The main comment I have is that you're still selling yourself as an astronomer rather than a data scientist. I want to know all about your transferable skills. Instead of telling me the astro-goals and astro-data you worked with, tell me what the problem or challenge was (in commercial terms if possible) and what skills you used to solve it, and where appropriate what outcome that produced - which doesn't have to be profit but saving time, resource, future effort / expense, etc. I want to see that you can come into a business and identify a problem, outline a plan to tackle it, and see that through to success with the end goal or target always in mind. And key to this beyond your advanced analysis skills is communication, project management and teamwork.
I know that's kind of a vague high-level summary so I'll try to highlight some specific ways to tailor your academic CV for a data science role.
This should be a concise summary of who you are and why you're *perfect* for the job. I want you to tell me you've got exceptional cutting-edge skills in statistics, maths, and computing (e.g. machine learning, optimisation, programming languages & algorithms), as well as a keen interest in the field of data science and commercial/industry applications and challenges. Crucial to this is your excellent transferable skills from managing team projects to communicating results. Don't tell me you've a heavy background in astrophysics because that tells me you're an astronomer and I'll worry you won't know how to handle problems outside of that field. Tell me all your skills that I'll be excited to have as part of my commercial team. I'll see later on that you've a background in astronomy and all the associated skills there, but before I get to that sell yourself purely as a data scientist first.
Go to town on any experience you have with a data science type of project you worked on! Seriously, I need to see what "real" data science experience you have under your belt so far. Show me that I'm looking at someone who knows the field and can hit the ground running. For example: how did you develop your ML code? Did it work? Who did you work with (independently, teammates, investors, stakeholders)? How did you measure success? How did you communicate your insights? What transferable skills did you use and did you pick up new? What advice/progress did you provide that they couldn't have achieved without you? Get me as interested in you as possible now while I'm fresh-eyed to your CV.
If you have little or no explicit commercial experience this is where it's difficult, as you need to really tailor your academic skills for non-academic roles. I suggest not to just title yourself as a "postdoc" since it can seem vague on its own, especially outside academia. Rather phrase it by project or break it down by skills. For example, were you called a "Data Analyst" or "Project Manager" or "Lead Developer" or similar, with or without "postdoc" attached to it. Obviously don't lie, just highlight the title you held on a project that means something to a non-academic and is still a true reflection of your position. In many academic roles you are the main driver of the effort, so emphasise any times that you led a team of astronomers to a result. Associated with this is any mentoring or supervision you've done as it shows real leadership. That is a great skill and something I'm delighted, as a hirer, to hear you've done - so tell me all about it! (Maybe call them scientists or researchers instead of astronomers, again just to remove the astro-specific side of it.) Tell me what skills you needed to lead, what your goals were, how you met them, what challenges you faced and how you were able to overcome them using your data science knowledge. I want to envision you doing the same thing for my company, so bring me on that journey. For example: "I led a team of 6 scientists to build and test a data pipeline that resulted in increased efficiency and new insight in blah. I managed the project from inception to success by engaging with key stakeholders, formulating milestones, communicating efficiently with the team, and meeting tight deadlines. My hard skills included bayesian modelling, developing python software, building unit tests, and utilising a version control system for teamwork and collaboration. I demonstrated our success / new results through data visualisations and monthly presentations and reports. The end goal improved data processing of blah by x% through improved efficiency and this translates to savings of $£€ in future research overheads/costs. As a direct result of my team's successes I was awarded blah / promoted to blah / presented with the opportunity to work on a bigger project / larger team / etc etc." Sell Sell Sell!
For your experiences as a grad student focus on all of the amazing skills you accumulated and demonstrated: project management, motivated/independent worker, strong research ability, insight, understanding, logical/critical thinking, imaginative, passionate and dedicated. Give examples of each, but again don't get caught up in astronomy-specifics of the data so much as the "challenge" you were presented with. E.g., don't say "redshift data blah to learn about galaxy formation blah", when you could say "noisy image data that required building a data cleaning & processing pipeline to analyse structures important for proving a cutting-edge statistical model, with measure of x% success". Focus on your skills rather than the astronomy. It requires effort for me reading your CV to try and put my commercial projects in the place of your astro-examples, so make it really easy for me to see how your training fits what I'm looking for and isn't tied only to astronomy.
Have a section on your technical skills and don't be humble or shy here. Mention everything you've ever dabbled with that you could talk about: from operating systems and coding languages to numerous software skills. A long list of different types of technical abilities is impressive here, which is generally true for modern astronomers. If useful, break it down into levels of proficiency. Have another section on your personal and professional development where you outline any online courses, teaching courses, seminars experience etc. and phrase it all again as having keen interest in various data science skills, data viz., communication, networking, etc. I want to see that you enjoy learning and keeping informed of advances in data science.
In your PhD your thesis details might confuse me (and your supervisors names might take up unnecessary room) so focus again on the transferable skills and technical abilities you gained. Maybe specifically list them in summary format, since you may already have detailed your projects above. E.g. quick google search lists:
I personally like to see an example of everything when it's mentioned, so try to succinctly do that as well. Demo every batch of skills you claim to have by an example case-study, where appropriate. For example, oral communication skills through monthly data presentations, leadership skills by chairing weekly team meetings, etc.
Beyond all of this, it's actually really important to tailor your CV for each specific opportunity, by highlighting all of the phrases and requirements in the job description and working those into your CV. I mention this for 2 reasons:
1) the HR/recruitment staff who first screen applications may simply use a list of requirements and scan your CV to tick them off, not knowing that your skills are transferable because it's not their domain of expertise, so if anything isn't there they might reject you;
2) anyone hiring wants to know that you're the perfect match on paper because bringing you in for interview is an effort for all involved, but is crucial to showing you can interact well and highlight your willingness to train and develop any skills gaps - something that's easier to do in person. You have to get in the door first! (This is why networking can be very important.)
So, for example, if it says you must know R then even if you have no R experience do some research into it so you can put it on your CV, because the truth is once you can code in one language you can pick up another very quickly, and this skill tends to snowball. But if it's not on your CV in the first place then you don't meet the requirement. In data science there are all sorts of "big data" skills like Hadoop/Spark/etc. that you should read up on to be able to talk about them and if necessary put them on your CV as something you're aware of but don't necessarily have working experience with yet. Be honest, but opportunistic! The point is you're skilled enough to pick these up very quickly compared to someone else. You've to show you understand the skills for the job or you'll be overlooked, especially at this early stage of your commercial experience. Getting to interview is key and you can study up for it as necessary, so really polish and tailor your CV often. Also don't be afraid if you think you only match half of a job description, they'll tend to ask for more than any one person usually can deliver (which is where the phrase "data science unicorn" comes in)!