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I understand that honesty is the best policy, but is it a good idea to say "I have no clue" when the SOP explicitly asks me to describe my "intentions relative to graduate study and life beyond the University"?

Basically, I don't have any ten-year plan. The main reason I'm going to apply for the Program at the University is that the Degree can give me great resources and offer me better choices after graduation. (Other reasons include I have friends in that area and I love the weather in California, but I guess those don't count?) I haven't really considered my life beyond the University, though: Life is just too dynamic for me to answer questions like whether to stay in academia or to enter the industry at this point, and I don't want to eliminate any possibility as early as now.

On the other hand, I do have some long-term goals, but I don't have a detailed plan on how to realize them. I just keep them in mind when making decisions. However, these goals are probably too ambitious, bold, and maybe stupid to be used as an intention: I'm going to develop a framework to unify Statistics and Machine Learning, turning all current work into "miscellaneous earlier efforts" like Newton did!

To clarify, I'm applying to both Masters and Ph.D. programs, because I don't really know what I'm after, so I'm just exploring different options and will take the best offered.

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    There are 2 close votes now, without a single comment to explain you need more focus on what specific aspect. Honestly, this question sounds quite detailed to me, so before you are going to cast a close vote, please comment to say how can I improve it. Thanks. – nalzok Dec 14 '19 at 11:12
  • Well, this sounds like a request for a list of items to put in your statement of purpose... We can't write that for you. – Solar Mike Dec 14 '19 at 11:57
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    @SolarMike It's my bad if many people think so, but I'm specifically asking about how to phrase the "Why School" part of my SOP without sounding like I have no idea what I'm doing. For the record, I find wimi's answer very helpful, even if s/he didn't provide a list. – nalzok Dec 14 '19 at 12:02
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"I have no clue" is not going to get you far. The committee will probably interpret that you will not be very motivated, and motivation plays a big role in succeeding in study programs, especially if they include research.

You are also not expected to know exactly what you want to do the following ten years. From your question, you seem to know as much or as little about your future plans as the average applicant to graduate study, maybe even above average.

You are interested in the topic, and want to study further to learn more about it and have a better chance to make valuable contributions, either in academia or in industry. Say that.

You are not sure yet whether you want to continue in industry or academia, but you want to experience research in academia and be able to make a better informed decision afterwards. Say that if it is true.

You can mention your long-term goal, but make sure not to make it sound too ambitious/impossible to do. For example, I am interested in analyzing Machine Learning from a statistical point of view, with the aim to hopefully provide the community with a better understanding of why artificial intelligence is so powerful. Suit this to your own needs.

The fact that you have friends there and like the weather is in my opinion also worth mentioning, but without focusing on it. Mention it last, and only in one short sentence. Although this does not say anything about your ability to do research, it adds to your motivation to go there.

And just in case, do not copy-paste any of my sentences, but use them as a guide to come up with your own. This is about your motivation (not mine), and answers on StackExchange are public and easy to find.

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I'm applying to both Masters and Ph.D. programs, because I don't really know what I'm after

Figure out what you want first, then apply for graduate school if necessary. The question clearly shows you are not ready for graduate school yet. Do something that pays well while you figure out your goals.

However, these goals are probably too ambitious, bold, and maybe stupid to be used as an intention: I'm going to develop a framework to unify Statistics and Machine Learning, turning all current work into "miscellaneous earlier efforts" like Newton did!

That's not too bold, just don't say you will do it next week. You might achieve that over the course of a career. It could be phrased better.

What are acceptable purposes in Statement of Purpose?

For a PhD, there is only one purpose: to conduct research in some specialized topic.

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