Generating a non-homogeneous Poisson process

Consider a Poisson process , with non-homogeneous intensity . Here, we consider a deterministic function, not a stochastic intensity. Define the cumulated intensity in the sense that the number of events that occurred between time  and  is a random variable that is Poisson distributed with parameter  . For example, consider here a cyclical Poisson process, with intensity … Continue reading Generating a non-homogeneous Poisson process

Simulation d’un processus de Poisson

Le prochain cours reviendra sur la solvabilité des compagnies d’assurance, et en particulier sur la modélisation et le calcul de la probabilité de ruine. En particulier, nous passerons pas mal de temps sur le “processus de Poisson“. Nous verrons en cours les notions de base sur les processus de Poisson. En particulier, nous verrons qu’ils … Continue reading Simulation d’un processus de Poisson

Simulation d’un processus de Lévy, et discrétisation

Avec @renaudjf, on discutait l’autre jour de la simulation d’un processus de Lévy. Et on se posait la question d’un algorithme optimal pour combiner un processus de Poisson (ou un process Poisson composé) avec un processus de Wiener (avec éventuellement un drift, voire une diffusion plus générale). En fait, pour générer des processus de Poisson, j’ai … Continue reading Simulation d’un processus de Lévy, et discrétisation

Econometrics vs. Machine Learning with Temporal Patterns

A few months ago, I did publish a (long) post entitled ‘some thoughts on economics, mathematics, econometrics, machine learning, etc‘. In that post, I was discussing possible differences between foundations of econometrics, and machine learning. I wanted to get back today on an important point, related to training/sampling datasets, when we have temporal data. I was … Continue reading Econometrics vs. Machine Learning with Temporal Patterns

Modelling Occurence of Events, with some Exposure

This afternoon, an interesting point was raised, and I wanted to get back on it (since I did publish a post on that same topic a long time ago). How can we adapt a logistic regression when all the observations do not have the same exposure. Here the model is the following: , the occurence of an … Continue reading Modelling Occurence of Events, with some Exposure

The odds of a cluster of airplane accidents

Recently, there have been a lot of airplane accidents. July, 17th 2014, Hrabove, Ukraine, Malaysia Airlines, Boeing 777, fatalities 298 (/298) July, 23rd 2014, Magong, Taiwan, TransAsia Airways, ATR 72-500, fatalities 47 (/58) July, 24th 2014, Aguelhok, Mali, Air Algerie, Mc Donnell Douglas MD-83, fatalities 116 (/116) It is simple to find a lot of … Continue reading The odds of a cluster of airplane accidents

Exposure as a possible explanatory variable

Iin insurance pricing, the exposure is usually used as an offset variable to model claims frequency. As explained many times on this blog (e.g. here), and in my notes, if we have to identical drivers, but one with an exposure of 6 months, and the other one of one year, it should be natural to … Continue reading Exposure as a possible explanatory variable

Exposure with binomial responses

Last week, we’ve seen how to take into account the exposure to compute nonparametric estimators of several quantities (empirical means, and empirical variances) incorporating exposure. Let us see what can be done if we want to model a binomial response. The model here is the following: , the number of claims  on the period  is … Continue reading Exposure with binomial responses

Overdispersion with different exposures

In actuarial science, and insurance ratemaking, taking into account the exposure can be a nightmare (in datasets, some clients have been here for a few years – we call that exposure – while others have been here for a few months, or weeks). Somehow, simple results because more complicated to compute just because we have … Continue reading Overdispersion with different exposures

The law of small numbers

In insurance, the law of large numbers (named loi des grands nombres initially by Siméon Poisson, see e.g. http://en.wikipedia.org/…) is usually mentioned to legitimate large portfolios, because of pooling and diversification: the larger the pool, the more ‘predictable’ the losses will be (in a given period). Of course, under standard statistical assumption, namely finite expected value, … Continue reading The law of small numbers

Circular or spherical data, and density estimation

I few years ago, while I was working on kernel based density estimation on compact support distribution (like copulas) I went through a series of papers on circular distributions. By that time, I thought it was something for mathematicians working on weird spaces…. but during the past weeks, I saw several potential applications of those … Continue reading Circular or spherical data, and density estimation

Machines, procedures and avoiding responsibility

Some people are trying to make us believe that artificial intelligence is a “revolution”. What if it wasn’t? Can we not simply see the logic of a process that goes back at least fifty years ago? Bureaucracy has pushed us to put in place simple procedures in all areas of everyday life, allowing everyone to … Continue reading Machines, procedures and avoiding responsibility

Les machines, les procédures, et la fuite de la responsabilité

On essaye de nous faire croire que l’intelligence artificielle est une « révolution ». Et s’il n’en était rien ? Ne peut-on pas voir tout simplement la logique d’un processus qui remonte au moins aux cinquante dernières années ? La bureaucratie nous a poussés à mettre en place dans tous les domaines de la vie de tous les … Continue reading Les machines, les procédures, et la fuite de la responsabilité

De la communication scientifique…

Vendredi dernier, j’étais convié à une matinée de discussion autour de la communication scientifique, par des universitaires, à destination des doctorants de la région. Muriel Lefebvre a fait une présentation captivante sur la communication scientifique, et comme promis, je vais mettre par écrit quelques notes prises (je pourrais préciser que j’ai rajouté des réflexions personnelles, … Continue reading De la communication scientifique…