Final Project
STAT 3303: Bayesian Analysis and Statistical Decision Making
Due: Sunday, April 28, 2024 (submit on Carmen by midnight)
INSTRUCTIONS
This is an exam and should be treated as such. DO NOT discuss any aspect of this exam with anyone,
including MSLC tutors, other than your instructor. This includes, but is not limited to, not discussing
report structure, coding problems, instructor expectations, how long the exam took you, whether you finished
it, etc. You are responsible for ensuring that other students do not have access to your exam. You may search
online for general coding questions (i.e., “how do I pass through my seed to rjags?”) through websites such
as StackExchange. Use of AI for coding or to assist with the write-up is highly inadvisable (see below).
Any violation of these instructions constitutes academic misconduct and will be reported to the university’s
Committee on Academic Misconduct.
PROBLEM STATEMENT
For sexually reproducing species, the equilibrium ratio of male and female individuals of reproductive age
is a 50/50 ratio. Fisher explained why this would be true – if the ratio deviated from 50/50, it would be
reproductively advantageous for a child to be born of the less frequent gender and the ratio would then
be restored. At birth, among the general population, this ratio is not met – more boys than girls are born
(the proportion of female births is 0.485). Fisher explained this fact is due to higher mortality rates (due
to disease and violence) among boys prior to reaching puberty, and so a disproportionate number of boys
“need” to be born to maintain the equilibrium.
The sex ratio can deviate from the overall average in subpopulations. We saw one example in class, where
placenta previa is associated with a male birth. We will study another possible example in this research
project.
An urban legend exists among U.S. Navy submariners that they disproportionately father girls.1 The belief is
common enough that in 2003 researchers at Bathesda Naval Hospital decided to formally examine whether
it was true and attempt to determine a cause. After obtaining national security and research ethics approvals,
they sent surveys to all submariners stationed at six submarine bases, asking if they had a child born in the
last 12 months, the sex of the child, and a number of work-related demographic questions. They received
responses from 1000 sailors.
A number of causes have been proposed for why submariners may have more girls (if such an effect exists).
The environment is highly stressful, with an erratic and limited sleep schedule. The atmosphere is enclosed
and differs from the normal Earth atmosphere – typical oxygen levels kept are 3-4 percentage points lower
than normal, CO2 levels can be high and require chemical treatment to prevent acute harm to sailors, and all
1At the time of the research this project is based on, submariners were all male. While that has changed, the number of babies
born to female submariners is too small for any useful analysis.
sorts of potentially harmful things like hydraulic oils and refrigerants can leak into the air and remain in the
closed environment. The effects of radiation, either from the nuclear reactor or from the nuclear warheads
carried on board some submarines, may also be a cause. To test these hypotheses, the researchers obtained
data on the following variables:
sea binary indicator where 1 indicates the sailor is currently assigned to a submarine. Sailors will typically
alternate between 2-3 years working directly onboard a submarine and 1-2 years in administrative
duties on shore.
BN binary indicator where 1 indicates the sailor is assigned to a ballistic missile submarine (if sea=1) or his
last command was a ballistic missile submarine (if sea=0). U.S. Navy submarines can be classified
into two types: those that carry nuclear-armed ballistic missiles and those that don’t.
engineering binary indicator where 1 indicates the sailor works directly with the nuclear reactor of a sub-
marine (again, if sea=0 this refers to his last assignment)
weaps binary indicator where 1 indicates the sailor works directly on nuclear weapons (again, if sea=0 this
refers to his last assignment)
time in service a quantitative variable that indicates time in years since the sailor began submarine service
girl binary indicator where 1 indicates the sailor’s child is a girl
ASSIGNMENT:
Write a formal research report as if you were one of the researchers at Bethesda reporting your findings to
your supervisor. Your report should begin with a general discussion of the research question, a description
of your data (don’t forget your exploratory data analysis) including limitations and potential sources of bias.
Only then should you move on to describing your model and reaching some conclusions. Be sure to define
all variables and interpret model parameters to your audience and state whether you have evidence of an
effect and whether or any particular cause can be supported by the data. You will be graded on the level of
professionalism in the report as well as the statistics, so obvious use of AI or any “hallucinations” will be
severely penalized.
Specific modeling guidelines:
1. You should propose a Bayesian regression model for the probability that a sailor with a certain set of
covariates has a girl. For your priors, you should use the guidance from the lecture notes on Bayesian
regression – you do not want to use a weakly uninformative prior as it is highly unlikely that there
will be very large effect sizes.
2. Specify your model in detail, including conditional independence and prior assumptions (providing
just your code is NOT sufficient).
3. Provide details on model fitting (what were your starting values, how many iterations did your algo-
rithm run, how did you diagnose convergence of the model fitting algorithm).
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4. Provide interpretations of the results of your statistical analysis in the context of the problem with
particular focus on what parameters have a high posterior probability of differing from zero.
5. You should include at least one posterior predictive estimate for the probability of a girl for a given
set of covariates.
FORMATTING GUIDELINES:
• Your report should be typed. You may use R Markdown if you wish, but DO NOT include any code
in the main body of your report.
• Again, carefully proofread and spell check your report. Write in complete sentences and in para-
graphs, not bulleted lists.
• Define all mathematical notation in the text of the report.
• Make sure all figures/tables are straightforward to understand, have captions, and are referenced in
the text.
• Include commented code in an appendix.
• You may assume that the reader is familiar with Bayesian statistics, but not that they are familiar with
the content of STAT 3303. For example, do not refer to specific examples that have been discussed in
lecture or homework.
Your report should be no longer than six pages double-spaced, including figures and tables. (Text, figures,
and tables that are after six pages may not be considered by the instructor.) Your appendix with code does
not count toward the six page limit.
Submit your final exam report as a single PDF file on Carmen before the deadline.