This is a list of books that I have been reading or constantly refering to in my research.

1. Bayesian theory, modeling and computation

Robert, C., (2007). The Bayesian choice.
Bernardo, J.M. and Smith, A.F., (2009). Bayesian theory.
Gelman, A., et al., (2013). Bayesian data analysis.
Robert, C. and Casella, G., (2004). Monte Carlo statistical methods.

2. Asymptotics and Bayesian nonparameterics

Van der Vaart, A.W., (2000). Asymptotic statistics.
Ghosh, J.K., and Ramamoorthi, R.V., (2003). Bayesian Nonparametrics.
Billingsley, P., (2013). Convergence of probability measures.
Müller, P., et al., (2015). Bayesian nonparametric data analysis.
Ghosal, S. and Van der Vaart, A., (2017). Fundamentals of nonparametric Bayesian inference.

3. Point process theory

Kingman, J.F.C., (1993). Poisson processes.
Daley, D.J. and Vere-Jones, D., (2003). An introduction to the theory of point processes, Volume 1, Volume 2.
Moller, J. and Waagepetersen, R.P., (2003). Statistical inference and simulation for spatial point processes.
Snyder, D.L. and Miller, M.I., (2012). Random point processes in time and space.

4. Markov chains, and time series theory, modeling and inference

Tong, H., (1990). Non-linear time series: a dynamical system approach.
Brockwell, P. J., and Richard A. D., (1991). Time series: theory and methods.
Meyn, S.P. and Tweedie, R.L., (1993). Markov chains and stochastic stability.
Hamilton, J.D., (1994). Time series analysis.
West, M. and Harrison, J., (1997). Bayesian forecasting and dynamic models.
Norris, J.R., (1998). Markov chains.
Tsay, R.S., (2005). Analysis of financial time series.

5. Spatial theory, modeling and inference

Stein, M.L., (1999). Interpolation of spatial data: some theory for kriging.
Rue, H. and Held, L., (2005). Gaussian Markov random fields: theory and applications.
Banerjee, S., et al., (2014). Hierarchical modeling and analysis for spatial data.
Cressie, N., (2015). Statistics for spatial data.
Schabenberger, O. and Gotway, C.A., (2017). Statistical methods for spatial data analysis.

6. Mixture model

McLachlan, G. and Peel, D., (2000). Finite mixture models.
Frühwirth-Schnatter, S., (2006). Finite mixture and Markov switching models.

7. Distribution and copula

Johnson, N.L. et al., (1996). Discrete multivariate distributions.
Joe, H., (1997). Multivariate models and multivariate dependence concepts.
Arnold, B.C., et al. (1999). Conditional specification of statistical models.
Kotz, S., et al., (2004). Continuous multivariate distributions, Volume 1.
Genton, M.G. ed., (2004). Skew-elliptical distributions and their applications.
Nelsen, R.B., (2008). An introduction to copulas.
Azzalini, A., (2013). The skew-normal and related families.
Joe, H., (2014). Dependence modeling with copulas.
Johnson, R.A. and Wichern, D.W., (2014). Applied multivariate statistical analysis.

8. Heavy tails and extreme value theory

De Haan, L., Ferreira, A. and Ferreira, A., (2006). Extreme value theory: an introduction.
Resnick, S.I., (2007). Heavy-tail phenomena: probabilistic and statistical modeling.
Embrechts, P., et al., (2013). Modelling extremal events: for insurance and finance.

9. Probability and stochastic process foundamentals

Williams, D., (1991). Probability with martingales.
Fristedt, B.E. and Gray, L.F., (1997). A modern approach to probability theory.
Grimmett, G. and Stirzaker, D., (2001). Probability and random processes.
Rosenthal, J.S., (2006). A first look at rigorous probability theory.
Resnick, S., (2014). A probability path.
Durrett, R., (2019). Probability: theory and examples.

10. Statistics

Casella, G. and Berger, R.L., (2002). Statistical inference.
Lehmann, E.L. and Casella, G., (2006). Theory of point estimation.
Schervish, M.J., (2012). Theory of statistics.
Efron, B. and Hastie, T., 2016. Computer age statistical inference.

11. Analysis and topology

Munkres, J.R., [1975]. Topology; a First Course.
Rudin, W., (1986). Real and complex analysis.
Rudin, W., (1991). Functional analysis.
Folland, G.B., (1999). Real analysis.
Stein, E.M. and Shakarchi, R., (2003). Princeton lectures in analysis, Fourier analysis, Real analysis, and Functional analysis.
Tao, T., (2009). Analysis, Volume 1, Volume 2.
Abbott, S., (2012). Understanding analysis.

12. Econometrics

Davidson, J., (1994). Stochastic limit theory: An introduction for econometricians.
Hayashi, F., (2001) Econometrics.
Davidson, R. and MacKinnon, J.G., (2004). Econometric theory and methods.
Wooldridge, J.M., (2010). Econometric analysis of cross section and panel data.

13. Statistical learning and probablistic graphical models

Lauritzen, S.L., (1996). Graphical models.
Friedman, J., et al., (2001). The elements of statistical learning.
Bishop, C.M. (2006). Pattern Recognition and Machine Learning.
Koller, D. and Friedman, N., (2009). Probabilistic graphical models.
James, G., et al., (2013). An introduction to statistical learning.

14. Miscellaneous topics

De Boor, C. and De Boor, C., (1978). A practical guide to splines.
Koenker, R., (2005). Quantile regression.
Monahan, J.F., (2008). A primer on linear models.
Hastie, T., eta., (2019). Statistical learning with sparsity: the lasso and generalizations.
Wang, Y., (2019). Smoothing splines: methods and applications.