Thanks for the article. I appreciate it and cherish probability theory. I did find it hard to read because of sloppy markdown though and recommend you replace:
(\theta)
with θ or (θ) depending on what you mean.
If struggling with Greek characters BTW you can rest confident in 2021 that almost any context in which you are writing or reading, unicode accepted (the days of uncertainty in this space while not completely behind us are effectively so). And so you can always search on-line for say "Unicode Theta" and copy/paste.
I'd also counsel against claims like:
"the often incorrect use of these terms interchangeably"
There is nothing, repeat, nothing incorrect about using these terms interchangeably. The claim rests in a misunderstanding or misrepresentation of language and its context. These terms are synonyms and they can be used interchangeably, as evidenced by the fact that they are!
When a specific discipline applies English words in a specific ways, then these terms are defined clearly for use within that discipline and often found well defined in texts on the subject (albeit often omitted from academic papers when the discipline is clear from the context - typically the journal publishing the paper and its narrow focus).
In this case you're referring specifically to Probability Theory in which Probability is generally an idea attached to outcomes or results while Likelihood is attached to hypothesis of models. Both describe in their own way confidence or uncertainty (on a scale of 0 certainly not to 1 certainly so and anything in between with 0.5 roughly anyman's guess or could go either way who knows?).
But probability is a measure of likelihood in common parlance likelihood is measured by probability in common parlance and that is not an error, that is, the common tongue, as distinct from the in-discipline jargon. To wit when using the terms one needs a clear context to be tabled, and lacking one, the common parlance is generally the safe assumption as anyone in-discipline will (and should) make the context clear.
Finally, a stylistic tip for on-line writing: In your into, start with the conclusion or premise if you will, the claim that the body will make clear .... I also found this a tad hard to read as I like many am an impatient on-line reader and I'm immediately into a section on what probability is and asking myself "cut to the chase" (as in I know what probability is). The introduction would work well to table the a priori claim that in probability theory, Probability is used to describe the chance of a given result or outcome, and Likelihood us used to describe the chance that a given hypothesis or model is accurate ... allow me to explain ... and then proceed into the two following sections. This whets the appetite, and draws a reader in if they want, and allows more experienced readers to nod, and think aha, good reminder and move on.
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Thanks for the article. I appreciate it and cherish probability theory. I did find it hard to read because of sloppy markdown though and recommend you replace:
(\theta)
with θ or (θ) depending on what you mean.
If struggling with Greek characters BTW you can rest confident in 2021 that almost any context in which you are writing or reading, unicode accepted (the days of uncertainty in this space while not completely behind us are effectively so). And so you can always search on-line for say "Unicode Theta" and copy/paste.
I'd also counsel against claims like:
"the often incorrect use of these terms interchangeably"
There is nothing, repeat, nothing incorrect about using these terms interchangeably. The claim rests in a misunderstanding or misrepresentation of language and its context. These terms are synonyms and they can be used interchangeably, as evidenced by the fact that they are!
When a specific discipline applies English words in a specific ways, then these terms are defined clearly for use within that discipline and often found well defined in texts on the subject (albeit often omitted from academic papers when the discipline is clear from the context - typically the journal publishing the paper and its narrow focus).
In this case you're referring specifically to Probability Theory in which Probability is generally an idea attached to outcomes or results while Likelihood is attached to hypothesis of models. Both describe in their own way confidence or uncertainty (on a scale of 0 certainly not to 1 certainly so and anything in between with 0.5 roughly anyman's guess or could go either way who knows?).
But probability is a measure of likelihood in common parlance likelihood is measured by probability in common parlance and that is not an error, that is, the common tongue, as distinct from the in-discipline jargon. To wit when using the terms one needs a clear context to be tabled, and lacking one, the common parlance is generally the safe assumption as anyone in-discipline will (and should) make the context clear.
Finally, a stylistic tip for on-line writing: In your into, start with the conclusion or premise if you will, the claim that the body will make clear .... I also found this a tad hard to read as I like many am an impatient on-line reader and I'm immediately into a section on what probability is and asking myself "cut to the chase" (as in I know what probability is). The introduction would work well to table the a priori claim that in probability theory, Probability is used to describe the chance of a given result or outcome, and Likelihood us used to describe the chance that a given hypothesis or model is accurate ... allow me to explain ... and then proceed into the two following sections. This whets the appetite, and draws a reader in if they want, and allows more experienced readers to nod, and think aha, good reminder and move on.