Optimal stopping problem for PhD apps- is a year for an MS worth it?

[bayeslord]

Undergrad Institution: IIT Kanpur (India)

Major: Stats and Data Science

GPA: 8.4/10

Type of Student: International

GRE 170Q 169V

TOEFL 113/120

Relevant courses:
Statistical computing, stochastic processes (A), Statistical inference, Time series analysis, Regression analysis, reinforcement learning (B+)
Analysis, Probability theory (both C+ unfortunately)

Research experience:
Worked for a few months on variational inference at the Uni of Warwick, publication possible but probably after application deadlines

Work experience
Quant research internship at a (not very famous) hedge fund

Recommendations
Two from professors at Warwick and one from a prof at IITK I did a couple of courses with. Not really sure about the strength

Programs I want to Apply for: PhDs in Statistics/DS. Also open to MS programs at reach schools if there's a decent PhD conversion rate

Research interests
Probabilistic machine learning, Bayesian non-parametrics(GPs, Bayesian optimization, active learning), statistical computing (MCMC, stochastic optimization), reinforcement learning

Can someone suggest some good programs for my profile?

My dilemma is whether I should apply this year or complete my BS-MS in another year. I think I should only apply this year to the unis I'd prefer over the expected outcome of waiting a year (probably something like Duke).

My professor's advice is to not wait another year since it won't be worth the additional value to my profile in terms of chances of getting into reach schools that are meaningfully different in terms of opportunities and research quality.

Benefits to completing an MS:

* I would gain more research experience and possibly publish something 
* I could work with some of the professors at my uni who have realy great networks and get much stronger LoRs

The downside is, of course an additional year. 

Would the potential upside in terms of P(getting into a reach uni like Stanford/Cal/CMU) be worth the extra year?

Also, what unis would I stand a decent chance of gettin into this year?

[BL4CKxP3NGU1N]

You've only listed stats classes here. What math classes have you taken, and how well did you do in those? Math courses matter more for PhD applications than stats classes.

[bayeslord]

Only took real and complex analysis in my third semester, didn't do too well in those tbh (C+ i.e. 7/10). I'm unsure what I can do at this point to demonstrate my mathematical readiness- probably take graduate level measure theory and functional analysis courses in my MS and try getting good grades in those perhaps.

(Also I missed mentioning that I did a Bayesian stats course as well)

[arborio]

US universities love international students from IIT schools in India, you'll be fine.