Literature Review

Extreme Value Theory¶

An Introduction to Statistical Modeling of Extreme Values - Stuart Coles (2001)

Probably the most comprehensive, applied introduction to extreme value theory. It’s a great introduction for applied people because it has a lot of examples. I did feel that it didn’t go into a lot of detail for some of the more advanced topics (the later chapters like Multivariate extremes and spatial extremes).

PyData - Extreme Value Analysis - Dimitry Venger(2022)

A nice introduction to EVT from a software perspective.

Weather Extremes

A good playlist for looking at weather extremes. They include topics like dynamical downscaling, simulating convective extremes, statistical modeling, and analyzing extreme events.

Workshop on Correlated Climate Extremes - Columbia (2020) - Day 1 | Day 2 | Day 3 | Day 4

A decent workshop with some videos on climate extremes. A variety of different talks.

ExtremeClimTwin

A youtube channel with a variety of videos for studying hydro-climate extremes in south-east Europe.

Quantitative Philosophy of Risk

A playlist on youtube which outlines extremes from a risk perspective. I found it much more intuitive to understand. It also digs more into the theory.

Applications of EVT¶

Fast and Scalable Inference for Spatial Extreme Value Models - Chen et al (2022)

A paper which accounts for spatial modeling of extreme values with Gaussian processes. They use a hierarchical Bayesian Model for their overall framework. They also improve the scaling aspect of GPs by using an approximate inference method, i.e., Integrated Nest Laplace Approximation (INLA) Their application is extreme snowfall forecasting.

A Bayesian hierarchical spatio-temporal model for extreme temperatures in Extremadura (Spain) simulated by a Regional Climate Model - Garcia et al (2023)

This paper accounts for spatial and temporal modeling of extreme values using Gaussian processes. They also improve the spatial consistency by including altitude coordinates in addition to lat/lon. They use a hierarchical Bayesian Model for their overall framework. Their application is extreme temperature for extremadura.

Time-varying models for extreme values - Huerta and Sanso (2007)

This paper accounts for the dynamics of the parameters when modeling extreme values. They use a hierarchical Bayesian Model for their overall framework. They implement a linear state space model for the parameters, a process convolution (approximate kernel) for the spatial process, and a standard GEVD for the extreme value data likelihood. Their application is ozone concentration in Mexico city.

Generalized extreme value distribution with time-dependence using the AR and MA models in state space form - Nakajimi et al (2012)

This paper accounts for the dynamics of the parameters when modeling extreme values. They use a hierarchical Bayesian Model for their overall framework. They implement a non-linear state space model for the parameters which is similar to the standard ARIMA model. They also use a mixture model for the data likelihood. Their application is daily stock data.

State-Space Models for Maxima Precipitation - Naveau & Poncet (2007)

This paper accounts for the dynamics of the parameters when modeling extreme values. They use a hierarchical Bayesian Model for their overall framework. They use a state-space model for the parameters. They also use a mixture model for the data likelihood. Their application is precipitation.

A spatio-temporal dynamic regression model for extreme wind speeds - Mahmoudian & Mohammadzadeh (2014)

This paper accounts for the dynamics of the parameters when modeling extremes. They also include temperature as a covariate. They use a state-space model for the parameters. They use a Gaussian process for the spatial process parameterization. Note: they do a very methodological introduction and slowly add complexity for their modeling assumptions (EXCELLENT). Their application is wind-speed in Iran.

Bayesian Hierarchical Modeling¶

A Practical Intro to Bayesian Hierarchical Modeling - Omar Sosa

A great introduction using a running example along with accompanying code. It includes a talk with a great step-by-step introduction. The example is featured on the numpyro ppl package

An Visual Introduction to Hierarchical Modeling

A great visual introduction. It takes you step by step with graphics.

Time Series Modeling¶

Time Series Modeling Playlist - Aric LaBarr

An excellent introduction to time series modeling within 5 minute chunks for each video. Probably the best tutorial to go from 0 to 100 with some of the basic models available in the literature. There is a similar talk with more about the Bayesian

Bayesian Dynamic Linear Models¶

BDLM 4 TS Data Analysis - Shervin Khazaili

A great intro video to time series modeling using Bayesian Dynamic Linear Models. A nice step-by-step approach showing the motivation as well as some simple applications.

Time Series Analysis by State Space Methods - Durbin & Koopman (2012)

A good reference book for introducing TS and how we can use state space models.

A Guide to State-Space Modeling of Ecological Time Series - Auger-Méthé et al, 2021

A paper which nicely outlines how one can introduce state-space models for modeling time series. I really like the step-by-step approach which slowly builds upon the model complexity by addressing some of the dataset assumptions 1-by-1.