Modelación y simulación

Many highly-cited papers (42% in the present analysis) present a SA of poor quality.

It is therefore essential to understand the impact of these uncertainties on the model output, if the model is to be used effectively and responsibly in any decision-making process.

sensitivity analysis is “the study of how the uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input”

uncertainty analysis (UA), which, as we define it here, characterizes the uncertainty in model prediction, without identifying which assumptions are primarily responsible

type and structure of model, parameters, resolution, calibration data and so forth

Monte Carlo simulation

“design sensitivity analysis” is used as a tool for structural optimisation

While most practitioners of SA distinguish it from UA, modellers overall tend to conflate the two terms, e.g. performing an uncertainty analysis and calling it a sensitivity analysis.

The sensitivity analysis methodology often relies on so-called local techniques which are invalid for nonlinear models.

The greatest density of papers is found in decision science

an even smaller fraction of papers that feature sensitivity analysis adopts a global SA approach.

at least one-third of highly cited papers, matching our search criteria, use deficient OAT methods.

sensitivity analysis is intrinsically attached to modelling, which itself is not a unified subject.

most scientists conflate the meaning of SA and UA.

global sensitivity analysis unavoidably requires a good background in statistics to implement and to interpret results.

the majority of practitioners remain scattered in isolated pockets, and sensitivity analysis is hence not part of a recognized syllabus.

Both uncertainty and sensitivity analysis should be based on a global exploration of the space of input factors, be it using an experimental design, Monte Carlo or other ad-hoc designs.

perform both uncertainty and sensitivity analysis

to focus the sensitivity analysis on the question addressed by the model rather than more generally on the model

If the model is wrong or if it is a poor representation of reality, determining the sensitivity of an individual parameter in the model is a meaningless pursuit

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling.

Sensitivity analysis (SA), in the most general sense, is the study of how the ‘outputs’ of a ‘system’ are related to, and are influenced by, its ‘inputs’.

‘factors’ in SA, may include model parameters, forcing variables, boundary and initial conditions, choices of model structural configurations, assumptions and constraints.

scientific discovery to explore causalities

dimensionality reduction

decision support

It has roots in ‘design of experiments’ (DOE) which is a broad family of statistical methods

We believe that SA is en route to becoming a mature and independent, but interdisciplinary and enabling, field of science.

opinions on the possible and desirable future evolutions of SA science and practice

The modern era of SA has focused on a notion that is commonly referred to as ‘Global Sensitivity Analysis (GSA)’

Such measures are said to be ‘derivative-based’ as they either analytically compute derivatives or numerically quantify the change in output when factors of interest (continuous or discrete) are perturbed around a point.

The full variance-based SA framework was laid down by Ilya Sobol’ in 1993

One persistent issue in SA is that nearly all applications, regardless of the method used, rest on the assumption that inputs are uncorrelated

ignoring correlation effects and multivariate distributional properties of inputs largely biases, or even falsifies, any SA results

Applications of SA are widespread across many fields, including earth system modeling (Wagener and Pianosi, 2019), engineering (Guo et al., 2016), biomechanics (Becker et al., 2011), water quality modeling (Koo et al., 2020a and 2020b), hydrology (Shin et al., 2013; Haghnegahdar and Razavi, 2017), water security (Puy et al., 2020c), nuclear safety (Saltelli and Tarantola, 2002; Iooss and Marrel, 2019) and epidemiology

it is not a formally recognized discipline

its application in some fields might appear under other titles.

why do I need to run SA for a given problem and what is the underlying question that SA is expected to answer?

how should I design the SA experiment to address that underlying question?

Teach SA more broadly and consistently

a dominant application of SA is for parameter screening, to support model calibration by identifying and fixing non-influential parameters.

Management of uncertainty through its characterization and attribution should be at the heart of the scientific method and, a fortiori, in the use of science for policy

while models are becoming more and more complex, they are treated more and more like a black-box, even by model developers themselves.

SA has significant potential to help in diagnosing the behavior of a mathematical model and for assessing how plausibly the model mimics the system under study for the given application.

To diagnostically test a model, one may compare SA results with expert knowledge on how the underlying system being modeled works.

Most models are poorly-identifiable, largely because of over-parameterization relative to the data and information available

SA and identifiability analysis (IA) are different but complementary

an insensitive parameter is non-identifiable, but the converse is not necessarily true, that is, a sensitive parameter may or may not be identifiable.

Model reduction, however, should be done with caution, as a parameter that seems non-influential under a particular condition might become quite influential under a new condition

fixing parameters that have small sensitivity indices may result in model variations that cannot be explained in the lower dimensional space

Development of research-specific software is at the core of modern modeling efforts.

Computational burden has been a major hindrance to the application of modern SA methods to real-world problems.

The application of SA with machine learning is further complicated because of the fundamental differences between machine learning and other types of models

calls for mutual trust between model developers and end users

The future, therefore, needs new generations of algorithms to keep pace with the ever-increasing complexity and dimensionality of the state-of-the-art models.

A complete assessment of the computational performance of any SA algorithm must be conducted across four aspects: efficiency, convergence, reliability and robustness.

an SA algorithm is robust to sampling variability if its performance remains almost ‘identical’ when applied on two different sample sets taken from the same model.

bootstrapping (Efron, 1987) is often used with SA algorithms to estimate robustness in the form of uncertainty distributions on sensitivity indices without requiring additional model evaluations.

The function evaluation procedure is typically the most computationally intensive component of SA.

future of SA may step more towards ‘sampling-free’ algorithms that can work on any ‘given data’

More recently, authors have proposed parameter estimation procedures based on nearest neighbors (Broto, 2020), rank statistics (Gamboa et al., 2020) and robustness-based optimization (Sheikholeslami and Razavi, 2020)

Higher dimensionality exacerbates the difficulty of assigning multivariate distributions to uncertain inputs

cases require excessively large sample sizes

sampling strategies

uncertainty estimate, it is notable that a minority of works apply this quantification systematically

Sensitivity analysis of sensitivity analysis

informal (and often local) SA has contributed and will continue to contribute to a variety of decision-making problems.

Understand whether the current state of knowledge on input uncertainty is sufficient to enable a decision to be taken

Computational burden is recognized as a major hindrance to the application of SA to cases where SA can be most useful, such as for high-dimensional problems

Their versatility, the variety of their methods, the impossibility of their falsification and their epistemic authority allow mathematical models to escape, better than other cases of quantification, the lenses of sociology and other humanistic disciplines

Models are thus both underexplored and overinterpreted

more actors should engage in practices such as assumption hunting, modelling of the modelling process, and sensitivity analysis and auditing

The state of exception also results from the pretence of neutrality customarily associated with mathematics, and from the asymmetry between developers and users.

‘Funny Numbers’ produced by econometricians to assess the risk of financial instruments

reciprocal domestication between models and society

models are special compared to other families of quantification

Modellers are regarded as endowed with privileged access to the foundations of reality.

Models do not meet classic (Popperian) criteria of scientificity.

a major problem in our use of mathematical models lies in assimilating them to physical laws, and hence treating their predictions with the same dignity

models act as integrators of a broad array of ingredients, including theoretical notions, mathematical concepts and techniques, stylized facts, empirical data, policy views, analogies and metaphors.

models are like metaphors that help us understand how we see the world

consequences of being special

asymmetry between developers and users

models universally known to be wrong continue to play a role in economic policy decisions

Models lend themselves to trans-science. Trans-science refers to scientific practices that appear to be formulated in the language of science, but that science cannot solve because of their sheer complexity or insufficient knowledge

Vulnerability to modelling hubris

models that are too complex (burdened by an excessive number of estimated parameters) may lead to greater imprecision due to error propagation.

Thinking about the reproducibility of models

malpractices such as HARK [Hypothesis After the Results are Known (Kerr Citation 1998)]

In practice, it is safest to treat each run of a model as an experiment.

Sensitivity analysis and sensitivity auditing

Reforming modelling will involve both the adoption of methods in the practice of research and their incorporation into teaching syllabuses.

Uncertainty quantification should be at the heart of the scientific method

there is an evident need for greater clarity on how risk numbers are computed.

The notion that a model can be an avenue of possibly instrumental ‘displacement’, in the sense of moving the attention from the system to its model, as discussed in Rayner ( Citation 2012), is still too radical for many practitioners to contemplate.

preregistration of modelling studies (Ioannidis Citation 2022) is still a long way off

predictions need to be transparent and humble to invite insight, not blame.

The COVID-19 pandemic illustrates perfectly how the operation of science changes when questions of urgency, stakes, values and uncertainty collide — in the ‘post-normal’ regime.

decision makers and citizens need to establish new social norms

Here we present a manifesto for best practices for responsible mathematical modelling

Mind the assumptions Assess uncertainty and sensitivity.

One way to mitigate these issues is to perform global uncertainty and sensitivity analyses.

Mind the hubris Complexity can be the enemy of relevance.

there is a trade-off between the usefulness of a model and the breadth it tries to capture

As more parameters are added, the uncertainty builds up (the uncertainty cascade effect)

The complexity of a model is not always an indicator of how well it captures the important features.

the time needed for water to percolate down to the underground repository level — was uncertain by three orders of magnitude, rendering the size of the model irrelevant

no one can be held accountable if the predictions are catastrophically wrong

Mind the framing Match purpose and context.

No one model can serve all purposes.

all presuppose a set of values about what matters

how to produce a model, assess its uncertainty and communicate the results.

Whenever a model is used for a new application with fresh stakeholders, it must be validated and verified anew.

Mind the consequences Quantification can backfire.

Undiscriminating use of statistical tests can substitute for sound judgement.

Spurious precision adds to a false sense of certainty.

some might imagine a confidence of two significant digits

trust is essential for numbers to be useful

Mind the unknowns Acknowledge ignorance.

models can hide ignorance

Experts should have the courage to respond that “there is no number-answer to your question”

Questions not answers Mathematical models are a great way to explore questions.

Asking models for certainty or consensus is more a sign of the difficulties in making controversial decisions than it is a solution

good modelling cannot be done by modellers alone. It is a social activity.

Following these five points will help to preserve mathematical modelling as a valuable tool.

evolution from local to global methods

future directions and areas of growth in the field

design of experiments

While uncertainty analysis studies the uncertainty in the output, sensitivity analysis studies how the uncertainty in the output can be allocated to the different sources of uncertainty in the input

Sensitivity analysis serves various purposes, including model validation, dimensionality reduction, prioritization of research efforts, pinpointing critical regions within the space of uncertainties under investigation, and aiding decision-making by quantifying how input variations impact outcome uncertainty

independent discipline recognised also by institutional guidelines (European Commission

This “global” understanding started in the 1970s

the sensitivity analysis panorama is still dominated in practically all disciplines by the so-called "local" approaches

tension still characterizing different schools of sensitivity analysis

a good date to set the start of sensitivity analysis is 1905, when Karl Pearson, the founder of modern statistics, proposed the idea of correlation ratio (known as the η2 index)

formalization of the experimental design in the 1920s and 1930s by the statistician Ronald Fisher.

process whereby statistics managed to adjudicate the authority to assess the ‘realism of causes’

World War 2 provided a significant impetus for the expansion and application of sensitivity analysis within the field of operational research

Experimental design continued to develop with several important advancements in this field in the 1950s, including the widespread adoption of factorial designs

Fourier amplitude sensitivity test (FAST) in the early 1970s

At the early stages of the 80's, a notable contribution was made by Efron and Stein (1981) on the variance decomposition into terms of increasing dimensionality

One of the key breakthroughs during this time was the adoption of random sampling techniques

In 1993, Sobol’ introduced an innovative approach to sensitivity analysis based on the decomposition of the output variance

Towards the end of the 1990s, a brand-new community of sensitivity-analysis practitioners emerged, reflecting on the concept of “global sensitivity analysis”

introduced the innovative winding stairs method for computing higher-order effects

emphasizing its application in various settings like factor prioritization, factor fixing, and variance reduction, stressing the need for global methods in order to treat non-linear and non-additive models

A first international conference on global sensitivity analysis (SAMO) was organized in 1995

local sensitivity analysis methods remained prevalent across disciplines

SA practitioners also started to compare the performance of sensitivity analysis methods using SA itself

researchers focused on developing methods for sensitivity analysis of computationally expensive models

The trend toward model complexification emphasized the importance of using sensitivity analysis to ensure accurate and reliable model outputs.

The COVID-19 pandemic was partly instrumental with this development, leading several authors to question the political use of models

Sensitivity analysis and auditing have recently been proposed as tools to jointly match the double demand for technical and normative quality in modelling

the penetration of global sensitivity analysis methods into the broader modelling community has not reached its full potential

Notably absent fields include finance and economics, and, to a lesser extent, medicine and related fields such as psychology and neuroscience

hypothesis testing (e.g Dunnett test), which are capable of answering similar questions.

If sensitivity analysis has not been widely adopted or promoted within a particular discipline, researchers might be less inclined to explore its potential benefits

there is a growing demand for user-friendly tools

In the future, sensitivity analysis is expected to play a pivotal role in guiding model development and decision-making processes, especially as simulation models become increasingly bigger and more complex

Post-Normal Science (PNS)

facts uncertain, values in dispute, stakes high and decisions urgent

it really applies to politics, and not to science

correctly defining the characteristics of both the world, and the relevant science

Post-Normal Science

there are essential social and political dimensions of the problem-solving practice

We use the two attributes of systems uncertainties and decision stakes to distinguish among these.

traditional methodologies are ineffective

The reductionist, analytical worldview which divides systems into ever smaller elements, studied by ever more esoteric specialism, is being replaced by a systemic, synthetic and humanistic approach

In this ‘normal’ state of science, uncertainties are managed automatically, values are unspoken, and foundational problems unheard of.

uncertainty is not banished but is managed, and values are not presupposed but are made explicit

quality of scientific information

problem-solving strategies, analysed in terms of uncertainties in knowledge and complexities in ethics.

uncertainty cannot be banished from science; but that good quality of information depends on good management of its uncertainties

applied science is ‘mission-oriented’; professional consultancy is ‘client-serving’; and post-normal science is ‘issue-driven’

issue-driven

their resolution requires new conceptions of scientific methodology

different kinds of uncertainty can be expressed, and used for an evaluation of quality of scientific information

three zones representing and characterizing three kinds of problem-solving strategies

the research exercise is generally not undertaken unless there is confidence that the uncertainties are low, that is that the problem is likely to be soluble by a normal, puzzle-solving approach

professional consultancy includes applied science

uncertainty is at the methodological level

will be in conflict, involving various human stakeholders and natural systems as well

Of engineering we could say that most routine engineering practice is a matter of empirical craft skills using the results of applied science, while at its highest levels it becomes true professional consultancy.

The outcomes of applied science exercises, like those of core science, have the features of reproducibility and prediction.

professional tasks deal with unique situations, however broadly similar they may be.

it would be unrealistic to expect two safety engineers to produce the same model (or the same conclusions) for a hazard analysis of a complex installation.

these policy issues involve professional consultancy, such disagreements should be seen as inevitable and healthy.

We can envisage four components in the problem-solving task; the process, the product, the person and the purpose

In professional consultancy there can be no simple, objective criteria or processes for quality assurance (beyond simple competence)

post-normal science occurs when uncertainties are either of the epistemological or the ethical kind, or when decision stakes reflect conflicting purposes among stakeholders

post-normal science is indeed a type of science, and not merely politics or public participation

Because of the high level of uncertainty, approaching sheer ignorance in some cases

The uncertainties go beyond those of the systems, to include ethics as well.

In post-normal science, the manifold uncertainties in both products and processes require that the relative importance of persons becomes enhanced.

It is important to appreciate that post-normal science is complementary to applied science and professional consultancy. It is not a replacement for traditional forms of science

modelers can better ponder whether the addition of detail truly matches the model’s purpose

transmission model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), based on more than 900 parameters

the development of finer-grained models often proceeds without having, at the scale required, specific data available to train or validate the model

modelers cannot benefit from existing statistical instruments that help balance model complexity with error so as to align with science’s quest for parsimony, such as Akaike’s (13) or Schwarz’s (14) information criterion

modelers can gauge the connection between model complexity and uncertainty at all stages of model development by calculating the model’s “effective dimensions,” that is, the number of influential parameters and active higher-order effects

effective dimensions

the addition of model detail in process-based models tends to produce more (and not less) uncertain estimates because it increases the model’s effective dimensions, which generally boost the output variance

statistical theory behind the connection between model uncertainty, complexity, and the notion of effective dimensions

how the concept of effective dimensions can help modelers balance model complexity with uncertainty

number of parameters and the pattern of their connections as key contributors to the complexity of mathematical models

aggregate complexity

The effective dimension ks is therefore the order of the highest effect that needs to be included in Eq. 1 to reach p

more complex models will generally display a higher effective dimension in kt and ks, an increase that promotes a larger output uncertainty

a model with more parameters does not necessarily lead to a larger uncertainty if n ≠ k

classic susceptible-infected-recovered (SIR) model is often enhanced with the addition of fine-grained features such as seasonality or age stratification

If the goal of the model is to gain insights into the effects that vaccination and nonpharmaceutical interventions may have on the spread of the virus, then the SIR(S-V) might be preferred over the more complex SIR(S-E) because the extra detail in the latter does not help clarify potential courses of action

importance of stripping mathematical models of superfluous parameters, processes, or linkages

Ti includes all terms in Eq. 3 with the index i

Propiedades del modelo

Anotación del modelo

Documentación de bloques y señales

Adición de notas a las capas del modelo

the output is flat most of the time, but shows a very fast sudden transition. This is typical of stiff systems.

compare the results between ode45 and ode23s

ode45 is not able to recover after the fast transition and keeps taking very small steps. In this specific example, ode45 required 3046 steps to solve the problem, while ode23s required only 91 steps! Ode23s may do more computations per step, but it can take fewer steps than ode45.

discourage

Apply fundamental Simulink® techniques for real-life dynamic physical systems modeling. Dive into modeling systems with multiple components and deepen your understanding of how Simulink® runs simulations behind the scenes.

Learn new modeling constructs, visualization techniques, and how to exchange data with Simulink.

Group related blocks into subsystems.

Introduction to Masking

Integrating Multiple Models

Creating Model References

Create Simulink libraries and manage library links.

Optimizing simulation performance and troubleshooting common performance issues.

Learn the basics of how to create, edit, and simulate models in Simulink®. Use block diagrams to represent real-world systems and simulate components and algorithms.

Learn about Simulink blocks and signals

Blocks and Parameters

MATLAB Workspace Variables

Review dynamic systems and learn how they relate to Simulink

Cultures of Prediction, which bridges history and philosophy, uncovers the dynamic history of prediction in science and engineering over four centuries.

cultures, or modes, of prediction in the history of science and engineering: rational, empirical, iterative-numerical, and exploratory-iterative.

how different modes of prediction, complementary concepts of mathematization, and technology coevolved

Hitting the Target with Mathematics

Engineering Knowledge, Autonomy, and Mathematics

Systems Thinking and the Limits to Growth

The list of sciences that make extensive use of computer simulation has grown to include astrophysics, particle physics, materials science, engineering, fluid mechanics, climate science, evolutionary biology, ecology, economics, decision theory, medicine, sociology, epidemiology, and many others.

In its narrowest sense, a computer simulation is a program that is run on a computer and that uses step-by-step methods to explore the approximate behavior of a mathematical model. Usually this is a model of a real-world system (although the system in question might be an imaginary or hypothetical one)

More broadly, we can think of computer simulation as a comprehensive method for studying systems.

Equation-based Simulations

Agent-based simulations

But some simulation models are hybrids of different kinds of modeling methods. Multiscale simulation models, in particular, couple together modeling elements from different scales of description.

Monte Carlo Simulations

MC simulations are computer algorithms that use randomness to calculate the properties of a mathematical model and where the randomness of the algorithm is not a feature of the target model.

Purposes of Simulation

What warrants our taking a computer simulation to be a severe test of some hypothesis about the natural world?

Verification can be divided into solution verification and code verification.

The principal strategy of validation involves comparing model output with observable data.

A simulation that accurately mimics a complex phenomenon contains a wealth of information about that phenomenon.

Philosophers, consequently, have begun to consider in what sense, if any, computer simulations are like experiments and in what sense they differ.

computer simulations have profound implications for our understanding of the structure of theories

The identity thesis. Computer simulation studies are literally instances of experiments.

Proceso de aprendizaje profesor-alumno, cuyos objetivos y correctivos son trazados por el profesor

Modelar gráficamente, por medio de un diagrama de bloques

cada "estudiante" se caracteriza, igual que el profesor, por parámetros relacionados con sus competencias, valores y actitudes.

un estudiante se puede ajustar al profesor, pero otro tal vez no lo haga y puede tratar de responsabilizarlo de sus problemas y de cambiar sus niveles de exigencia o a al mismo profesor (<b>principio de mínimo esfuerzo</b>)

la adaptación es inherente al ser humano, que deben resolver entre ellos los problemas y desacuerdos que surjan para no desestabilizar todo el proceso de enseñanza (<b>principio de subsidiariedad</b>)

el "profesor" es una clase genérica que se caracteriza por medio de parámetros

los conceptos matemáticos tienen aplicabilidad más allá del contexto en que son originalmente desarrollados.

El milagro de la adecuación del lenguaje matemático para la formulación de las leyes de la física es un regalo maravilloso que no entendemos ni tampoco merecemos.

la estructura matemática de una teoría física a menudo señala el camino para futuros avances en aquella teoría o incluso en predicciones empíricas.

Herramienta de Matlab para el análisis de sensibilidad global y local (OAT) y análisis de incertidumbre de sistemas dinámicos y sistemas estáticos utilizando métodos basados en la varianza. La herramienta se puede descargar libremente desde Mathworks en este enlace. Se incluyen diversos ejemplos, los cuales sirven como base para la solución de otros problemas.

El análisis dimensional es un método que se ocupa del análisis de las relaciones entre diferentes cantidades físicas por medio de la identificación de sus dimensiones sin necesidad de una teoría. Por ejemplo, se pueden establecer los exponentes de expresiones matemáticas que dependen de magnitudes conocidas.

El Enfoque de Sistemas (Teoría de sistemas, Pensamiento sistémico, Teoría General de Sistemas, Ciencia de los sistemas, Sistémica) es el estudio interdisciplinario que proporciona una visión general para la solución integrada y holística de problemas de diversa naturaleza (científicos, sociales, económicos, ecológicos, etc.) con un énfasis en los patrones de cambio y las interacciones, y la integración y transferencia de conocimientos, conceptos y principios de diversas áreas, reduciendo la duplicación del esfuerzo teórico. Este enfoque pretende encontrar reglas y métodos útiles para aplicarse a cualquier tipo de sistema, independientemente del área específica de estudio. De un enfoque no sistémico se dice que es reduccionista.

A continuación, se formulan algunas prácticas para realizar utilizando MATLAB y Simulink, con el fin de aplicar las ideas y métodos presentados en el libro al modelo matemático no lineal en variables de estado de un sistema dinámico real dado en la bibliografía científico. El informe aplica los pasos de la metodología de la investigación y se de presentar en un formato IMRAD que incluye los siguientes aspectos: introducción (descripción del problema e hipótesis), métodos específicos del problema, (cómo), resultados (qué) e interpretación (por qué); en este enlace se describe con detalle los aspectos más importantes para la escritura de un informe tipo artículo científico. Se propone una rúbrica para la evaluación de cada práctica. En el documento de Casos de estudio se dan ejemplos de cómo abordar el estudio de estos sistemas dinámicos.

Los modelos de simulación son imitaciones aproximadas de los sistemas del mundo real y nunca imitan exactamente el sistema del mundo real

la verificación de un modelo es el proceso de confirmar que se implementa correctamente con respecto al modelo conceptual (coincide con las especificaciones y los supuestos que se consideran aceptables para el propósito de la aplicación)

La validación verifica la precisión de la representación del modelo del sistema real.

Esta perspectiva evalúa el progreso reciente en el modelado de los sistemas naturaleza-sociedad para informar el desarrollo sostenible.

Para cada una de las cuatro etapas de la práctica de modelado (definición del propósito, selección de componentes, análisis de interacciones y evaluación de intervenciones), destacamos ejemplos de métodos de modelado dinámico y avances en su aplicación que han mejorado la comprensión y han comenzado a informar la acción.

la aplicación de estos métodos ayuda a los investigadores interesados en aprovechar los conocimientos sobre sectores y ubicaciones específicos para abordar el bienestar humano, centrarse en escalas de tiempo relevantes para la sostenibilidad y atender las diferencias de poder entre los actores.

la aplicación de estos métodos de modelado está ayudando a avanzar en la teoría de los sistemas naturaleza-sociedad al mejorar la aceptación y la utilidad de los marcos, aclarar conceptos clave a través de definiciones más rigurosas e informar el desarrollo de arquetipos que pueden ayudar al desarrollo y la prueba de hipótesis.

Las analogías electromecánicas se utilizan para modelizar el funcionamiento de un sistema mecánico mediante un sistema eléctrico equivalente, estableciendo analogías entre parámetros mecánicos y eléctricos.

Una analogía electromecánica consiste en la representación de un sistema mecánico mediante un circuito eléctrico.

Este enfoque es especialmente útil en el diseño de filtros mecánicos, ya que se utilizan simples dispositivos eléctricos para emular sistemas mecánicos mucho más caros y complejos.

el distanciamiento social moderado normalmente funciona mejor que el intento de cuarentena

el distanciamiento social exhaustivo suele funcionar mejor que cualquier otro

la propagación puede ralentizarse si la gente pone en práctica el “distanciamiento social” evitando los lugares públicos y, en general, limitando sus movimientos.

El rozamiento seco es el producido entre dos superficies, no lubricadas, en contacto.

El rozamiento por rodadura es el que se produce cuando dos sólidos están en contacto y uno rueda sobre el otro.

Cuando el fluido es muy viscoso y la velocidad del objeto es pequeña, puede hacerse la aproximación de que la fuerza de rozamiento es proporcional a la velocidad

Para un objeto que se mueve en aire a una velocidad alta (pero no próximo a la barrera del sonido o supersónica) puede ser una mejor aproximación una ley cuadrática con la velocidad (ley de Rayleigh)

Rozamiento estático: se produce cuando las dos superficies están en reposo relativo

Rozamiento dinámico: se da cuando una de las superficies desliza sobre la otra.

Rozamiento viscoso Un tipo de rozamiento diferente se da en el caso del movimiento de un sólido en el interior de un fluido (líquido o gas). Este rozamiento está causado por las colisiones con las partículas del fluido, que deben ser apartadas para que el sólido pueda moverse por él.

tal escepticismo parece cada vez más común y cada vez más independiente de la posición ideológica

¿el tono de este tipo de ataques refleja un colapso de la confianza en la empresa científica y en su papel social e institucional?

la sociedad puede estar menos dispuesta a aceptar tales afirmaciones que en el pasado

los peligros para la ciencia se hacen más evidentes cuando los modelos —resúmenes de problemas más complejos del mundo real, generalmente expresados en términos matemáticos— se utilizan como herramientas de política.

serie particularmente accesible de historias de terror sobre el mal uso de los modelos y el consiguiente fracaso de las políticas

la precisión y el valor de las predicciones en sí mismas terminan estando en el centro de los debates políticos y distraen de la necesidad y la capacidad de abordar el problema a pesar de las incertidumbres actuales.

"todos los modelos son erróneos, pero algunos son útiles"

se deben adoptar criterios estrictos de transparencia cuando los modelos se utilizan como base para las evaluaciones de políticas

cuanto más se entiende el clima, más inciertas se vuelven las predicciones de los modelos de futuros climáticos específicos

Muchas pequeñas incertidumbres multiplicadas juntas producen enormes incertidumbres agregadas.

El desafío se vuelve aún más desalentador cuando los modeladores centran su atención en las consecuencias económicas de los cambios en la composición atmosférica.

Semejante esfuerzo está tan alejado de la capacidad predictiva actual que raya en lo irresponsable.

la mayoría de los aspectos de la mayoría de los modelos no estarán sujetos a un escrutinio tan minucioso

se basan en lo que los modelos pronostican sobre el futuro, con poca o ninguna sensibilidad a los límites de lo que los modelos son realmente capaces de pronosticar con precisión.

proponemos siete reglas que, en su conjunto, forman una lista de verificación para el desarrollo y uso responsable de los modelos.

análisis de sensibilidad global

El análisis de sensibilidad global evalúa la importancia relativa de los factores de entrada en términos del impacto de su incertidumbre en la salida del modelo.

¿Cuál de esas incertidumbres tiene el mayor impacto en el resultado?

"auditoría de sensibilidad"

La "auditoría" hace hincapié en la idea de la rendición de cuentas a un público más amplio (en este caso, los responsables de la formulación de políticas y el público) y, por lo tanto, exige que el modelo sea accesible y transparente y que la experiencia no se defina de manera estrecha para excluir a todos excepto a quienes crearon el modelo

La auditoría de sensibilidad no tiene como objetivo mejorar el modelo; Más bien, al igual que una auditoría fiscal, se produce al final del proceso, en el momento en que el modelo se convierte en una herramienta para la evaluación de políticas, cuando todos los desarrolladores han llevado a cabo toda la calibración posible del modelo, la optimización, la asimilación de datos y similares utilizando las herramientas de su oficio.

Regla 1: Usa los modelos para aclarar, no para oscurecer.

La Regla 1 prescribe que se deben plantear preguntas sobre quién se beneficia del modelo y qué motivaciones e incentivos animan a los desarrolladores de modelos.

Regla 2: Adopta una actitud de "caza de suposiciones"

Se requieren nuevos procesos para el desarrollo y uso de modelos, en los que las partes interesadas comprometidas trabajen con expertos disciplinarios para desarrollar nuevos modelos que puedan utilizarse para probar diversas opciones de política

exige que los modelos utilizados para guiar las decisiones regulatorias se pongan a disposición de un tercero para permitir la evaluación del impacto de cambiar los supuestos o parámetros de entrada en la conclusión basada en el modelo.

Regla 3: Detectar la pseudociencia.

definimos la pseudociencia como la práctica de ignorar u ocultar las incertidumbres en las entradas del modelo para garantizar que las salidas del modelo se puedan vincular a las opciones de política preferidas.

Un indicador común de este tipo de pseudociencia es la precisión espuria, por ejemplo, cuando se da un resultado con un número de dígitos que excede (a veces ridículamente) cualquier estimación plausible de la precisión asociada.

C. F. Gauss, "la falta de cultura matemática no se revela en ninguna parte de manera tan conspicua como en la precisión sin sentido en los cálculos numéricos"

No publique sus inferencias sin haber realizado una cuidadosa auditoría de sensibilidad.

Regla 4: Encuentra suposiciones sensibles antes de que te encuentren.

"Confesarás en presencia de la sensibilidad. Corolario: Anticiparás la crítica"

Cualquier inferencia basada en modelos que se introduzca en el entorno político sin ir acompañada de un análisis de sensibilidad técnicamente sólido debe considerarse sospechosa.

<b _istranslated="1">Regla 5: Apunta a la transparencia.</b> Las partes interesadas deben ser capaces de dar sentido y, si es posible, replicar los resultados del análisis.

las representaciones de modelos simples o parsimoniosos son mejores que los modelos más "sofisticados" o complejos, cuando se utilizan para evaluaciones de impacto de políticas.

<b _istranslated="1">Regla 6: No te limites a "hacer bien las sumas", sino "hacer las sumas correctas".</b> Cuando se descuidan los puntos de vista relevantes de las partes interesadas, los modeladores pueden centrarse o abordar las incertidumbres equivocadas.

<font _mstmutation="1" _msttexthash="5643729" _msthash="402">un error de tipo uno es un falso positivo: se determina que una práctica es insegura cuando es segura</font><span class="diigoHighlightCommentLocator"></span>, o que una intervención no es beneficiosa cuando es beneficiosa. <font _mstmutation="1" _msttexthash="1845259" _msthash="404">Un error de tipo dos es lo contrario: un falso negativo.</font><span class="diigoHighlightCommentLocator"></span> <font _mstmutation="1" _msttexthash="14838902" _msthash="406">Un error de tipo tres, por el contrario, es aquel en el que el análisis en sí mismo se enmarca incorrectamente y, por lo tanto, el problema se caracteriza erróneamente.</font>

es fácil caer en lo que podemos llamar "lamp-posting", en el que las incertidumbres o parámetros que se examinan con más detenimiento son los menos relevantes pero más fáciles de analizar

<b _istranslated="1">Regla 7: Enfoca el análisis.</b> No haga análisis de sensibilidad superficiales, simplemente cambiando un factor a la vez.

Por ejemplo, en un sistema con 10 factores inciertos, si se mueve solo uno a la vez, se corre el riesgo de explorar solo una pequeña parte de la incertidumbre de entrada potencial total.

la elección de una línea de base es en sí misma un proceso cargado de suposiciones y, por lo tanto, está sujeta a críticas y análisis de sensibilidad.

Una auditoría de sensibilidad creíble no debe estar anclada a bases de referencia que son en sí mismas subjetivas; Deben evaluar el efecto de cualquier entrada, mientras que todas las demás entradas también pueden variar.

Nuestra opinión es que las prácticas actuales de modelización, en su desarrollo y uso, son una amenaza significativa para la legitimidad y la utilidad de la ciencia en entornos políticos controvertidos.