class: center, middle, inverse, title-slide .title[ # From
Cats
to
Stats
] .author[ ### Charlotte M. Jones-Todd ] .date[ ###
] --- ###
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On paper <br> <br> <img src="https://upload.wikimedia.org/wikipedia/commons/b/bb/Shield_of_Aberystwyth_University.svg" width = "5%"> *Prifysgol Aberystwyth* BSc (Hons) in Mathematics <br> <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6e/University_of_St_Andrews_arms.svg/200px-University_of_St_Andrews_arms.svg.png" width = "5%"> *University of St Andrews* MSc in Statistics <br> <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6e/University_of_St_Andrews_arms.svg/200px-University_of_St_Andrews_arms.svg.png" width = "5%"> *University of St Andrews* PhD in Statistics --- background-image: url("img/animals.png") background-size: fill ### IRL --- ## *Cats* to *Stats* <br> <br> <img src="https://downesvet.co.uk/wp-content/uploads/2020/03/Downes-landscape-Bi-e1585074389382.png" width = "10%"> *Veterinary nurse/assistant/receptionist* John Downes Surgery, 2009–2013 <br> <img src="https://i.vimeocdn.com/portrait/26128833_300x300.webp" width = "10%"> *Statistician* National Institute of Water and Atmospheric Research (NIWA), 2018–2019 <br> <img src="https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcS-eXMxc_sEOwFYHehTYyYGTZUyRnTDA_0B7A818ihjuwR69Cc&s" width = "10%"> *Lecturer/Senior Lecturer* University of Auckland, 2019–present --- ## Why maths/stats? -- .center[ <img src="https://media.tenor.com/ZnbjLl6MkAoAAAAC/peaky-blinders.gif"/> ] --- class: inverse .center[ ## A brief foray back into the *real world* ] --- ## NIWA > Crown Research Institutes (CRIs) are crown-owned companies that carry out scientific research for the benefit of New Zealand. .center[ <img src="https://careers.sciencenewzealand.org/skins/default/images/slider-cris-2021.png" alt="Logos of NZs CRIs" /> ] --- ## NIWA .pull-left[ **Colleagues** <img src="https://niwa.co.nz/sites/niwa.co.nz/files/2022_PHOTO_COMP_DSC_5892JPG.jpg" alt="NIWA diver reaches out for a scallop in Whangarei Harbour, Northland."/> ] -- .pull-right[ **Me** <img src="https://pbs.twimg.com/media/Exa0gi7XEAAtiRp.jpg", alt="Sheldon cooper debugging Oh that's why meme" /> ] --- ##
Back to academia .center[ <img src="img/split.png"/> ] --- class: inverse .center[ # Research <img src="https://img.freepik.com/premium-photo/magnificent-medieval-fantasy-library-with-countless-books-scrolls-dramatic-lighting-candleli_961179-424.jpg" alt="fantasy library"/> ] --- <br> <br>
Journal of the Royal Statistical Society: Series C (Applied Statistics) (2017)
A spatiotemporal multispecies model of a semicontinuous response
Jones‐Todd, Charlotte M. et. al.
Statistics in Medicine (2018)
Identifying prognostic structural features in tissue sections of colon cancer patients using point pattern analysis
Jones-Todd, Charlotte M. et. al.
Ecological Applications (2021)
Discrete‐space continuous‐time models of marine mammal exposure to Navy sonar
Jones‐Todd, Charlotte M. et. al.
--- <br> <br>
Journal of the Royal Statistical Society Series A: Statistics in Society (2018)
A Bayesian Approach to Modelling Subnational Spatial Dynamics of Worldwide Non-State Terrorism, 2010–2016
Python, André et. al.
Ecography (2019)
Understanding species distribution in dynamic populations: a new approach using spatio‐temporal point process models
Soriano‐Redondo, Andrea et. al.
PLOS ONE (2023)
Using individual-based bioenergetic models to predict the aggregate effects of disturbance on populations: A case study with beaked whales and Navy sonar
Hin, Vincent et. al.
---
Statistics in Medicine (2018)
Identifying prognostic structural features in tissue sections of colon cancer patients using point pattern analysis
Jones-Todd, Charlotte M. et. al.
.panelset[ .panel[.panel-name[Pretty plot] .center[ <img src="img/cancer_im.png" width="100%" style="display: block; margin: auto;" /> ] ] .panel[.panel-name[Maths] .center[ <img src="https://pbs.twimg.com/media/DuKns0KX4AAvApq?format=jpg&name=small" width="40%" /> ] ] .panel[.panel-name[More Maths] .center[ <img src="img/cancer_nn.png" width="80%" style="display: block; margin: auto;" /> ] ] ] --- ###
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if you use a running App -- .center[ <img src="img/run.png" width="829" height="500" /> ] ---
Ecological Applications (2021)
Discrete‐space continuous‐time models of marine mammal exposure to Navy sonar
Jones‐Todd, Charlotte M. et. al.
.center[ <img src="img/tag.jpg" alt="Blainville's beaked whale, tagged" height="400"/> .footnote[
Charlotte Dunn] ] --- .pull-left[ ## The data <img src="img/autec.png" /> ] .pull-right[ <img src="https://upload.wikimedia.org/wikipedia/commons/8/8a/AUTEC_Andros_Ranges_w_border.jpg" /> ] --- ### Continuous-time correlated random walk model (CTCRW) For each coordinate `\(c = 1,2\)` of the observed location of an animal at time `\(t\)` ( `\(t = 1,2,...,n\)` ): <br> -- - instantaneous velocity of the animal `\(v_{ct}\)` is described by a Ornstein-Uhlenbeck process; -- <br> - integrating over the velocity process gives the location process `\(\mu_{ct}\)`; -- <br> - measurement equation is given by `\(y_{ct} = \mu_{ct} + \epsilon_{ct}\)`, where `\(y_{ct}\)` is the `\(c\)`th coordinate of the observed location of an animal at time `\(t\)` with measurement error term `\(\epsilon_{ct}\)`. The joint distribution of `\(\epsilon_{1t}\)` and `\(\epsilon_{2t}\)` is a bivariate `\(t\)`-distribution. --- ### Continuous-time correlated random walk model (CTCRW) .center[ <img src="img/track_example.png" width="640" height="500" /> ] --- ### Discrete-space continuous-time A continuous-time Markov model describes how an individual transitions between states in continuous time. .center[ <img src="nzmasp_2023_files/figure-html/markov-1.png" width="600" /> ] --- ### Discrete-space continuous-time <br> Let `\(q_{rs}(t,z(t))\)` represent the immediate risk of moving from one state `\(r\)` to another state `\(s\)`: <br> `$$q_{rs}(t,z(t)) = \text{lim}_{\delta t \rightarrow 0} \mathbb{P}(S(t + \delta t) = s|S(t) = r)/\delta t.$$` <br> These transition rates form a square matrix `\(\bf{Q}\)` with elements `\(q_{rs}\)`. -- <br> Here `\(q_{rr}=-\Sigma_{s{\neq}r}q_{rs}\)` (i.e., the rows of **Q** sum to zero and `\(q_{rs}\geq0\)` for `\(r{\neq}s\)`). --- ### Discrete-space continuous-time <br> We have `\(r, s = \{1,2\}\)` where state `\(1=\)` off-range (i.e., outside the area used by the Navy for military operations) and state `\(2=\)` on-range: <br> <br> `$$\begin{array}{ccc} \bf{Q} = \left [\begin{array}{cc} q_{1 1} & q_{1 2} \\ q_{2 1} & q_{2 2} \end{array}\right ] & \text{where} \: q_{r r} = -q_{r s}, & \text{for}\: r \neq s. \end{array}$$` --- ### Including exposure information We let <br> `$$\text{log}(q_{k, rs}(\mathbf{z}_k(t))) = (\beta_{0,rs} + u_{k, rs}) + \beta_{1,rs}\text{exp}(- \beta_{2,rs} \mathbf{z}_k(t)),$$` where `$$\mathbf{z}_k(t) \left\{ \begin{array}{rl} = 0 & \text{during exposure} \\ \geq 0 & \text{otherwise}\end{array} \right.$$` is the number of days since an individual was exposed to a sonar event and `\(\beta_{2,rs} \geq 0\)` `\(\forall\: r \neq s\)`. --- ### Including exposure information We let <br> `$$\text{log}(q_{k, rs}(\mathbf{z}_k(t))) = (\color{red}{\beta_{0,rs}} + u_{k, rs}) + \beta_{1,rs}\text{exp}(- \beta_{2,rs} \mathbf{z}_k(t)),$$` where `$$\mathbf{z}_k(t) \left\{ \begin{array}{rl} = 0 & \text{during exposure} \\ \geq 0 & \text{otherwise}\end{array} \right.$$` is the number of days since an individual was exposed to a sonar event and `\(\beta_{2,rs} \geq 0\)` `\(\forall\: r \neq s\)`. <br> .red[some baseline transition rate] --- ### Including exposure information We let <br> `$$\text{log}(q_{k, rs}(\mathbf{z}_k(t))) = (\beta_{0,rs} + u_{k, rs}) + \color{red}{\beta_{1,rs}}\text{exp}(- \beta_{2,rs} \mathbf{z}_k(t)),$$` where `$$\mathbf{z}_k(t) \left\{ \begin{array}{rl} = 0 & \text{during exposure} \\ \geq 0 & \text{otherwise}\end{array} \right.$$` is the number of days since an individual was exposed to a sonar event and `\(\beta_{2,rs} \geq 0\)` `\(\forall\: r \neq s\)`. <br> .red[change in transition rate during exposure] --- ### Including exposure information We let <br> `$$\text{log}(q_{k, rs}(\mathbf{z}_k(t))) = (\beta_{0,rs} + u_{k, rs}) + \beta_{1,rs}\text{exp}(\color{red}{- \beta_{2,rs}} \mathbf{z}_k(t)),$$` where `$$\mathbf{z}_k(t) \left\{ \begin{array}{rl} = 0 & \text{during exposure} \\ \geq 0 & \text{otherwise}\end{array} \right.$$` is the number of days since an individual was exposed to a sonar event and `\(\beta_{2,rs} \geq 0\)` `\(\forall\: r \neq s\)`. <br> .red[exponential decay of transition rates towards some baseline] --- ### Including exposure information We let <br> `$$\text{log}(q_{k, rs}(\mathbf{z}_k(t))) = (\beta_{0,rs} + \color{red}{u_{k, rs}}) + \beta_{1,rs}\text{exp}(- \beta_{2,rs} \mathbf{z}_k(t)),$$` where `$$\mathbf{z}_k(t) \left\{ \begin{array}{rl} = 0 & \text{during exposure} \\ \geq 0 & \text{otherwise}\end{array} \right.$$` is the number of days since an individual was exposed to a sonar event and `\(\beta_{2,rs} \geq 0\)` `\(\forall\: r \neq s\)`. <br> .red[individual level random effect] --- **Results** .center[ <img src="img/autec_results.png" width="600" height="600" /> ] --- **Results** .panelset[ .panel[.panel-name[93232] .center[ <br> <br> <img src="img/whale1.png" width="80%" /> ] ] .panel[.panel-name[11164] .center[ <br> <br> <img src="img/whale2.png" width="80%" /> ] ] .panel[.panel-name[111670] .center[ <br> <br> <img src="img/whale3.png" width="80%" /> ] ] .panel[.panel-name[129715] .center[ <br> <br> <img src="img/whale4.png" width="80%" /> ] ] .panel[.panel-name[129719] .center[ <br> <br> <img src="img/whale5.png" width="80%" /> ] ] .panel[.panel-name[129720] .center[ <br> <br> <img src="img/whale6.png" width="80%" /> ] ] .panel[.panel-name[129721] .center[ <br> <br> <img src="img/whale7.png" width="80%" /> ] ] ] --- ### Current research
CRAN: R package version 1.0.1. (2023)
stelfi: Hawkes and Log-Gaussian Cox Point Processes Using Template Model Builder
Charlotte M. Jones-Todd; Alec van Helsdingen
.center[ <img src="img/hawked_fitted.png" width ="90%" /> ] --- ###
.center[ <img src="img/niwa.png" width ="60%" /> ] --- ### A self-exciting point process (Hawkes model) <br> <br> `$$\lambda(t) = \color{red} \mu + \color{blue} \alpha \Sigma_{i:\tau_i<t}\text{exp}(-\color{green}\beta * (t-\tau_i))$$` - `\(\color{red} \mu\)`, background rate - `\(\color{blue} \alpha\)`, increase in intensity after an event - `\(\color{green}\beta\)`, exponential decay - `\(\Sigma_{i:\tau_i<t} \cdots\)`, historic dependence - `\(\frac{\color{blue} \alpha}{\color{green}\beta}\)`, branching ratio (average number events triggered by an event) - `\(\frac{1}{\color{green}\beta}\)`, rate of decay of self-excitement .center[ <img src="img/hawkes_example.png" width ="50%" /> ] --- ### Temporal rate of retweets .center[ <img src="img/niwa_fit.png" width ="80%" /> ] --- ### Temporal rate of retweets <br> <br> <br> `$$\lambda(t) = \color{red} \mu + \color{blue} \alpha \Sigma_{i:\tau_i<t}\text{exp}(-\color{green}\beta * (t-\tau_i))$$` + `\(n = 4890\)` retweets over `\(\text{T} = 3143\)` mins (~2 days) + `\(\color{red} {\hat{\mu}} \text{T} = 0.063 \times 3143 \sim 198\)` 'baseline' tweets + Expected number of retweets triggered by any one tweet `\(\frac{\color{blue}{\hat{\alpha}}}{\color{green}{\hat{\beta}}} \sim 0.94\)` + Rate of decay for the self-excitement `\(\frac{1}{\color{green}{\hat{\beta}}} = \frac{1}{0.079} \sim 12\)` mins --- ### Extension: a marked model Here, the conditional intensity for the `\(j^{th}\)` ( `\(j = 1, ..., N\)` ) stream is given by `$$\lambda(t)^{j*} = \mu_j + \Sigma_{k = 1}^N\Sigma_{i:\tau_i<t} \alpha_{jk} e^{(-\beta_j * (t-\tau_i))},$$` where `\(j, k \in (1, ..., N)\)`. Here, `\(\alpha_{jk}\)` is the excitement caused by the `\(k^{th}\)` stream on the `\(j^{th}\)`. .center[ ![](img/multi_hawkes.png) ] --- class: inverse .center[ # Teaching <img src="https://i.pinimg.com/736x/7c/7c/75/7c7c75507dd63faa29ee63ce0dcb8fdf.jpg" alt="empty lecture room" /> ] --- .panelset[ .panel[.panel-name[Illustrations] .center[ ![](https://raw.githubusercontent.com/BIOSCI738/cowstats/main/img/distributions.png) ] ] .panel[.panel-name[Mini Games] .center[
[statbiscuit.github.io/mini_games/](https://statbiscuit.github.io/mini_games/) <iframe src="https://statbiscuit.github.io/mini_games/" width="900" height="400"></iframe> ] ] .panel[.panel-name[Virtual experiments] .center[
[statbiscuit.shinyapps.io/vested/](https://statbiscuit.shinyapps.io/vested/) <iframe src="https://statbiscuit.shinyapps.io/vested/" width="900" height="400"></iframe> ] ] ] --- class:inverse # Service + Manuscript reviewing + Seminar organisation + Committee membership + Faculty-level commitments + ... --- class:inverse # Charlotte's advice for life... > It's *mainly* about who you grab a drink with (at morning tea or the pub) .center[ <img src="https://errantscience.com/wp-content/uploads/Academic-confrence-progression.png" /> ] --- # ![](https://www.stats.org.nz/wp-content/uploads/2017/09/NZSA-logo-words-e1505785105112-1.png) **Many of you who are not studying statistics may find yourself in a role with some stats responsibilities.** .pull-left[ <img src="img/community.jpg" height=400/> ] .pull-right[
[stats.org.nz](https://www.stats.org.nz) - Free for students - Early Career section with meetups/activities - Mentoring program ] --- ### [
<i class="fas fa-laptop faa-float animated "></i>
cmjt.github.io](https://cmjt.github.io/) .pull-left[ .animate__animated.animate__bounceInDown[ ``` [1] " __________________" [2] "< Diolch am wrando >" [3] " ------------------" [4] " \\ / \\ //\\" [5] " \\ |\\___/| / \\// \\\\" [6] " /0 0 \\__ / // | \\ \\ " [7] " / / \\/_/ // | \\ \\ " [8] " @_^_@'/ \\/_ // | \\ \\ " [9] " //_^_/ \\/_ // | \\ \\" [10] " ( //) | \\/// | \\ \\" [11] " ( / /) _|_ / ) // | \\ _\\" [12] " ( // /) '/,_ _ _/ ( ; -. | _ _\\.-~ .-~~~^-." [13] " (( / / )) ,-{ _ `-.|.-~-. .~ `." [14] " (( // / )) '/\\ / ~-. _ .-~ .-~^-. \\" [15] " (( /// )) `. { } / \\ \\" [16] " (( / )) .----~-.\\ \\-' .~ \\ `. \\^-." [17] " ///.----..> \\ _ -~ `. ^-` ^-_" [18] " ///-._ _ _ _ _ _ _}^ - - - - ~ ~-- ,.-~" [19] " /.-~" ``` ] ]