Here are a few references and tutorials we think might be useful.  They are arranged by topic in alphabetical order, with a short description indicating the level of difficulty. Many topics overlap, so for example, you might find useful information on Bayesian statistics in an image processing resource.  Follow the links to the resources themselves, or at least to where you might obtain them.  This is not intended to be an exhaustive list.  There are many books out there on all these topics.  If you have any suggestions for topics, or resources, please contact us!

References

• Bayesian statistics
  1.  Bayesian Logical Data Analysis for the Physical Sciences (P. C. Gregory)
     • introduction to Bayesian statistics with astronomical applications.
  2. Doing Bayesian Data Analysis (J. Kruschke)
     • exceptionally clear and insightful introduction to the Bayesian framework (advanced undergraduate).
  3. Bayesian Data Analysis (A. Gelman et al.)
     • the ultimate (and most complete) reference for Bayesian data analysis (graduate level).

• Image processing
  1. Digital Image Processing (R. C. Gonzalez & R. E. Woods)
     • fundamental and basic algorithms in image processing.

• Machine learning
  1. An Introduction to Statistical Learning with Applications in R (G. James et al.)
     • introduction to some basic algorithms in statistical learning.
  2. The Elements of Statistical Learning (T. Hastie et al.)
     • more advanced treatment of statistical learning.
  3. Pattern Classification (R. O. Duda et al.)
     • classic textbook on finding patterns in data through machine learning algorithm (graduate level).

• Multi-resolution analysis
  1. Image Processing and Data Analysis: The Multiscale Approach (Starck et al.)
     • discusses many different multi-scale transforms (such as wavelets) applied to one and two dimensional data (graduate level).
  2. Handbook of Astronomical Data Analysis (J. L. Starck & F. Murtagh)
     • filtering, deconvolution and other topics with astronomical applications (advanced undergraduate level).

• Non-parametric statistics
  1. All of Nonparametric Statistics (L. Wasserman)
     • a highly condensed textbook that covers lots of aspects (graduate level).

• Solar Information Processing
  1. Solar Physics, vol. 228, Issue 1-2, (2005), ‘Solar Image Processing’
  2. Solar Physics, vol. 248, Issue 2, (2008), ‘Solar Image Analysis and Visualization’
  3. Solar Physics, vol. 262, Issue 2, (2010), ‘Solar Image Processing and Analysis’
     • collected research-level papers on the application of many different image analysis algorithms on outstanding challenges in solar physics.

• Solar Physics

• Sparse image processing

• Statistics and treatment of errors
  1. Modern Statistical Methods for Astronomers with R Applications (E. D. Feigelson & G. J. Babu)
     • fundamental results of probability theory and statistical inference, before exploring several fields of applied statistics, such as data smoothing, regression, multivariate analysis and classification, treatment of non-detections, time series analysis, and spatial point processes (advanced undergraduate).
  2. An Introduction to the Bootstrap (B. Efron & R. J. Tibshirani)
     • one of the first reference books that describes the bootstrap and other methods for assessing statistical accuracy. The first six chapters give the basics of the bootstrap; the following chapters delve into particular issues (graduate level).

• Time series analysis

Tutorials

There are plenty of tutorials out there.  YouTube contains a large number of tutorial videos that can be a great way to learn.  Here are some recommendations.

• mathematicalmonk
  • Videos about mathematics, at the graduate level or upper-level undergraduate.  Includes probability, optimization and machine learning.