Two-component mixture model for compound screening

The task is to develop a two-component mixture model for compound screening (Mr. Zweifach’s data.)

**You have to submit a short paper and an R program.**

The paper has to be written in either LaTeX or Microsoft Word and its structure must be as follows:

Title

Author name

Date

Introduction to the data and a brief explanation of the z-score

The Model – include the formulas, and plots of the mixture model. A brief explanation of the EM algorithm. Explain how the model is used to control the Type-I error, the False Discovery Rate, and the odds ratio.

Simulation studies

Conclusions

References

Appendix – should include the derivations of the parameter estimates, and instructions on how to use the program.

The program should be written in R. It must run without errors, and contain clear documentation, and references to your paper (e.g., when you are using a formula for a maximum likelihood estimate, refer to the formula’s number in your paper).

The program must include functions to perform simulations, fitting the two-component mixture model fitting, generating summaries of the fitting procedure, and diagnostic plots. For example, draw a histogram of the simulated (or real) data overlaid with the fitted mixture, and a plot of the power vs. the variance. The summaries have to include the parameter estimates, the estimated FDR, probability of Type-I error, and power.