risk on Dan MacKinlayhttps://danmackinlay.name/tags/risk.htmlRecent content in risk on Dan MacKinlayHugo -- gohugo.ioen-usTue, 02 May 2023 07:27:25 +1000Monte Carlo gradient estimationhttps://danmackinlay.name/notebook/mc_grad.htmlTue, 02 May 2023 07:27:25 +1000https://danmackinlay.name/notebook/mc_grad.htmlScore function estimator Rao-Blackwellization Parametric “Measure-valued” Tooling Reparameterization trick Optimising Monte Carlo References Taking gradients through integrals using randomness. A thing with similar name but which is not the same is Stochastic Gradient MCMC which uses stochastic gradients to sample from a target posterior distribution. Some similar tools and concepts pop up in both uses.
Score function estimator A.k.a. REINFORCE, all-caps, for some reason. Could do with a decent intro.Elliptical distributionshttps://danmackinlay.name/notebook/elliptical_distributions.htmlTue, 03 Jan 2023 17:56:51 +1100https://danmackinlay.name/notebook/elliptical_distributions.htmlRecommended reading Elliptical processes Incoming References References Generalising multivariate Gaussians to anything which has a density function of the form \[ f(x)\propto g((x-\mu )'\Sigma ^{-1}(x-\mu ))\] where \(\mu\) is the mean vector, \(\Sigma\) is a positive definite matrix, and \(g:\mathbb{R}^+\to\mathbb{R}^+\). In fact, we do not need the density function to exist; it’s ok if \(\Sigma\) is positive semi-definite or to allow \(g\) to be a generalised function. Baby steps! If the mean of such an \(X\sim f\) RV exists, it is \(\mu\), and \(\Sigma\) is proportional to the covariance matrix of \(X\) if such a covariance matrix exists.COVID-19 in practicehttps://danmackinlay.name/notebook/covid_19.htmlWed, 07 Dec 2022 12:36:19 +1100https://danmackinlay.name/notebook/covid_19.htmlEpidemiology of Testing dynamics Personal risk calculators Airborne transmission Evaluating societal cost Virulence and risks upon infection Death and life years Relative rate compared to normal life risk Long covid Comorbidities Omicron variant Transmission Modeliing airborne transmission Treating topical sprays Vitamin D Simulating Current restrictions where I live Tracking Australia’s contagion Incoming References Epidemiology of See also epidemiology, contact tracing.
Testing dynamics Current public health advice boils down to a heuristic that the Rapid Antigen Tests (🐀) are a good proxy for actual contagiousness.Physical infrastructurehttps://danmackinlay.name/notebook/infrastructure.htmlSat, 24 Sep 2022 18:16:48 +1000https://danmackinlay.name/notebook/infrastructure.htmlReferences Would a journal of infrastructure complexity be any good? Brian Potter, Construction and the Toyota Production System Why We Can’t Have Nice Things How high are infrastructure costs? Analyzing Interstate construction spending Australia’s infrastructure cost conundrum Trump Infrastructure Plan: Cost Will be an Issue. Here’s Why. Why do roads, rail, and infrastructure cost so much to build in the US? SMART Infrastructure Facility - University of Wollongong References Brogan, Steve.Farming and husbandry of black swans and dragon kingshttps://danmackinlay.name/notebook/black_swan_farming.htmlSat, 30 Apr 2022 16:00:51 +1000https://danmackinlay.name/notebook/black_swan_farming.htmlBlack swans Dragon kings Knightian uncertainty Countercyclical philanthropy References There are several things that people seem to conflate when talking about black swans: heavy tails and unknown unknowns, nonstationarity… Nassim Taleb has indeed talked about all of these concepts; He does not refer to them all as swans tho’ AFAIK.
What I think of in this context is portfolio theory for a world of outliers.
I have nothing new to add yet, so I’ll just punt you to my bookmarked favoured essays on this theme.Life-adjusted quality yearshttps://danmackinlay.name/post/come_to_our_party.htmlTue, 15 Mar 2022 16:32:49 +1100https://danmackinlay.name/post/come_to_our_party.htmlWhat is the risk of this event to me in absolute terms? If I am prepared to go to this kind of event at some point, is now the right time to go to it, or should I hold out for the next one? Appendix A: How about mediocre parties? Appendix B: What is it like in Sydney right now? References Here is the scenario: There is a party coming up, in Sydney.Science for policyhttps://danmackinlay.name/notebook/science_for_policy.htmlWed, 22 Sep 2021 08:34:38 +1000https://danmackinlay.name/notebook/science_for_policy.htmlMeasuring results in wicked problems Stylized simulation Causation in policy How to do science for policy Designing systems that manage themselves Post normal science Planning under uncertainty To Read References OK, so we can’t hope for predictions of the outcome of complex, large and unique things within the usual setup of control-trial scientific research What can we hope for? What should we do with it?
Measuring results in wicked problems Is hard.Heavy tailshttps://danmackinlay.name/notebook/heavy_tails.htmlSat, 18 Sep 2021 11:10:48 +1000https://danmackinlay.name/notebook/heavy_tails.htmlIncoming References Heavy tailed RVs do some weird things that make them unintuitive. I should collect a list of what. See also densities and intensities, survival analysis, extreme value theory, risk management
Also, should list the many diverse phenomena that are associated, e.g. fractals etc. 🏗
Incoming Logs, Tails, Long Tails – Ryan Moulton’s Articles References Asmussen, Søren, Klemens Binswanger, and Bjarne Højgaard. 2000. “Rare Events Simulation for Heavy-Tailed Distributions.Extreme value theoryhttps://danmackinlay.name/notebook/extreme_value_theory.htmlWed, 30 Jun 2021 17:30:03 +1000https://danmackinlay.name/notebook/extreme_value_theory.htmlTail limit theorems Generalized Pareto Distribution Generalized Extreme Value distributions Burr distribution References In a satisfying way, it turns out that there are only so many shapes that probability densities can assume as they head off toward infinity. Extreme value theory makes this notion precise, and gives us some tools to work with them. Important application: understanding the kinds of heavy tailed variables we can observe in nature.
See also densities and intensities, survival analysis.Monte Carlo optimisationhttps://danmackinlay.name/notebook/mc_opt.htmlWed, 30 Sep 2020 10:59:22 +1000https://danmackinlay.name/notebook/mc_opt.htmlReferences Optimisation via Monte Carlo Simulation. Annealing and all that. TBD.
References Abernethy, Jacob, and Elad Hazan. 2016. “Faster Convex Optimization: Simulated Annealing with an Efficient Universal Barrier.” In International Conference on Machine Learning, 2520–28. PMLR. Botev, Zdravko I., and Dirk P. Kroese. 2008. “An Efficient Algorithm for Rare-Event Probability Estimation, Combinatorial Optimization, and Counting.” Methodology and Computing in Applied Probability 10 (4): 471–505. Dalalyan, Arnak S. 2017. “Further and Stronger Analogy Between Sampling and Optimization: Langevin Monte Carlo and Gradient Descent.Splitting simulationhttps://danmackinlay.name/notebook/splitting_simulation.htmlMon, 28 Sep 2020 10:38:21 +1000https://danmackinlay.name/notebook/splitting_simulation.htmlReferences Splitting is a method for zooming in to the important region of an intractable probability distribution
I have just spent so much time writing about this that I had better pause for a while and leave this as a placeholder.
References Aalen, Odd O., Ørnulf Borgan, and S. Gjessing. 2008. Survival and Event History Analysis: A Process Point of View. Statistics for Biology and Health. New York, NY: Springer.Quantitative risk measurementhttps://danmackinlay.name/notebook/qrm.htmlTue, 22 Sep 2020 10:10:13 +1000https://danmackinlay.name/notebook/qrm.htmlValue-at-Risk Expected shortfall Subadditivity/coherence G-expectation Sensitivity to parameters of risk measures Rosenblatt transform Knightian risk References Actuarial bread-and-butter. The mathematical study of measuring the chances of something terrible happening. This is usually a financial risk, but can also be extreme weather conditions, earthquakes, whatever. BTW, this is distinct from the “risk” in “statistical risk bounds”, which is the domain of statistical learning theory.
How do you evaluate how bad the worst cases are when deciding whether to do something?Gaussian process quantile regressionhttps://danmackinlay.name/notebook/gp_quantile_regression.htmlWed, 16 Sep 2020 13:44:32 +1000https://danmackinlay.name/notebook/gp_quantile_regression.htmlReferences How to do quantile regression with GPs.
References Boukouvalas, Alexis, Remi Barillec, and Dan Cornford. 2012. “Gaussian Process Quantile Regression Using Expectation Propagation.” In ICML 2012. Reich, Brian J. 2012. “Spatiotemporal Quantile Regression for Detecting Distributional Changes in Environmental Processes.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 61 (4): 535–53. Reich, Brian J., Montserrat Fuentes, and David B. Dunson. 2011. “Bayesian Spatial Quantile Regression.” Journal of the American Statistical Association 106 (493): 6–20.Copula functionshttps://danmackinlay.name/notebook/copula.htmlTue, 23 Jun 2015 18:28:30 +0200https://danmackinlay.name/notebook/copula.htmlElliptical Vine copulas References A neat way of quantifying dependence structures between random variables. Useful in, e.g. Quantitative Risk Management.
The trick is simple: Informally, you look at the marginal iCDF of each of \(n\) variables, and fiddle with the joint distribution of those marginals on \([0,1]^n\). (That’s assuming variables are absolutely continuous w.r.t some underlying measure space; distribution with atoms are more fiddly.)
This is a good trick, although I need to sit down and think it through.Normal accidentshttps://danmackinlay.name/notebook/normal_accidents.htmlWed, 03 Jun 2015 10:02:37 +0200https://danmackinlay.name/notebook/normal_accidents.htmlOn the certainty of disaster.
Cars driving on a wheel and a prayer:
But on the whole, the safety architecture is a house of cards. It is possible for a large percentage of the failsafes to be disabled at the same time that the throttle control is lost. […]
Koopman was highly critical of Toyota’s computer engineering process. The accepted, albeit voluntary, industry coding standards were first set by Motor Industry Software Reliability Association (MISRA) in 1995.