| 1. |
- Diaz-Pachón, Daniel Andrés, et al.
(författare)
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Assessing, Testing and Estimating the Amount of Fine-Tuning by Means of Active Information
- 2022
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Ingår i: Entropy. - : MDPI AG. - 1099-4300. ; 24:10
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Tidskriftsartikel (refereegranskat)abstract
- A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes use of in order to reach a certain target. A function f quantifies specificity for each possible outcome x of a search, so that the target of the algorithm is a set of highly specified states, whereas fine-tuning occurs if it is much more likely for the algorithm to reach the target as intended than by chance. The distribution of a random outcome X of the algorithm involves a parameter θ that quantifies how much background information has been infused. A simple choice of this parameter is to use θf in order to exponentially tilt the distribution of the outcome of the search algorithm under the null distribution of no tuning, so that an exponential family of distributions is obtained. Such algorithms are obtained by iterating a Metropolis–Hastings type of Markov chain, which makes it possible to compute their active information under the equilibrium and non-equilibrium of the Markov chain, with or without stopping when the targeted set of fine-tuned states has been reached. Other choices of tuning parameters θ are discussed as well. Nonparametric and parametric estimators of active information and tests of fine-tuning are developed when repeated and independent outcomes of the algorithm are available. The theory is illustrated with examples from cosmology, student learning, reinforcement learning, a Moran type model of population genetics, and evolutionary programming.
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| 2. |
- Díaz-Pachón, Daniel Andrés, et al.
(författare)
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Is It Possible to Know Cosmological Fine-tuning?
- 2024
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Ingår i: Astrophysical Journal Supplement Series. - 0067-0049 .- 1538-4365. ; 271:2
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Tidskriftsartikel (refereegranskat)abstract
- Fine-tuning studies whether some physical parameters, or relevant ratios between them, are located within so-called life-permitting intervals of small probability outside of which carbon-based life would not be possible. Recent developments have found estimates of these probabilities that circumvent previous concerns of measurability and selection bias. However, the question remains whether fine-tuning can indeed be known. Using a mathematization of the concepts of learning and knowledge acquisition, we argue that most examples that have been touted as fine-tuned cannot be formally assessed as such. Nevertheless, fine-tuning can be known when the physical parameter is seen as a random variable and it is supported in the nonnegative real line, provided the size of the life-permitting interval is small in relation to the observed value of the parameter.
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| 3. |
- Díaz-Pachón, Daniel Andrés, et al.
(författare)
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Sometimes Size Does Not Matter
- 2023
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 53:1
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Tidskriftsartikel (refereegranskat)abstract
- Recently Díaz, Hössjer and Marks (DHM) presented a Bayesian framework to measure cosmological tuning (either fine or coarse) that uses maximum entropy (maxent) distributions on unbounded sample spaces as priors for the parameters of the physical models (https://doi.org/10.1088/1475-7516/2021/07/020). The DHM framework stands in contrast to previous attempts to measure tuning that rely on a uniform prior assumption. However, since the parameters of the models often take values in spaces of infinite size, the uniformity assumption is unwarranted. This is known as the normalization problem. In this paper we explain why and how the DHM framework not only evades the normalization problem but also circumvents other objections to the tuning measurement like the so called weak anthropic principle, the selection of a single maxent distribution and, importantly, the lack of invariance of maxent distributions with respect to data transformations. We also propose to treat fine-tuning as an emergence problem to avoid infinite loops in the prior distribution of hyperparameters (common to all Bayesian analysis), and explain that previous attempts to measure tuning using uniform priors are particular cases of the DHM framework. Finally, we prove a theorem, explaining when tuning is fine or coarse for different families of distributions. The theorem is summarized in a table for ease of reference, and the tuning of three physical parameters is analyzed using the conclusions of the theorem.
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| 4. |
- Ekheden, Erland, 1982-, et al.
(författare)
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Analysis of the Stochasticity of Mortality Using Variance Decomposition
- 2014
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Ingår i: Modern Problems in Insurance Mathematics. - Cham : Springer Publishing Company. - 9783319066523 ; , s. 199-222
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Bokkapitel (refereegranskat)abstract
- We analyse the stochasticity in mortality data from the USA, the UK and Sweden, and in particular to which extent mortality rates are explained by systematic variation, due to various risk factors, and random noise. We formalise this in terms of a mixed regression model with a logistic link function, and decomposethe variance of the observations into three parts: binomial risk, the variance due to random mortality variation in a finite population, systematic risk explained by the covariates and unexplained systematic risk, variance that comes from real changes in mortality rates, not captured by the covariates. The fraction of unexplained variance caused by binomial risk provides a limit in terms of the resolution that can be achieved by a model. This can be used as a model selection tool for selecting the number of covariates and regression parameters of the deterministic part of the regression function, and for testing whether unexplained systematic variation should be explicitly modelled or not. We use a two-factor model with ageand calendar year as covariates, and perform the variance decomposition for a simple model with a linear time trend on the logit scale. The population size turns out to be crucial, and for Swedish data, the simple model works surprisingly well, leaving only a small fraction of unexplained systematic risk, whereas for the UK and the USA, the amount of unexplained systematic risk is larger, so that more elaborate models might work better.
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| 5. |
- Ekheden, Erland, 1982-, et al.
(författare)
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Multivariate Time Series Modeling, Estimation and Prediction of Mortalities
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a mixed regression model for morality data whichcan be decomposed into a deterministic trend component explainedby the covariates age and calendar year, a multivariate Gaussian timeseries part not explained by the covariates, and binomial risk. Datacan be analyzed by means of a simple logistic regression model whenthe multivariate Gaussian time series component is absent and there isno overdispersion, as in Ekheden and Hössjer (2014). In this paper werather allow for overdispersion and the mixed regression model is ttedto mortality data from the United States and Sweden, with the aim toprovide prediction and condence intervals for future mortality, as wellas smoothing historical data, using the best linear unbiased predictor.We nd that the form of the Gaussian time series has a large impact onthe width of the prediction intervals, and it poses some new questionson proper model selection.
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| 6. |
- Ekheden, Erland, 1982-, et al.
(författare)
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Pricing catastrophe risk in life (re)insurance
- 2014
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Ingår i: Scandinavian Actuarial Journal. - London : Taylor & Francis. - 0346-1238 .- 1651-2030. ; 2014:4, s. 352-367
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Tidskriftsartikel (refereegranskat)abstract
- What is the catastrophe risk a life insurance company faces? What is the correct price of a catastrophe cover? During a review of the current standard model, due to Strickler, we found that this model has some serious shortcomings. We therefore present a new model for the pricing of catastrophe excess of loss cover (Cat XL). The new model for annual claim cost C is based on a compound Poisson processof catastrophe costs. To evaluate the distribution of the cost of each catastrophe, we use the Peaks Over Threshold model for the total number of lost lives in each catastrophe and the beta binomial model for the proportion of these corresponding to customers of the insurance company. To be able to estimate the parameters of the model, international and Swedish data were collected and compiled,listing accidents claiming at least twenty and four lives, respectively. Fitting the new model to data, we find the fit to be good. Finally we give the price of a Cat XL contract and perform a sensitivity analysis of how some of the parameters affect the expected value and standard deviation of the cost and thus the price.
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| 7. |
- Hössjer, Ola, 1964-, et al.
(författare)
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A Formal Framework for Knowledge Acquisition : Going beyond Machine Learning
- 2022
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Ingår i: Entropy. - : MDPI AG. - 1099-4300. ; 24:10
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Tidskriftsartikel (refereegranskat)abstract
- Philosophers frequently define knowledge as justified, true belief. We built a mathematical framework that makes it possible to define learning (increasing number of true beliefs) and knowledge of an agent in precise ways, by phrasing belief in terms of epistemic probabilities, defined from Bayes’ rule. The degree of true belief is quantified by means of active information I+: a comparison between the degree of belief of the agent and a completely ignorant person. Learning has occurred when either the agent’s strength of belief in a true proposition has increased in comparison with the ignorant person (I+>0), or the strength of belief in a false proposition has decreased (I+<0). Knowledge additionally requires that learning occurs for the right reason, and in this context we introduce a framework of parallel worlds that correspond to parameters of a statistical model. This makes it possible to interpret learning as a hypothesis test for such a model, whereas knowledge acquisition additionally requires estimation of a true world parameter. Our framework of learning and knowledge acquisition is a hybrid between frequentism and Bayesianism. It can be generalized to a sequential setting, where information and data are updated over time. The theory is illustrated using examples of coin tossing, historical and future events, replication of studies, and causal inference. It can also be used to pinpoint shortcomings of machine learning, where typically learning rather than knowledge acquisition is in focus.
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| 8. |
- Hössjer, Ola, 1964-, et al.
(författare)
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An Information Theoretic Approach to Prevalence Estimation and Missing Data
- 2024
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 70:5, s. 3567-3582
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Tidskriftsartikel (refereegranskat)abstract
- Many data sources, including tracking social behavior to election polling to testing studies for understanding disease spread, are subject to sampling bias whose implications are not fully yet understood. In this paper we study estimation of a given feature (such as disease, or behavior at social media platforms) from biased samples, treating non-respondent individuals as missing data. Prevalence of the feature among sampled individuals has an upward bias under the assumption of individuals’ willingness to be sampled. This can be viewed as a regression model with symptoms as covariates and the feature as outcome. It is assumed that the outcome is unknown at the time of sampling, and therefore the missingness mechanism only depends on the covariates. We show that data, in spite of this, is missing at random only when the sizes of symptom classes in the population are known; otherwise data is missing not at random. With an information theoretic viewpoint, we show that sampling bias corresponds to external information due to individuals in the population knowing their covariates, and we quantify this external information by active information. The reduction in prevalence, when sampling bias is adjusted for, similarly translates into active information due to bias correction, with opposite sign to active information due to testing bias. We develop unified results that show that prevalence and active information estimates are asymptotically normal under all missing data mechanisms, when testing errors are absent and present respectively. The asymptotic behavior of the estimators is illustrated through simulations.
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| 9. |
- Hössjer, Ola, 1964-, et al.
(författare)
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Assessment of the Global Variance Effective Size of Subdivided Populations, and Its Relation to Other Effective Sizes
- 2023
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Ingår i: Acta Biotheoretica. - 0001-5342 .- 1572-8358. ; 71:3
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Tidskriftsartikel (refereegranskat)abstract
- The variance effective population size (N-eV) is frequently used to quantify the expected rate at which a population's allele frequencies change over time. The purpose of this paper is to find expressions for the global N-eV of a spatially structured population that are of interest for conservation of species. Since N-eV depends on allele frequency change, we start by dividing the cause of allele frequency change into genetic drift within subpopulations (I) and a second component mainly due to migration between subpopulations (II). We investigate in detail how these two components depend on the way in which subpopulations are weighted as well as their dependence on parameters of the model such a migration rates, and local effective and census sizes. It is shown that under certain conditions the impact of II is eliminated, and N-eV of the metapopulation is maximized, when subpopulations are weighted proportionally to their long term reproductive contributions. This maximal N-eV is the sought for global effective size, since it approximates the gene diversity effective size N-eGD, a quantifier of the rate of loss of genetic diversity that is relevant for conservation of species and populations. We also propose two novel versions of N-eV, one of which (the backward version of N-eV) is most stable, exists for most populations, and is closer to N-eGD than the classical notion of N-eV. Expressions for the optimal length of the time interval for measuring genetic change are developed, that make it possible to estimate any version of N-eV with maximal accuracy.
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| 10. |
- Hössjer, Ola, 1964-
(författare)
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Coalescence theory for a general class of structured populations with fast migration
- 2011
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Ingår i: Advances in Applied Probability. - : Cambridge University Press (CUP). - 0001-8678 .- 1475-6064. ; 43:4, s. 1027-1047
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study a general class of population genetic models where the total population is divided into a number of subpopulations or types. Migration between subpopulations is fast. Extending the results of Nordborg and Krone (2002) and Sagitov and Jagers (2005), we prove, as the total population size N tends to infinity, weak convergence of the joint ancestry of a given sample of haploid individuals in the Skorokhod topology towards Kingman's coalescent with a constant change of time scale c. Our framework includes age-structured models, geographically structured models, and combinations thereof. We also allow each individual to have offspring in several subpopulations, with general dependency structures between the number of offspring of various types. As a byproduct, explicit expressions for the coalescent effective population size N/c are obtained.
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