**You can always select all. **
Historically there has been some unnecessary competition between different methods of doing nlp, this is kind of artificial and basically just harming progress. Rules and statistics and neural networks are just tools to do things, you cannot really reach optimal result without using right tools. Especially in academia people have always been enamoured to following pure approaches, in practice it's like playing a game of how far can you go blindfolded with hands tied.
There's a very simple, rule of thumb kind of logic to when and where to use which approaches:
- rule-based approach is based on knowledge and logic, if you can figure something out by using just pieces of information that can be encoded (e.g. in dictionaries~lexical databases) and deduction that can be described to computers (e.g. logical rules in programming language), you will be guaranteed a 100 % success rate
- when you eventually face something that you cannot explain based on linguistic knowledge of words and deduction (and anything else), knowledge derived from statistics counted from large corpora of words is obvious next source of information (this is statistical NLP)
- when you eventually face something that does not appear to be solved by throwing simple statistics from corpora at it, neural networks can be trained to learn to imitate more complex patterns from data
There are so many linguistic questions we have 100 % guaranteed answer that we know that starting with pure neural network approach is absolutely waste of time, to give a simple example an application that only needs to figure out single words linguistic features (is it spelled correctly? what language is it? what are it's possible parts-of-speech, morphological analyses, translations to language X?), we all know this can be looked up from a dictionary, while counting statistics and learning neural networks from relevant data might not even lead to correct answer 100 % of the time. Here is where being allergic to rule-based NLP can really cost a lot. On the other hand, some simple related tasks of these examples: if the word is not spelled correctly in language X, what might be a correct spelling; if word has multiple possible analyses, what are more likely etc.; you can get very far with only collecting linguistic evidence that is not based on statistics and frequencies, however, statistics and frequencies are actually linguistic evidence as well so it would be illogical to ignore them. The cases where neither all the knowledge you can gather up from words and contexts and frequencies and statistics are not enough to give good answers in end user applications are many, this is why neural networks have been such a killer app for NLP, and their most prominent use: guessing the next word in sentence given the first few words; if you understand linguistics, or logics or mathematics or anything really, you know this is a very ill-defined task, there is no logically superior solution to such questions it is simply guessing from input that definitely has not got sufficient data to have one correct and complete solution; but there are some solutions that seem more acceptable than others and knowledge and logic and statistics (of the words that are there) alone do not seem to lead to this solution alone. Neural networks can be optimised to do this prediction by training them specifically and it may encode something we cannot put into code, data or statistics that is usable information about, should one say, linguistic intuition and world knowledge? To give a less contested example, the word sense disambiguation in machine translation is ideal task to see whether you can explain something with pure linguistics and logics based on local context (the words you see in same sentence ~ paragraph), whether you have to resort to statistics when explaining your decision or whether it's up to language intuition; as any competent linguist is likely to use all three to explain translations so should a computer when translating, no?