Nanoinformatics

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Nanoinformatics 

Nanoinformatics is the application of informatics to nanotechnology. It is an interdisciplinary field that develops methods and software tools for understanding nanomaterials, their properties, and their interactions with biological entities, and using that information more efficiently. It differs from cheminformatics in that nanomaterials usually involve nonuniform collections of particles that have distributions of physical properties that must be specified. The nanoinformatics infrastructure includes ontologies for nanomaterials, file formats, and data repositories.

Nanoinformatics has applications for improving workflows in fundamental research, manufacturing, and environmental health, allowing the use of high-throughput data-driven methods to analyze broad sets of experimental results. Nanomedicine applications include analysis of nanoparticle-based pharmaceuticals for structure–activity relationships in a similar manner to bioinformatics.

Background

Context of nanoinformatics as a convergence of science and practice at the nexus of safety, health, well-being, and productivity; risk management; and emerging nanotechnology.

While conventional chemicals are specified by their chemical composition, and concentration, nanoparticles have other physical properties that must be measured for a complete description, such as size, shape, surface properties, crystallinity, and dispersion state. In addition, preparations of nanoparticles are often non-uniform, having distributions of these properties that must also be specified. These molecular-scale properties influence their macroscopic chemical and physical properties, as well as their biological effects. They are important in both the experimental characterization of nanoparticles and their representation in an informatics system. The context of nanoinformatics is that effective development and implementation of potential applications of nanotechnology requires the harnessing of information at the intersection of safety, health, well-being, and productivity; risk management; and emerging nanotechnology.

A graphical representation of a working definition of nanoinformatics as a life-cycle process

One working definition of nanoinformatics developed through the community-based Nanoinformatics 2020 Roadmap and subsequently expanded is:

• Determining which information is relevant to meeting the safety, health, well-being, and productivity objectives of the nanoscale science, engineering, and technology community;
• Developing and implementing effective mechanisms for collecting, validating, storing, sharing, analyzing, modeling, and applying the information;
• Confirming that appropriate decisions were made and that desired mission outcomes were achieved as a result of that information; and finally
• Conveying experience to the broader community, contributing to generalized knowledge, and updating standards and training.

Data representations

Although nanotechnology is the subject of significant experimentation, much of the data are not stored in standardized formats or broadly accessible. Nanoinformatics initiatives seek to coordinate developments of data standards and informatics methods.

Ontologies

An overview of the eNanoMapper nanomaterial ontology

In the context of information science, an ontology is a formal representation of knowledge within a domain, using hierarchies of terms including their definitions, attributes, and relations. Ontologies provide a common terminology in a machine-readable framework that facilitates sharing and discovery of data. Having an established ontology for nanoparticles is important for cancer nanomedicine due to the need of researchers to search, access, and analyze large amounts of data.

The NanoParticle Ontology is an ontology for the preparation, chemical composition, and characterization of nanomaterials involved in cancer research. It uses the Basic Formal Ontology framework and is implemented in the Web Ontology Language. It is hosted by the National Center for Biomedical Ontology and maintained on GitHub. The eNanoMapper Ontology is more recent and reuses wherever possible already existing domain ontologies. As such, it reuses and extends the NanoParticle Ontology, but also the BioAssay Ontology, Experimental Factor Ontology, Unit Ontology, and ChEBI.

File formats

Flowchart depicting the ways to identify different components of a material sample to guide the creation of an ISA-TAB-Nano Material file

ISA-TAB-Nano is a set of four spreadsheet-based file formats for representing and sharing nanomaterial data, based on the ISA-TAB metadata standard. In Europe, other templates have been adopted that were developed by the Institute of Occupational Medicine, and by the Joint Research Centre for the NANoREG project.

Tools

Nanoinformatics is not limited to aggregating and sharing information about nanotechnologies, but has many complementary tools, some originating from chemoinformatics and bioinformatics.

Databases and repositories

Over the last couple of years, various databases have been made available.

caNanoLab, developed by the U.S. National Cancer Institute, focuses on nanotechnologies related to biomedicine. The NanoMaterials Registry, maintained by RTI International, is a curated database of nanomaterials, and includes data from caNanoLab.

The eNanoMapper database, a project of the EU NanoSafety Cluster, is a deployment of the database software developed in the eNanoMapper project. It has since been used in other settings, such as the EU Observatory for NanoMaterials (EUON).

Other databases include the Center for the Environmental Implications of NanoTechnology's NanoInformatics Knowledge Commons (NIKC) and NanoDatabank, PEROSH's Nano Exposure & Contextual Information Database (NECID), Data and Knowledge on Nanomaterials (DaNa), and Springer Nature's Nano database.

Applications

Nanoinformatics has applications for improving workflows in fundamental research, manufacturing, and environmental health, allowing the use of high-throughput data-driven methods to analyze broad sets of experimental results.

Nanoinformatics is especially useful in nanoparticle-based cancer diagnostics and therapeutics. They are very diverse in nature due to the combinatorially large numbers of chemical and physical modifications that can be made to them, which can cause drastic changes in their functional properties. This leads to a combinatorial complexity that far exceeds, for example, genomic data. Nanoinformatics can enable structure–activity relationship modelling for nanoparticle-based drugs. Nanoinformatics and biomolecular nanomodeling provide a route for effective cancer treatment. Nanoinformatics also enables a data-driven approach to the design of materials to meet health and environmental needs.

Modeling and NanoQSAR

Viewed as a workflow process, nanoinformatics deconstructs experimental studies using data, metadata, controlled vocabularies and ontologies to populate databases so that trends, regularities and theories will be uncovered for use as predictive computational tools. Models are involved at each stage, some material (experiments, reference materials, model organisms) and some abstract (ontology, mathematical formulae), and all intended as a representation of the target system. Models can be used in experimental design, may substitute for experiment or may simulate how a complex system changes over time.

At present, nanoinformatics is an extension of bioinformatics due to the great opportunities for nanotechnology in medical applications, as well as to the importance of regulatory approvals to product commercialization. In these cases, the models target, their purposes, may be physico-chemical, estimating a property based on structure (quantitative structure–property relationship, QSPR); or biological, predicting biological activity based on molecular structure (quantitative structure–activity relationship, QSAR) or the time-course development of a simulation (physiologically based toxicokinetics, PBTK). Each of these has been explored for small molecule drug development with a supporting body of literature.

Particles differ from molecular entities, especially in having surfaces that challenge nomenclature system and QSAR/PBTK model development. For example, particles do not exhibit an octanol–water partition coefficient, which acts as a motive force in QSAR/PBTK models; and they may dissolve in vivo or have band gaps. Illustrative of current QSAR and PBTK models are those of Puzyn et al. and Bachler et al. The OECD has codified regulatory acceptance criteria, and there are guidance roadmaps with supporting workshops to coordinate international efforts.

Communities

Communities active in nanoinformatics include the European Union NanoSafety Cluster, The U.S. National Cancer Institute National Cancer Informatics Program's Nanotechnology Working Group, and the US–EU Nanotechnology Communities of Research.

Nanoinformatics roles, responsibilities, and communication interfaces

Individuals who engage in nanoinformatics can be viewed as fitting across four categories of roles and responsibilities for nanoinformatics methods and data:

• Customers, who need either the methods to create the data, the data itself, or both, and who specify the scientific applications and characterization methods and data needs for their intended purposes;
• Creators, who develop relevant and reliable methods and data to meet the needs of customers in the nanotechnology community;
• Curators, who maintain and ensure the quality of the methods and associated data; and
• Analysts, who develop and apply methods and models for data analysis and interpretation that are consistent with the quality and quantity of the data and that meet customers’ needs.

In some instances, the same individuals perform all four roles. More often, many individuals must interact, with their roles and responsibilities extending over significant distances, organizations, and time. Effective communication is important across each of the twelve links (in both directions across each of the six pairwise interactions) that exist among the various customers, creators, curators, and analysts.

History

One of the first mentions of nanoinformatics was in the context of handling information about nanotechnology.

An early international workshop with substantial discussion of the need for sharing all types of information on nanotechnology and nanomaterials was the First International Symposium on Occupational Health Implications of Nanomaterials held 12–14 October 2004 at the Palace Hotel, Buxton, Derbyshire, UK. The workshop report included a presentation on Information Management for Nanotechnology Safety and Health that described the development of a Nanoparticle Information Library (NIL) and noted that efforts to ensure the health and safety of nanotechnology workers and members of the public could be substantially enhanced by a coordinated approach to information management. The NIL subsequently served as an example for web-based sharing of characterization data for nanomaterials.

The National Cancer Institute prepared in 2009 a rough vision of, what was then still called, nanotechnology informatics, outlining various aspects of what nanoinformatics should comprise. This was later followed by two roadmaps, detailing existing solutions, needs, and ideas on how the field should further develop: the Nanoinformatics 2020 Roadmap and the EU US Roadmap Nanoinformatics 2030.

A 2013 workshop on nanoinformatics described current resources, community needs and the proposal of a collaborative framework for data sharing and information integration.

Statistical inference

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Statistical_inference

 

Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.

Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term inference is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as training or learning (rather than inference), and using a model for prediction is referred to as inference (instead of prediction); see also predictive inference.

Introduction

Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling. Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.

Konishi & Kitagawa state, "The majority of the problems in statistical inference can be considered to be problems related to statistical modeling". Relatedly, Sir David Cox has said, "How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis".

The conclusion of a statistical inference is a statistical proposition. Some common forms of statistical proposition are the following:

• a point estimate, i.e. a particular value that best approximates some parameter of interest;
• an interval estimate, e.g. a confidence interval (or set estimate), i.e. an interval constructed using a dataset drawn from a population so that, under repeated sampling of such datasets, such intervals would contain the true parameter value with the probability at the stated confidence level;
• a credible interval, i.e. a set of values containing, for example, 95% of posterior belief;
• rejection of a hypothesis;
• clustering or classification of data points into groups.

Models and assumptions

Main articles: Statistical model and Statistical assumptions

Any statistical inference requires some assumptions. A statistical model is a set of assumptions concerning the generation of the observed data and similar data. Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference. Descriptive statistics are typically used as a preliminary step before more formal inferences are drawn.

Degree of models/assumptions

Statisticians distinguish between three levels of modeling assumptions;

• Fully parametric: The probability distributions describing the data-generation process are assumed to be fully described by a family of probability distributions involving only a finite number of unknown parameters. For example, one may assume that the distribution of population values is truly Normal, with unknown mean and variance, and that datasets are generated by 'simple' random sampling. The family of generalized linear models is a widely used and flexible class of parametric models.
• Non-parametric: The assumptions made about the process generating the data are much less than in parametric statistics and may be minimal. For example, every continuous probability distribution has a median, which may be estimated using the sample median or the Hodges–Lehmann–Sen estimator, which has good properties when the data arise from simple random sampling.
• Semi-parametric: This term typically implies assumptions 'in between' fully and non-parametric approaches. For example, one may assume that a population distribution has a finite mean. Furthermore, one may assume that the mean response level in the population depends in a truly linear manner on some covariate (a parametric assumption) but not make any parametric assumption describing the variance around that mean (i.e. about the presence or possible form of any heteroscedasticity). More generally, semi-parametric models can often be separated into 'structural' and 'random variation' components. One component is treated parametrically and the other non-parametrically. The well-known Cox model is a set of semi-parametric assumptions.

Importance of valid models/assumptions

See also: Statistical model validation

The above image shows a histogram assessing the assumption of normality, which can be illustrated through the even spread underneath the bell curve.

Whatever level of assumption is made, correctly calibrated inference, in general, requires these assumptions to be correct; i.e. that the data-generating mechanisms really have been correctly specified.

Incorrect assumptions of 'simple' random sampling can invalidate statistical inference. More complex semi- and fully parametric assumptions are also cause for concern. For example, incorrectly assuming the Cox model can in some cases lead to faulty conclusions. Incorrect assumptions of Normality in the population also invalidates some forms of regression-based inference. The use of any parametric model is viewed skeptically by most experts in sampling human populations: "most sampling statisticians, when they deal with confidence intervals at all, limit themselves to statements about [estimators] based on very large samples, where the central limit theorem ensures that these [estimators] will have distributions that are nearly normal." In particular, a normal distribution "would be a totally unrealistic and catastrophically unwise assumption to make if we were dealing with any kind of economic population." Here, the central limit theorem states that the distribution of the sample mean "for very large samples" is approximately normally distributed, if the distribution is not heavy-tailed.

Approximate distributions

Main articles: Statistical distance, Asymptotic theory (statistics), and Approximation theory

Given the difficulty in specifying exact distributions of sample statistics, many methods have been developed for approximating these.

With finite samples, approximation results measure how close a limiting distribution approaches the statistic's sample distribution: For example, with 10,000 independent samples the normal distribution approximates (to two digits of accuracy) the distribution of the sample mean for many population distributions, by the Berry–Esseen theorem. Yet for many practical purposes, the normal approximation provides a good approximation to the sample-mean's distribution when there are 10 (or more) independent samples, according to simulation studies and statisticians' experience. Following Kolmogorov's work in the 1950s, advanced statistics uses approximation theory and functional analysis to quantify the error of approximation. In this approach, the metric geometry of probability distributions is studied; this approach quantifies approximation error with, for example, the Kullback–Leibler divergence, Bregman divergence, and the Hellinger distance.

With indefinitely large samples, limiting results like the central limit theorem describe the sample statistic's limiting distribution if one exists. Limiting results are not statements about finite samples, and indeed are irrelevant to finite samples. However, the asymptotic theory of limiting distributions is often invoked for work with finite samples. For example, limiting results are often invoked to justify the generalized method of moments and the use of generalized estimating equations, which are popular in econometrics and biostatistics. The magnitude of the difference between the limiting distribution and the true distribution (formally, the 'error' of the approximation) can be assessed using simulation. The heuristic application of limiting results to finite samples is common practice in many applications, especially with low-dimensional models with log-concave likelihoods (such as with one-parameter exponential families).

Randomization-based models

Main article: Randomization

See also: Random sample and Random assignment

For a given dataset that was produced by a randomization design, the randomization distribution of a statistic (under the null-hypothesis) is defined by evaluating the test statistic for all of the plans that could have been generated by the randomization design. In frequentist inference, the randomization allows inferences to be based on the randomization distribution rather than a subjective model, and this is important especially in survey sampling and design of experiments. Statistical inference from randomized studies is also more straightforward than many other situations. In Bayesian inference, randomization is also of importance: in survey sampling, use of sampling without replacement ensures the exchangeability of the sample with the population; in randomized experiments, randomization warrants a missing at random assumption for covariate information.

Objective randomization allows properly inductive procedures. Many statisticians prefer randomization-based analysis of data that was generated by well-defined randomization procedures. (However, it is true that in fields of science with developed theoretical knowledge and experimental control, randomized experiments may increase the costs of experimentation without improving the quality of inferences.) Similarly, results from randomized experiments are recommended by leading statistical authorities as allowing inferences with greater reliability than do observational studies of the same phenomena. However, a good observational study may be better than a bad randomized experiment.

The statistical analysis of a randomized experiment may be based on the randomization scheme stated in the experimental protocol and does not need a subjective model.

However, at any time, some hypotheses cannot be tested using objective statistical models, which accurately describe randomized experiments or random samples. In some cases, such randomized studies are uneconomical or unethical.

Model-based analysis of randomized experiments

It is standard practice to refer to a statistical model, e.g., a linear or logistic models, when analyzing data from randomized experiments. However, the randomization scheme guides the choice of a statistical model. It is not possible to choose an appropriate model without knowing the randomization scheme. Seriously misleading results can be obtained analyzing data from randomized experiments while ignoring the experimental protocol; common mistakes include forgetting the blocking used in an experiment and confusing repeated measurements on the same experimental unit with independent replicates of the treatment applied to different experimental units.

Model-free randomization inference

Model-free techniques provide a complement to model-based methods, which employ reductionist strategies of reality-simplification. The former combine, evolve, ensemble and train algorithms dynamically adapting to the contextual affinities of a process and learning the intrinsic characteristics of the observations.

For example, model-free simple linear regression is based either on

• a random design, where the pairs of observations ${\displaystyle (X_1,Y_1),(X_2,Y_2),\cdots ,(X_n,Y_n)}$ are independent and identically distributed (iid), or
• a deterministic design, where the variables ${\displaystyle X_1,X_2,\cdots ,X_n}$ are deterministic, but the corresponding response variables ${\displaystyle Y_1,Y_2,\cdots ,Y_n}$ are random and independent with a common conditional distribution, i.e., ${\displaystyle P\left(Y_j\le y|X_j=x\right)=D_x(y)}$, which is independent of the index ${\displaystyle j}$.

In either case, the model-free randomization inference for features of the common conditional distribution ${\displaystyle D_x(.)}$ relies on some regularity conditions, e.g. functional smoothness. For instance, model-free randomization inference for the population feature conditional mean, ${\displaystyle \mu (x)=E(Y|X=x)}$, can be consistently estimated via local averaging or local polynomial fitting, under the assumption that ${\displaystyle \mu (x)}$ is smooth. Also, relying on asymptotic normality or resampling, we can construct confidence intervals for the population feature, in this case, the conditional mean, ${\displaystyle \mu (x)}$.

Paradigms for inference

Different schools of statistical inference have become established. These schools—or "paradigms"—are not mutually exclusive, and methods that work well under one paradigm often have attractive interpretations under other paradigms.

Bandyopadhyay & Forster describe four paradigms: The classical (or frequentist) paradigm, the Bayesian paradigm, the likelihoodist paradigm, and the Akaikean-Information Criterion-based paradigm.

Frequentist inference

Main article: Frequentist inference

This paradigm calibrates the plausibility of propositions by considering (notional) repeated sampling of a population distribution to produce datasets similar to the one at hand. By considering the dataset's characteristics under repeated sampling, the frequentist properties of a statistical proposition can be quantified—although in practice this quantification may be challenging.

Examples of frequentist inference

• p-value
• Confidence interval
• Null hypothesis significance testing

Frequentist inference, objectivity, and decision theory

One interpretation of frequentist inference (or classical inference) is that it is applicable only in terms of frequency probability; that is, in terms of repeated sampling from a population. However, the approach of Neyman develops these procedures in terms of pre-experiment probabilities. That is, before undertaking an experiment, one decides on a rule for coming to a conclusion such that the probability of being correct is controlled in a suitable way: such a probability need not have a frequentist or repeated sampling interpretation. In contrast, Bayesian inference works in terms of conditional probabilities (i.e. probabilities conditional on the observed data), compared to the marginal (but conditioned on unknown parameters) probabilities used in the frequentist approach.

The frequentist procedures of significance testing and confidence intervals can be constructed without regard to utility functions. However, some elements of frequentist statistics, such as statistical decision theory, do incorporate utility functions. In particular, frequentist developments of optimal inference (such as minimum-variance unbiased estimators, or uniformly most powerful testing) make use of loss functions, which play the role of (negative) utility functions. Loss functions need not be explicitly stated for statistical theorists to prove that a statistical procedure has an optimality property. However, loss-functions are often useful for stating optimality properties: for example, median-unbiased estimators are optimal under absolute value loss functions, in that they minimize expected loss, and least squares estimators are optimal under squared error loss functions, in that they minimize expected loss.

While statisticians using frequentist inference must choose for themselves the parameters of interest, and the estimators/test statistic to be used, the absence of obviously explicit utilities and prior distributions has helped frequentist procedures to become widely viewed as 'objective'.

Bayesian inference

See also: Bayesian inference

The Bayesian calculus describes degrees of belief using the 'language' of probability; beliefs are positive, integrate into one, and obey probability axioms. Bayesian inference uses the available posterior beliefs as the basis for making statistical propositions. There are several different justifications for using the Bayesian approach.

Examples of Bayesian inference

• Credible interval for interval estimation
• Bayes factors for model comparison

Bayesian inference, subjectivity and decision theory

Many informal Bayesian inferences are based on "intuitively reasonable" summaries of the posterior. For example, the posterior mean, median and mode, highest posterior density intervals, and Bayes Factors can all be motivated in this way. While a user's utility function need not be stated for this sort of inference, these summaries do all depend (to some extent) on stated prior beliefs, and are generally viewed as subjective conclusions. (Methods of prior construction which do not require external input have been proposed but not yet fully developed.)

Formally, Bayesian inference is calibrated with reference to an explicitly stated utility, or loss function; the 'Bayes rule' is the one which maximizes expected utility, averaged over the posterior uncertainty. Formal Bayesian inference therefore automatically provides optimal decisions in a decision theoretic sense. Given assumptions, data and utility, Bayesian inference can be made for essentially any problem, although not every statistical inference need have a Bayesian interpretation. Analyses which are not formally Bayesian can be (logically) incoherent; a feature of Bayesian procedures which use proper priors (i.e. those integrable to one) is that they are guaranteed to be coherent. Some advocates of Bayesian inference assert that inference must take place in this decision-theoretic framework, and that Bayesian inference should not conclude with the evaluation and summarization of posterior beliefs.

Likelihood-based inference

Main article: Likelihoodism

Likelihood-based inference is a paradigm used to estimate the parameters of a statistical model based on observed data. Likelihoodism approaches statistics by using the likelihood function, denoted as ${\displaystyle L(\theta |x)}$, quantifies the probability of observing the given data ${\displaystyle x}$, assuming a specific set of parameter values ${\displaystyle \theta }$. In likelihood-based inference, the goal is to find the set of parameter values that maximizes the likelihood function, or equivalently, maximizes the probability of observing the given data.

The process of likelihood-based inference usually involves the following steps:

1. Formulating the statistical model: A statistical model is defined based on the problem at hand, specifying the distributional assumptions and the relationship between the observed data and the unknown parameters. The model can be simple, such as a normal distribution with known variance, or complex, such as a hierarchical model with multiple levels of random effects.
2. Constructing the likelihood function: Given the statistical model, the likelihood function is constructed by evaluating the joint probability density or mass function of the observed data as a function of the unknown parameters. This function represents the probability of observing the data for different values of the parameters.
3. Maximizing the likelihood function: The next step is to find the set of parameter values that maximizes the likelihood function. This can be achieved using optimization techniques such as numerical optimization algorithms. The estimated parameter values, often denoted as ${\displaystyle \overline{y}}$, are the maximum likelihood estimates (MLEs).
4. Assessing uncertainty: Once the MLEs are obtained, it is crucial to quantify the uncertainty associated with the parameter estimates. This can be done by calculating standard errors, confidence intervals, or conducting hypothesis tests based on asymptotic theory or simulation techniques such as bootstrapping.
5. Model checking: After obtaining the parameter estimates and assessing their uncertainty, it is important to assess the adequacy of the statistical model. This involves checking the assumptions made in the model and evaluating the fit of the model to the data using goodness-of-fit tests, residual analysis, or graphical diagnostics.
6. Inference and interpretation: Finally, based on the estimated parameters and model assessment, statistical inference can be performed. This involves drawing conclusions about the population parameters, making predictions, or testing hypotheses based on the estimated model.

AIC-based inference

Main article: Akaike information criterion

The Akaike information criterion (AIC) is an estimator of the relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection.

AIC is founded on information theory: it offers an estimate of the relative information lost when a given model is used to represent the process that generated the data. (In doing so, it deals with the trade-off between the goodness of fit of the model and the simplicity of the model.)

Other paradigms for inference

Minimum description length

Main article: Minimum description length

The minimum description length (MDL) principle has been developed from ideas in information theory and the theory of Kolmogorov complexity. The (MDL) principle selects statistical models that maximally compress the data; inference proceeds without assuming counterfactual or non-falsifiable "data-generating mechanisms" or probability models for the data, as might be done in frequentist or Bayesian approaches.

However, if a "data generating mechanism" does exist in reality, then according to Shannon's source coding theorem it provides the MDL description of the data, on average and asymptotically. In minimizing description length (or descriptive complexity), MDL estimation is similar to maximum likelihood estimation and maximum a posteriori estimation (using maximum-entropy Bayesian priors). However, MDL avoids assuming that the underlying probability model is known; the MDL principle can also be applied without assumptions that e.g. the data arose from independent sampling.

The MDL principle has been applied in communication-coding theory in information theory, in linear regression, and in data mining.

The evaluation of MDL-based inferential procedures often uses techniques or criteria from computational complexity theory.

Fiducial inference

Main article: Fiducial inference

Fiducial inference was an approach to statistical inference based on fiducial probability, also known as a "fiducial distribution". In subsequent work, this approach has been called ill-defined, extremely limited in applicability, and even fallacious. However this argument is the same as that which shows that a so-called confidence distribution is not a valid probability distribution and, since this has not invalidated the application of confidence intervals, it does not necessarily invalidate conclusions drawn from fiducial arguments. An attempt was made to reinterpret the early work of Fisher's fiducial argument as a special case of an inference theory using upper and lower probabilities.

Structural inference

Developing ideas of Fisher and of Pitman from 1938 to 1939, George A. Barnard developed "structural inference" or "pivotal inference", an approach using invariant probabilities on group families. Barnard reformulated the arguments behind fiducial inference on a restricted class of models on which "fiducial" procedures would be well-defined and useful. Donald A. S. Fraser developed a general theory for structural inference based on group theory and applied this to linear models. The theory formulated by Fraser has close links to decision theory and Bayesian statistics and can provide optimal frequentist decision rules if they exist.

Inference topics

The topics below are usually included in the area of statistical inference.

1. Statistical assumptions
2. Statistical decision theory
3. Estimation theory
4. Statistical hypothesis testing
5. Revising opinions in statistics
6. Design of experiments, the analysis of variance, and regression
7. Survey sampling
8. Summarizing statistical data

Predictive inference

Predictive inference is an approach to statistical inference that emphasizes the prediction of future observations based on past observations.

Initially, predictive inference was based on observable parameters and it was the main purpose of studying probability, but it fell out of favor in the 20th century due to a new parametric approach pioneered by Bruno de Finetti. The approach modeled phenomena as a physical system observed with error (e.g., celestial mechanics). De Finetti's idea of exchangeability—that future observations should behave like past observations—came to the attention of the English-speaking world with the 1974 translation from French of his 1937 paper, and has since been propounded by such statisticians as Seymour Geisser.

Chinese whispers

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Chinese_whispers

Chinese whispers (some Commonwealth English), or telephone (American English and Canadian English), is an internationally popular children's game in which messages are whispered from person to person and then the original and final messages are compared. This sequential modification of information is called transmission chaining in the context of cultural evolution research, and is primarily used to identify the type of information that is more easily passed on from one person to another.

Players form a line or circle, and the first player comes up with a message and whispers it to the ear of the second person in the line. The second player repeats the message to the third player, and so on. When the last player is reached, they announce the message they just heard, to the entire group. The first person then compares the original message with the final version. Although the objective is to pass around the message without it becoming garbled along the way, part of the enjoyment is that, regardless, this usually ends up happening. Errors typically accumulate in the retellings, so the statement announced by the last player differs significantly from that of the first player, usually with amusing or humorous effect. Reasons for changes include anxiousness or impatience, erroneous corrections, or the difficult-to-understand mechanism of whispering.

The game is often played by children as a party game or on the playground. It is often invoked as a metaphor for cumulative error, especially the inaccuracies as rumours or gossip spread, or, more generally, for the unreliability of typical human recollection.

Etymology

United Kingdom, Australian, and New Zealand usage

The Great Wall, one potential origin of the name "Chinese whispers"

In the UK, Australia and New Zealand, the game is typically called "Chinese whispers"; in the UK, this is documented from 1964.

Various reasons have been suggested for naming the game after the Chinese, but there is no concrete explanation. One suggested reason is a widespread British fascination with Chinese culture in the 18th and 19th centuries during the Enlightenment. Another theory posits that the game's name stems from the supposed confused messages created when a message was passed verbally from tower to tower along the Great Wall of China.

Critics who focus on Western use of the word Chinese as denoting "confusion" and "incomprehensibility" look to the earliest contacts between Europeans and Chinese people in the 17th century, attributing it to a supposed inability on the part of Europeans to understand China's culture and worldview. In this view, using the phrase "Chinese whispers" is taken as evidence of a belief that the Chinese language itself is not understandable. Yunte Huang, a professor of English at the University of California, Santa Barbara, has said that: "Indicating inaccurately transmitted information, the expression 'Chinese Whispers' carries with it a sense of paranoia caused by espionage, counterespionage, Red Scare, and other war games, real or imaginary, cold or hot." Usage of the term has been defended as being similar to other expressions such as "It's all Greek to me" and "Double Dutch".

Alternative names

As the game is popular among children worldwide, it is also known under various other names depending on locality, such as Russian scandal, whisper down the lane, broken telephone, operator, grapevine, gossip, secret message, the messenger game, and pass the message, among others. In Turkey, this game is called kulaktan kulağa, which means "from (one) ear to (another) ear". In France, it is called téléphone arabe ("Arabic telephone") or téléphone sans fil ("wireless telephone"). In Germany the game is known as Stille Post ("quiet mail"). In Poland it is called głuchy telefon, meaning "deaf telephone". In Medici-era Florence it was called the "game of the ear".

The game has also been known in English as Russian Scandal, Russian Gossip and Russian Telephone.

In North America, the game is known under the name telephone. Alternative names used in the United States include Broken Telephone, Gossip, and Rumors. This North American name is followed in a number of languages where the game is known by the local language's equivalent of "broken telephone", such in Malaysia as telefon rosak, in Israel as telefon shavur (טלפון שבור), in Finland as rikkinäinen puhelin, and in Greece as halasmeno tilefono (χαλασμένο τηλέφωνο).

Game

The game has no winner: the entertainment comes from comparing the original and final messages. Intermediate messages may also be compared; some messages will become unrecognizable after only a few steps.

As well as providing amusement, the game can have educational value. It shows how easily information can become corrupted by indirect communication. The game has been used in schools to simulate the spread of gossip and its possible harmful effects. It can also be used to teach young children to moderate the volume of their voice, and how to listen attentively; in this case, a game is a success if the message is transmitted accurately with each child whispering rather than shouting. It can also be used for older or adult learners of a foreign language, where the challenge of speaking comprehensibly, and understanding, is more difficult because of the low volume, and hence a greater mastery of the fine points of pronunciation is required.

Notable games

In 2008 1,330 children and celebrities set a world record for the game of Chinese Whispers involving the most people. The game was held at the Emirates Stadium in London and lasted two hours and four minutes. Starting with "together we will make a world of difference", the phrase morphed into "we're setting a record" part way down the chain, and by the end had become simply "haaaaa". The previous record, set in 2006 by the Cycling Club of Chengdu, China, had involved 1,083 people.

In 2017 a new world record was set for the largest game of Chinese Whispers in terms of the number of participants by schoolchildren in Tauranga, New Zealand. The chain involved 1,763 school children and other individuals and was held as part of Hearing Week 2017. The starting phrase was "Turn it down". As of 2022 this remained the world record for the largest game of Chinese Whispers by number of participants according to the Guinness Book of Records.

In 2012 a global game of Chinese Whispers was played spanning 237 individuals speaking seven different languages. Beginning in St Kilda Library in Melbourne, Australia, the starting phrase "Life must be lived as play" (a paraphrase of Plato) had become "He bites snails" by the time the game reached its end in Alaska 26 hours later. In 2013, the Global Gossip Game had 840 participants and travelled to all 7 continents.

Variants

A variant of Chinese Whispers is called Rumors. In this version of the game, when players transfer the message, they deliberately change one or two words of the phrase (often to something more humorous than the previous message). Intermediate messages can be compared. There is a second derivative variant, no less popular than Rumors, known as Mahjong Secrets (UK), or Broken Telephone (US), where the objective is to receive the message from the whisperer and whisper to the next participant the first word or phrase that comes to mind in association with what was heard. At the end, the final phrase is compared to the first in front of all participants.

A game of Eat Poop You Cat, starting with "Only the good die young" and ending with "The three vikings visit Christ".

The pen-and-paper game Telephone Pictionary (also known as Eat Poop You Cat) is played by alternately writing and illustrating captions, the paper being folded so that each player can only see the previous participant's contribution. The game was first implemented online by Broken Picture Telephone in early 2007. Following the success of Broken Picture Telephone, commercial boardgame versions Telestrations and Cranium Scribblish were released two years later in 2009. Drawception, and other websites, also arrived in 2009.

A translation relay is a variant in which the first player produces a text in a given language, together with a basic guide to understanding, which includes a lexicon, an interlinear gloss, possibly a list of grammatical morphemes, comments on the meaning of difficult words, etc. (everything except an actual translation). The text is passed on to the following player, who tries to make sense of it and casts it into their language of choice, then repeating the procedure, and so on. Each player only knows the translation done by his immediate predecessor, but customarily the relay master or mistress collects all of them. The relay ends when the last player returns the translation to the beginning player.

Another variant of Chinese whispers is shown on Ellen's Game of Games under the name of Say Whaaat?. However, the difference is that the four players will be wearing earmuffs; therefore the players have to read their lips. A similar game, Shouting One Out, in which participants wearing noise-canceling headphones had to interpret the lip movements of the preceding player, appeared in multiple editions of the ITV2 panel game series Celebrity Juice.

The CBBC game show Copycats featured several rounds played in a Chinese whispers format, in which each player on a team in turn had to interpret and recreate the mimed actions, drawing or music performed by the preceding person in line, with the points value awarded based on how far down the line the correct starting prompt had travelled before mutating into something else.

A party game variant of telephone known as "wordpass" involves saying words out loud and saying a related word, until a word is repeated.

As a metaphor

Chinese whispers is used in a number of fields as a metaphor for imperfect data transmission over multiple iterations. For example the British zoologist Mark Ridley in his book Mendel's demon used Chinese Whispers as an analogy for the imperfect transmission of genetic information across multiple generations. another example, Richard Dawkins used Chinese Whispers as a metaphor for infidelity in memetic replication, referring specifically to children trying to reproduce drawing of a Chinese junk in his essay Chinese Junk and Chinese Whispers. It was used in the movie Tár to represent gossip circling within an orchestra.

Historical method

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Historical_method

A sculpted bust depicting Thucydides (c. 460-c. 400 BC) dubbed the "father of scientific history" (a copy of a copy of 4th Century BCE Greek work)

Historical method is the collection of techniques and guidelines that historians use to research and write histories of the past. Secondary sources, primary sources and material evidence such as that derived from archaeology may all be drawn on, and the historian's skill lies in identifying these sources, evaluating their relative authority, and combining their testimony appropriately in order to construct an accurate and reliable picture of past events and environments.

In the philosophy of history, the question of the nature, and the possibility, of a sound historical method is raised within the sub-field of epistemology. The study of historical method and of different ways of writing history is known as historiography.

Source criticism

Main article: Source criticism

Source criticism (or information evaluation) is the process of evaluating the qualities of an information source, such as its validity, reliability, and relevance to the subject under investigation.

Gilbert J. Garraghan and Jean Delanglez divide source criticism into six inquiries:

1. When was the source, written or unwritten, produced (date)?
2. Where was it produced (localization)?
3. By whom was it produced (authorship)?
4. From what pre-existing material was it produced (analysis)?
5. In what original form was it produced (integrity)?
6. What is the evidential value of its contents (credibility)?

The first four are known as higher criticism; the fifth, lower criticism; and, together, external criticism. The sixth and final inquiry about a source is called internal criticism. Together, this inquiry is known as source criticism.

R. J. Shafer on external criticism: "It sometimes is said that its function is negative, merely saving us from using false evidence; whereas internal criticism has the positive function of telling us how to use authenticated evidence."

Noting that few documents are accepted as completely reliable, Louis Gottschalk sets down the general rule, "for each particular of a document the process of establishing credibility should be separately undertaken regardless of the general credibility of the author". An author's trustworthiness in the main may establish a background probability for the consideration of each statement, but each piece of evidence extracted must be weighed individually.

Procedures for contradictory sources

Bernheim (1889) and Langlois & Seignobos (1898) proposed a seven-step procedure for source criticism in history:

1. If the sources all agree about an event, historians can consider the event proven.
2. However, majority does not rule; even if most sources relate events in one way, that version will not prevail unless it passes the test of critical textual analysis.
3. The source whose account can be confirmed by reference to outside authorities in some of its parts can be trusted in its entirety if it is impossible similarly to confirm the entire text.
4. When two sources disagree on a particular point, the historian will prefer the source with most "authority"—that is the source created by the expert or by the eyewitness.
5. Eyewitnesses are, in general, to be preferred especially in circumstances where the ordinary observer could have accurately reported what transpired and, more specifically, when they deal with facts known by most contemporaries.
6. If two independently created sources agree on a matter, the reliability of each is measurably enhanced.
7. When two sources disagree and there is no other means of evaluation, then historians take the source which seems to accord best with common sense.

Subsequent descriptions of historical method, outlined below, have attempted to overcome the credulity built into the first step formulated by the nineteenth century historiographers by stating principles not merely by which different reports can be harmonized but instead by which a statement found in a source may be considered to be unreliable or reliable as it stands on its own.

Core principles for determining reliability

The following core principles of source criticism were formulated by two Scandinavian historians, Olden-Jørgensen (1998) and Thurén Torsten (1997):

• Human sources may be relics such as a fingerprint; or narratives such as a statement or a letter. Relics are more credible sources than narratives.
• Any given source may be forged or corrupted. Strong indications of the originality of the source increase its reliability.
• The closer a source is to the event which it purports to describe, the more one can trust it to give an accurate historical description of what actually happened.
• An eyewitness is more reliable than testimony at second hand, which is more reliable than hearsay at further remove, and so on.
• If a number of independent sources contain the same message, the credibility of the message is strongly increased.
• The tendency of a source is its motivation for providing some kind of bias. Tendencies should be minimized or supplemented with opposite motivations.
• If it can be demonstrated that the witness or source has no direct interest in creating bias then the credibility of the message is increased.

Eyewitness evidence

R. J. Shafer offers this checklist for evaluating eyewitness testimony:

1. Is the real meaning of the statement different from its literal meaning? Are words used in senses not employed today? Is the statement meant to be ironic (i.e., mean other than it says)?
2. How well could the author observe the thing he reports? Were his senses equal to the observation? Was his physical location suitable to sight, hearing, touch? Did he have the proper social ability to observe: did he understand the language, have other expertise required (e.g., law, military); was he not being intimidated by his wife or the secret police?
3. How did the author report?, and what was his ability to do so?
   1. Regarding his ability to report, was he biased? Did he have proper time for reporting? Proper place for reporting? Adequate recording instruments?
   2. When did he report in relation to his observation? Soon? Much later? Fifty years is much later as most eyewitnesses are dead and those who remain may have forgotten relevant material.
   3. What was the author's intention in reporting? For whom did he report? Would that audience be likely to require or suggest distortion to the author?
   4. Are there additional clues to intended veracity? Was he indifferent on the subject reported, thus probably not intending distortion? Did he make statements damaging to himself, thus probably not seeking to distort? Did he give incidental or casual information, almost certainly not intended to mislead?
4. Do his statements seem inherently improbable: e.g., contrary to human nature, or in conflict with what we know?
5. Remember that some types of information are easier to observe and report on than others.
6. Are there inner contradictions in the document?

Louis Gottschalk adds an additional consideration: "Even when the fact in question may not be well-known, certain kinds of statements are both incidental and probable to such a degree that error or falsehood seems unlikely. If an ancient inscription on a road tells us that a certain proconsul built that road while Augustus was princeps, it may be doubted without further corroboration that that proconsul really built the road, but would be harder to doubt that the road was built during the principate of Augustus. If an advertisement informs readers that 'A and B Coffee may be bought at any reliable grocer's at the unusual price of fifty cents a pound,' all the inferences of the advertisement may well be doubted without corroboration except that there is a brand of coffee on the market called 'A and B Coffee.'"

Indirect witnesses

Garraghan says that most information comes from "indirect witnesses", people who were not present on the scene but heard of the events from someone else. Gottschalk says that a historian may sometimes use hearsay evidence when no primary texts are available. He writes, "In cases where he uses secondary witnesses...he asks: (1) On whose primary testimony does the secondary witness base his statements? (2) Did the secondary witness accurately report the primary testimony as a whole? (3) If not, in what details did he accurately report the primary testimony? Satisfactory answers to the second and third questions may provide the historian with the whole or the gist of the primary testimony upon which the secondary witness may be his only means of knowledge. In such cases the secondary source is the historian's 'original' source, in the sense of being the 'origin' of his knowledge. Insofar as this 'original' source is an accurate report of primary testimony, he tests its credibility as he would that of the primary testimony itself." Gottschalk adds, "Thus hearsay evidence would not be discarded by the historian, as it would be by a law court merely because it is hearsay."

Oral tradition

Gilbert Garraghan maintains that oral tradition may be accepted if it satisfies either two "broad conditions" or six "particular conditions", as follows:

1. Broad conditions stated.
   1. The tradition should be supported by an unbroken series of witnesses, reaching from the immediate and first reporter of the fact to the living mediate witness from whom we take it up, or to the one who was the first to commit it to writing.
   2. There should be several parallel and independent series of witnesses testifying to the fact in question.
2. Particular conditions formulated.
   1. The tradition must report a public event of importance, such as would necessarily be known directly to a great number of persons.
   2. The tradition must have been generally believed, at least for a definite period of time.
   3. During that definite period it must have gone without protest, even from persons interested in denying it.
   4. The tradition must be one of relatively limited duration. [Elsewhere, Garraghan suggests a maximum limit of 150 years, at least in cultures that excel in oral remembrance.]
   5. The critical spirit must have been sufficiently developed while the tradition lasted, and the necessary means of critical investigation must have been at hand.
   6. Critical-minded persons who would surely have challenged the tradition – had they considered it false – must have made no such challenge.

Other methods of verifying oral tradition may exist, such as comparison with the evidence of archaeological remains.

More recent evidence concerning the potential reliability or unreliability of oral tradition has come out of fieldwork in West Africa and Eastern Europe.

Anonymous sources

Historians do allow for the use of anonymous texts to establish historical facts.

Synthesis: historical reasoning

Once individual pieces of information have been assessed in context, hypotheses can be formed and established by historical reasoning.

Argument to the best explanation

C. Behan McCullagh lays down seven conditions for a successful argument to the best explanation:

1. The statement, together with other statements already held to be true, must imply yet other statements describing present, observable data. (We will henceforth call the first statement 'the hypothesis', and the statements describing observable data, 'observation statements'.)
2. The hypothesis must be of greater explanatory scope than any other incompatible hypothesis about the same subject; that is, it must imply a greater variety of observation statements.
3. The hypothesis must be of greater explanatory power than any other incompatible hypothesis about the same subject; that is, it must make the observation statements it implies more probable than any other.
4. The hypothesis must be more plausible than any other incompatible hypothesis about the same subject; that is, it must be implied to some degree by a greater variety of accepted truths than any other, and be implied more strongly than any other; and its probable negation must be implied by fewer beliefs, and implied less strongly than any other.
5. The hypothesis must be less ad hoc than any other incompatible hypothesis about the same subject; that is, it must include fewer new suppositions about the past which are not already implied to some extent by existing beliefs.
6. It must be disconfirmed by fewer accepted beliefs than any other incompatible hypothesis about the same subject; that is, when conjoined with accepted truths it must imply fewer observation statements and other statements which are believed to be false.
7. It must exceed other incompatible hypotheses about the same subject by so much, in characteristics 2 to 6, that there is little chance of an incompatible hypothesis, after further investigation, soon exceeding it in these respects.

McCullagh sums up, "if the scope and strength of an explanation are very great, so that it explains a large number and variety of facts, many more than any competing explanation, then it is likely to be true".

Statistical inference

McCullagh states this form of argument as follows:

1. There is probability (of the degree p₁) that whatever is an A is a B.
2. It is probable (to the degree p₂) that this is an A.
3. Therefore, (relative to these premises) it is probable (to the degree p₁ × p₂) that this is a B.

McCullagh gives this example:

1. In thousands of cases, the letters V.S.L.M. appearing at the end of a Latin inscription on a tombstone stand for Votum Solvit Libens Merito.
2. From all appearances the letters V.S.L.M. are on this tombstone at the end of a Latin inscription.
3. Therefore, these letters on this tombstone stand for Votum Solvit Libens Merito.

This is a syllogism in probabilistic form, making use of a generalization formed by induction from numerous examples (as the first premise).

Argument from analogy

The structure of the argument is as follows:

1. One thing (object, event, or state of affairs) has properties p₁ . . .  p_n and p_{n + 1}.
2. Another thing has properties p₁ . . . p_n.
3. So the latter has property p_{n + 1}.

McCullagh says that an argument from analogy, if sound, is either a "covert statistical syllogism" or better expressed as an argument to the best explanation. It is a statistical syllogism when it is "established by a sufficient number and variety of instances of the generalization"; otherwise, the argument may be invalid because properties 1 through n are unrelated to property n + 1, unless property n + 1 is the best explanation of properties 1 through n. Analogy, therefore, is uncontroversial only when used to suggest hypotheses, not as a conclusive argument.