Some journals request that authors follow a specific style manual (e.g., APA or Chicago manuals of style).
One style rule is to avoid starting a sentence with an abbreviation (with some exceptions).
However, I found it unnecessary to spell out abbreviations like ANOVA (analysis of variance) or FMM (finite mixture models) every time I start sentences with them.
Should I strictly follow such rules in academic writing?
Edit: My field is biohealth sciences.
Your writing should strive for maximal clarity in conveying your intended meaning to the reader -- that is the ultimate goal that overrides all other considerations. Style manuals are simply sets of rules that people came up with that aid writers to achieve that ultimate goal. To the extent that I would perceive a particular style rule on a particular occasion to be in conflict with the goal of conveying meaning effectively and concisely, I would see myself as free to ignore the rule.
The upshot is that as long as it doesn't happen too frequently, ignoring style rules is fine if you do it not out of laziness but out of a sincere desire to make the writing as clear as possible. If you do find yourself wanting to break the rules very frequently, you may want to consider the possibility that your intuition about what makes for clear writing is not yet sufficiently well-developed for you to make the best judgment calls on such things. In that case I would try to stick with the rules until you gain more experience.
I don't know about your field, but in mine you get a rocket if you deviate too much/too often. So I'd suggest you follow it pretty strictly, except for (as you note) terms such as ANOVA that, by the readership you're writing for, are better-known in that form than in the spelt-out form.
The first thing to know is that while some journals request that authors follow a specific style guide, it's rather rare that they enforce that rule. So you should be fine even if you insist on starting sentences with "ANOVA". I guess the answer to the question in your title is: to the extent that you find acceptable.
Worst case scenario, the editor will asks you to make some changes to the style.
This being said, I would try to follow the guidelines as much as possible. The rules generally have sound bases in terms of legibility, and at any rate it will not make your writing worse.
For example, I agree that starting sentences with "ANOVA is..." is bad style and I would stumble on every instance (is it a Germanism maybe?). But that doesn't mean you have to spell it out each time, actually you shouldn't do that. Just rephrase adding a determinant or changing the object.
In general, before violating a rule (or even following it, ideally), understand why it's there. Many rules help good writing. But others don't, but good style guides tend to avoid those—say, "don't start a sentence with a coordinating conjunction, like and, yet or but" (like in this sentence). http://www.writingconsultants.com/Guberman%27s%20Grammar%20Myths.pdf
I don't have my usage book with me and Google doesn't want to help me, but I'd think abbreviations, especially obscure, especially hard-to-pronounce ones (unlike ANOVA) make it harder to even start reading a sentence. Papers are hard enough to read otherwise. Imagine reading, dunno,
C18H21NO3 helps patients to overcome syndroms such as...
I made this example up on the spot so it's not great, but hopefully helps.
Indeed, the Chicago Manual of Style is fine with acronyms like ANOVA. http://www.chicagomanualofstyle.org/qanda/data/faq/topics/Abbreviations/faq0032.html
