value has only rhetorical utility. We need to know: 1) How much rain in cm. ? 2) In which locations? 3) During what time span? Does 70% probability mean that it rains in 70% of the locations or 70% of the time or what? Your instincts are correct. That example is severely flawed because we have not made the experiment clear. Continue to question the simple examples. You will learn from it. Although in this case, in the US, the definition is quite precise for the National Weather Service. From their Operations Manual, it is "the likelihood of occurrence...of a precipitation event at any given point in the forecast area. The time period to which the PoP applies must be clearly stated (or unambiguously inferred from the forecast wording) since, without this, a numerical PoP value is meaningless." Elsewhere in the Ops Manual, a "precipitation event" is the occurrence of at least 0.01" of liquid equivalent precipitation (i.e., rain, melted snow). It has been shown that, given this definition, the PoP is equal to the expected areal coverage of the precipitation. Whether other groups issuing PoPs (media, other countries' weather services) follow the same definition, I don't know.At the locations where verification data are available, NWS PoP forecasts out through 48 hours are remarkably reliable. That is, if the PoP is N%, precipitation occurs very close to N% of the time. Harold -- [EMAIL PROTECTED] http://www.nssl.noaa.gov/~brooks/ Standard disclaimer Head, Mesoscale Applications Group, National Severe Storms Laboratory Norman, Oklahoma = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: probability definition
In article [EMAIL PROTECTED], James Ankeny [EMAIL PROTECTED] wrote: Hello, I have a question regarding the definition of probability. If I understand correctly, probability may be defined using just axioms. However, my textbook also uses a relative frequency definition, in which a probability is defined as being the proportion of times an outcome occurs in repeated trials of an experiment. This makes sense when one flip of the coin is one trial, and in repeated trials, the proportion of heads is 1/2. But what about a situation (an ex. in my textbook) where the probability of rain tomorrow is 0.70. How do you define this experiment? Perhaps you measure rainfall, temperature, pressure, etc. for each day over a long time period. Then the probability of rain tomorrow is the proportion of times that rain occurred on days with similar values for temp., humidity, etc.? This seems a bit awkard to me. Also, how many trials must one perform an experiment, before you know that the proportion converges to a particular fraction? Any help on interpretation of relative frequency probabilities would be greatly appreciated. In many cases, it seems difficult, at least for textbook examples, to define what the actual experiment is. I think it is dangerous, and even useless, to ATTEMPT to define probability. In physics, one no longer even tries to define length or mass, just specify their properties. It is the same with probability. A quantum mechanical model has a joint probability distribution for observations, but is worse between them. Just as we use the postulated properties for length and mass, we should use those for probabilities. We do have the nasty problem that there is no way we can accurately calculate probabilities, unless very strong additional assumptions are made. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =