Mini-project 2

Topics in MCMC and poisson processes

Mini-projects should explore an application, illustration, implementation, or extension of a topic discussed in class. The expectation is that students will work in pairs or threes to produce: (a) a 10-15 minute in-class presentation; and (b) a 1-2 page written summary for an audience of peers. This second project should relate to topics in either MCMC or point processes. The in-class presentation will be held on Wednesday, March 4; the written deliverable is due by Friday, March 6, at 11:59pm.

Projects may be more applied (e.g., a data application, a worked example from the text or elsewhere, or a software tutorial/vignette) or more methodological (e.g., simulation experiments, an extension not covered in lecture, or an exposition of a particular model, estimation technique, or algorithm). You may choose one of the options below, or craft your own. Please confirm your topic with me (a quick email will suffice) before going ahead.

Software implementations of MCMC

  • MCMC with the nimble package

    • Goal: illustrate syntax to construct an MCMC sampler using a simple example of your choosing (could be from class, hw, book); focus on model specification
    • see this [vignette] for guidance (but don’t copy the pump model verbatim)
    • show how to adjust proposals (see this [vignette] and this portion of the [documentation])
    • show how to construct and interpret diagnostics, estimates, intervals
    • nimble documentation: [https://r-nimble.org]

  • fitting GLMMs using MCMC [R script]

    • Goal: explore how to fit mixed models using MCMC and show an application to NBA shot attempt data
    • following the provided script, explain the model specification for a Poisson GLMM for grouped data with a random intercept and review how to construct an MCMC routine in nimble for this model
    • use the provided example to fit a model to NBA shot attempt data and answer the question, is there evidence of a home-court effect on shot attempts?

  • Hamiltonian Monte Carlo (HMC) [R script]

    • Goal: explore how using gradient information for MCMC proposals compares with random-walk Metropolis
    • use the example script to compare HMC and random walk Metropolis for sampling from a bivariate normal likelihood with varying correlation strength (compare \(\rho = 0.2, 0.5, 0.8, 0.9, 0.99\))
    • plot ESS for each algorithm as a function of \(\rho\)
    • compare trace plots for one higher-correlation setting of your choosing
    • reference: Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(1), 1593-1623.

Point processes

  • tropical rain forests on Barro Colorado Island [R script]

    • Goal: fit a Poisson process model to tropical rain forest data with a spatial covariate
    • start with the provided example and hypothesize the effect of elevation based on visualizations of the data
    • refit the Poisson process model with elevation as a covariate
    • visualize the effect of elevation on intensity
    • answer the question, how does forest density change with elevation?

  • spatial point process modeling of earthquake data in CA

    • Goal: fit a Poisson process model to the spatial distribution of earthquakes in California during a time period of your choosing
    • follow the in-class earthquake data example to pull USGS data for a time period of your choosing
    • use nearest neighbor distances to check for spatial clustering
    • bin the data spatially and fit a nonhomogeneous Poisson process model (see the provided script for the tropical rain forests project or the in-class example for a template to follow); in your write-up/presentation, explain the model specification (high-level is fine)
    • visualize the estimated intensity spatially

  • effect of odor puff stimulation on cockroach antennal lobe neurons [data] [R script]

    • Goal: compare effect of odor puff stimulation on firing rate of two neurons
    • use the provided script to visualize neurons 2 and 3 and form a hypothesis about the effect of stimulation
    • fit nonhomogeneous Poisson process models (one per neuron) with trial random effects and a stimulus covariate to estimate the effect of citronella odor puffs on each of neurons 2 and 3
    • in your presentation/writeup, explain the model specification
    • visualize the effect of the stimulus on firing intensity for each neuron
    • answer the question: do citronellal odor puffs affect the firing rate of cockroach antennal lobe neurons, and if so, is the effect uniform across neurons?

Find your own topic

Please consult with me briefly if you want to focus on your own topic. I will probably approve, but we should agree on some tasks and minimum requirements similar to those above.