Prior knowledge elicitation: The past, present, and future

Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. Prior elicitation transforms domain knowledge of various kinds into well-defined prior distributions, and offers a solution to the prior specification problem, in principle. In practice, however, we are still fairly far from having usable prior elicitation tools that could significantly influence the way we build probabilistic models in academia and industry. We lack elicitation methods that integrate well into the Bayesian workflow and perform elicitation efficiently in terms of costs of time and effort. We even lack a comprehensive theoretical framework for understanding different facets of the prior elicitation problem.Why are we not widely using prior elicitation? We analyze the state of the art by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert. The existing prior elicitation literature is reviewed and categorized in these terms. This allows recognizing under-studied directions in prior elicitation research, finally leading to a proposal of several new avenues to improve prior elicitation methodology.Fil: Mikkola, Petrus. Aalto University; FinlandiaFil: Martín, Osvaldo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Aalto University; FinlandiaFil: Chandramoul, Suyog. Aalto University; FinlandiaFil: Hartmann, Marcelo. University of Helsinki; FinlandiaFil: Abril Pla, Oriol. University of Helsinki; FinlandiaFil: Thomas, Owen. University of Oslo; NoruegaFil: Pesonen, Henri. University of Oslo; NoruegaFil: Corander, Jukka. University of Oslo; NoruegaFil: Vehtari, Aki. Aalto University; FinlandiaFil: Kaski, Samuel. Aalto University; FinlandiaFil: Bürkner, Paul Christian. University Of Stuttgart; AlemaniaFil: Klami, Arto. University of Helsinki; Finlandi

Prior knowledge elicitation: The past, present, and future

Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. Prior elicitation transforms domain knowledge of various kinds into well-defined prior distributions, and offers a solution to the prior specification problem, in principle. In practice, however, we are still fairly far from having usable prior elicitation tools that could significantly influence the way we build probabilistic models in academia and industry. We lack elicitation methods that integrate well into the Bayesian workflow and perform elicitation efficiently in terms of costs of time and effort. We even lack a comprehensive theoretical framework for understanding different facets of the prior elicitation problem.Why are we not widely using prior elicitation? We analyze the state of the art by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert. The existing prior elicitation literature is reviewed and categorized in these terms. This allows recognizing under-studied directions in prior elicitation research, finally leading to a proposal of several new avenues to improve prior elicitation methodology.Fil: Mikkola, Petrus. Aalto University; FinlandiaFil: Martín, Osvaldo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Aalto University; FinlandiaFil: Chandramoul, Suyog. Aalto University; FinlandiaFil: Hartmann, Marcelo. University of Helsinki; FinlandiaFil: Abril Pla, Oriol. University of Helsinki; FinlandiaFil: Thomas, Owen. University of Oslo; NoruegaFil: Pesonen, Henri. University of Oslo; NoruegaFil: Corander, Jukka. University of Oslo; NoruegaFil: Vehtari, Aki. Aalto University; FinlandiaFil: Kaski, Samuel. Aalto University; FinlandiaFil: Bürkner, Paul Christian. University Of Stuttgart; AlemaniaFil: Klami, Arto. University of Helsinki; Finlandi

Modelos de novas clásicas con MESA

Classical novae are thermonuclear runaways at the envelope of a WD due to the piling up of H-rich accreted material. They have been observed to produce heavy elements during the explosion, and their role in galactical abundances for some specific elements may not be negligible. MESA (Modules for Experiments in Stellar Astrophysics) code has been thoroughly studied for its application to nova explosions. Detailed know-how of nova simulations with MESA has been achieved, leading the road of future studies using this tool. Its capablities in the field have been tested, demonstrating to reach further than what has been done in previous literature. MESA has been shown to give accurate nucleosynthesis yields for solar-like accreted material without any further postprocessing up to 50 nova bursts. The dependance of the nova outburst properties with the burst number have been anayzed. However, more simulations are needed in order to extract meaningful conclusions about the role of the burst number in the properties of novae outbursts. The key role of the nuclear reaction network has been highlighted, showing that simulations of consecutive novae outbursts require nuclear reactions networks specifically tested for the work. Many nuclear reaction networks that were thoroughly tested in a single nova explosion have not been capable of properly simulating 10 consecutive outbursts. The role of convective overshoot mixing as implemented in MESA has also been tested. It has been found that as shown in previous literature, it does account for dredge up. We plan to extend this work with simulations of consecutive nova outbursts implementing convective overshoot.Les noves clàssiques són explosions nuclears que es duen a terme a l'embolcall d'una nana blanca, degut a l'accreció de matèria rica en hidrogen. S'ha observat la producció d'elements pesats en aquest tipus d'explosions, i podrien tenir un paper important en les abundancies del elements químics a nivell galàctic. S'ha estudiat l'aplicació del codi MESA (Modules for Experiments in Stellar Astrophysics) a la simulació de noves clàssiques, obtenint conèixement detallat sobre com fer aquestes simulacions i demostrant que les possibilitats d'aplicació de MESA van més enllà del que s'ha publicat fins ara. S'ha comprovat que MESA sol, sense cap tipus de postprocessat és capaç d'obtenir factors de produció de nucleosyntesi en noves fins a 50 explosions consecutives. També s'ha estudiat la dependència de varies propietats de les noves en funció del numero d'explosió. Malgrat tot, calen més simulacions per poder extreure conclusions definitives. El paper clau de la xarxa de reaccions nuclears considerada també ha estat posat de manifest, mostrant que cal pensar les xarxes específicament per aquest tipus de problemes, i que comprovar que són adequades per a una sola explosió de nova no és suficient. El paper de la implementació en 1D de les inestabilitats hidrodinamiques degudes a la convecció també s'ha estudiat, comprovant que el model utilitzat en MESA és prou bo per simular la barreja entre les capes esteriors de la nana blanca i el material accretat

Modelos de novas clásicas con MESA

Classical novae are thermonuclear runaways at the envelope of a WD due to the piling up of H-rich accreted material. They have been observed to produce heavy elements during the explosion, and their role in galactical abundances for some specific elements may not be negligible. MESA (Modules for Experiments in Stellar Astrophysics) code has been thoroughly studied for its application to nova explosions. Detailed know-how of nova simulations with MESA has been achieved, leading the road of future studies using this tool. Its capablities in the field have been tested, demonstrating to reach further than what has been done in previous literature. MESA has been shown to give accurate nucleosynthesis yields for solar-like accreted material without any further postprocessing up to 50 nova bursts. The dependance of the nova outburst properties with the burst number have been anayzed. However, more simulations are needed in order to extract meaningful conclusions about the role of the burst number in the properties of novae outbursts. The key role of the nuclear reaction network has been highlighted, showing that simulations of consecutive novae outbursts require nuclear reactions networks specifically tested for the work. Many nuclear reaction networks that were thoroughly tested in a single nova explosion have not been capable of properly simulating 10 consecutive outbursts. The role of convective overshoot mixing as implemented in MESA has also been tested. It has been found that as shown in previous literature, it does account for dredge up. We plan to extend this work with simulations of consecutive nova outbursts implementing convective overshoot.Les noves clàssiques són explosions nuclears que es duen a terme a l'embolcall d'una nana blanca, degut a l'accreció de matèria rica en hidrogen. S'ha observat la producció d'elements pesats en aquest tipus d'explosions, i podrien tenir un paper important en les abundancies del elements químics a nivell galàctic. S'ha estudiat l'aplicació del codi MESA (Modules for Experiments in Stellar Astrophysics) a la simulació de noves clàssiques, obtenint conèixement detallat sobre com fer aquestes simulacions i demostrant que les possibilitats d'aplicació de MESA van més enllà del que s'ha publicat fins ara. S'ha comprovat que MESA sol, sense cap tipus de postprocessat és capaç d'obtenir factors de produció de nucleosyntesi en noves fins a 50 explosions consecutives. També s'ha estudiat la dependència de varies propietats de les noves en funció del numero d'explosió. Malgrat tot, calen més simulacions per poder extreure conclusions definitives. El paper clau de la xarxa de reaccions nuclears considerada també ha estat posat de manifest, mostrant que cal pensar les xarxes específicament per aquest tipus de problemes, i que comprovar que són adequades per a una sola explosió de nova no és suficient. El paper de la implementació en 1D de les inestabilitats hidrodinamiques degudes a la convecció també s'ha estudiat, comprovant que el model utilitzat en MESA és prou bo per simular la barreja entre les capes esteriors de la nana blanca i el material accretat

Rugby base model

This dataset contains the result of fitting a Bayesian model using PyMC to results of the Six Nations Championship.The Six Nations Championship is a yearly rugby competition between Italy, Ireland, Scotland, England, France and Wales. Fifteen games are played each year, representing all combinations of the six teams. This example uses and includes results from 2014 - 2017, comprising 60 total games. It models latent parameters for each team's attack and defense hierarchically, with an extra global parameter for the home field advantage.See https://github.com/arviz-devs/arviz_example_data/blob/main/code/rugby/rugby.ipynb for the whole model specification.</p

base_model.nc

Base model for the analysis of LaLiga 2022-2023 results.</p

Rugby hierarchical model on both team and field

A variant of the 'rugby' ArviZ example dataset. Like the 'rugby' dataset, it contains the result of fitting a Bayesian model using PyMC to results of the Six Nations Championship.The Six Nations Championship is a yearly rugby competition between Italy, Ireland, Scotland, England, France and Wales. Fifteen games are played each year, representing all combinations of the six teams. This example uses and includes results from 2014 - 2017, comprising 60 total games. It models latent parameters for each team's attack and defense, with each team having different values depending on them being home or away team.See https://github.com/arviz-devs/arviz_example_data/blob/main/code/rugby_field/rugby_field.ipynb for the whole model specification."</p

nofield_model.nc

Base model for the analysis of LaLiga 2022-2023 results.</p

budget_model.nc

Budget model for the analysis of LaLiga 2022-2023 results.</p

Approximate Laplace approximations for scalable model selection

Includes supplementary materials for the online appendix.We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model selection properties. However, when the sample size is large or one considers many models the cost of the required optimizations becomes impractical. ALA reduces the cost to that of solving a least-squares problem for each model. Further, it enables efficient computation across models such as sharing pre-computed sufficient statistics and certain operations in matrix decompositions. We prove that in generalized (possibly non-linear) models ALA achieves a strong form of model selection consistency for a suitably-defined optimal model, at the same functional rates as exact computation. We consider fixed- and high-dimensional problems, group and hierarchical constraints, and the possibility that all models are misspecified. We also obtain ALA rates for Gaussian regression under non-local priors, an important example where the LA can be costly and does not consistently estimate the integrated likelihood. Our examples include non-linear regression, logistic, Poisson and survival models. We implement the methodology in the R package mombf.Spanish Government grants Europa Excelencia, Grant/Award Number: EUR2020-112096, RYC-2015-18544 and PGC2018-101643-B-I00; NIH, Grant/Award Number: R01 CA158113DMS-01