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Royal Society Open Science RSS feed -- recent Mathematics articles2054-5703Royal Society Open Science<![CDATA[Beyond 'significance: principles and practice of the Analysis of Credibility]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/5/1/171047?rss=1
The inferential inadequacies of statistical significance testing are now widely recognized. There is, however, no consensus on how to move research into a ‘post p < 0.05’ era. We present a potential route forward via the Analysis of Credibility, a novel methodology that allows researchers to go beyond the simplistic dichotomy of significance testing and extract more insight from new findings. Using standard summary statistics, AnCred assesses the credibility of significant and non-significant findings on the basis of their evidential weight, and in the context of existing knowledge. The outcome is expressed in quantitative terms of direct relevance to the substantive research question, providing greater protection against misinterpretation. Worked examples are given to illustrate how AnCred extracts additional insight from the outcome of typical research study designs. Its ability to cast light on the use of p-values, the interpretation of non-significant findings and the so-called ‘replication crisis’ is also discussed.
]]>2018-01-17T00:05:51-08:00info:doi/10.1098/rsos.171047hwp:master-id:royopensci;rsos.1710472018-01-17Mathematics51171047171047<![CDATA[Modelling science trustworthiness under publish or perish pressure]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/5/1/171511?rss=1
Scientific publication is immensely important to the scientific endeavour. There is, however, concern that rewarding scientists chiefly on publication creates a perverse incentive, allowing careless and fraudulent conduct to thrive, compounded by the predisposition of top-tier journals towards novel, positive findings rather than investigations confirming null hypothesis. This potentially compounds a reproducibility crisis in several fields, and risks undermining science and public trust in scientific findings. To date, there has been comparatively little modelling on factors that influence science trustworthiness, despite the importance of quantifying the problem. We present a simple phenomenological model with cohorts of diligent, careless and unethical scientists, with funding allocated by published outputs. This analysis suggests that trustworthiness of published science in a given field is influenced by false positive rate, and pressures for positive results. We find decreasing available funding has negative consequences for resulting trustworthiness, and examine strategies to combat propagation of irreproducible science.
]]>2018-01-10T00:05:22-08:00info:doi/10.1098/rsos.171511hwp:master-id:royopensci;rsos.1715112018-01-10Mathematics51171511171511<![CDATA[Spatial utilization predicts animal social contact networks are not scale-free]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/12/171209?rss=1
While heterogeneity in social behaviour has been described in many human contexts it is often assumed to be less common in the animal kingdom even though scale-free networks are observed. This homogeneity raises the question of whether the patterns of behaviour necessary to account for scale-free social contact networks, where the degree distribution follows a power law, i.e. a few individuals are very highly connected but most have only a few connections, occur in animals, or whether other mechanisms are needed to produce realistic contact network architectures. We develop a space-utilization model for individual animal behaviour to predict the individuals' social contact network. Using basic properties of the ^{2} distribution we present a simple analytical result that allows the model to give a range of predictions with minimal computational effort. The model results are tested on data collected in New Zealand for the social contact networks of the wild brushtail possum (Trichosurus vulpecula). Our model provides a better prediction of network architecture than other simple models, including a scale-free model.
]]>2017-12-13T00:05:39-08:00info:doi/10.1098/rsos.171209hwp:master-id:royopensci;rsos.1712092017-12-13Mathematics412171209171209<![CDATA[The reproducibility of research and the misinterpretation of p-values]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/12/171085?rss=1
We wish to answer this question: If you observe a ‘significant’ p-value after doing a single unbiased experiment, what is the probability that your result is a false positive? The weak evidence provided by p-values between 0.01 and 0.05 is explored by exact calculations of false positive risks. When you observe p = 0.05, the odds in favour of there being a real effect (given by the likelihood ratio) are about 3 : 1. This is far weaker evidence than the odds of 19 to 1 that might, wrongly, be inferred from the p-value. And if you want to limit the false positive risk to 5%, you would have to assume that you were 87% sure that there was a real effect before the experiment was done. If you observe p= 0.001 in a well-powered experiment, it gives a likelihood ratio of almost 100 : 1 odds on there being a real effect. That would usually be regarded as conclusive. But the false positive risk would still be 8% if the prior probability of a real effect were only 0.1. And, in this case, if you wanted to achieve a false positive risk of 5% you would need to observe p = 0.00045. It is recommended that the terms ‘significant’ and ‘non-significant’ should never be used. Rather, p-values should be supplemented by specifying the prior probability that would be needed to produce a specified (e.g. 5%) false positive risk. It may also be helpful to specify the minimum false positive risk associated with the observed p-value. Despite decades of warnings, many areas of science still insist on labelling a result of p < 0.05 as ‘statistically significant’. This practice must contribute to the lack of reproducibility in some areas of science. This is before you get to the many other well-known problems, like multiple comparisons, lack of randomization and p-hacking. Precise inductive inference is impossible and replication is the only way to be sure. Science is endangered by statistical misunderstanding, and by senior people who impose perverse incentives on scientists.
]]>2017-12-06T00:05:33-08:00info:doi/10.1098/rsos.171085hwp:master-id:royopensci;rsos.1710852017-12-06Mathematics412171085171085<![CDATA[Kidnapping model: an extension of Selten's game]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/12/171484?rss=1
Selten's game is a kidnapping model where the probability of capturing the kidnapper is independent of whether the hostage has been released or executed. Most often, in view of the elevated sensitivities involved, authorities put greater effort and resources into capturing the kidnapper if the hostage has been executed, in contrast with the case when a ransom is paid to secure the hostage's release. In this paper, we study the asymmetric game when the probability of capturing the kidnapper depends on whether the hostage has been executed or not and find a new uniquely determined perfect equilibrium point in Selten's game.
]]>2017-12-06T00:51:18-08:00info:doi/10.1098/rsos.171484hwp:master-id:royopensci;rsos.1714842017-12-06Mathematics412171484171484<![CDATA[Do-it-yourself networks: a novel method of generating weighted networks]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/11/171227?rss=1
Network theory is finding applications in the life and social sciences for ecology, epidemiology, finance and social–ecological systems. While there are methods to generate specific types of networks, the broad literature is focused on generating unweighted networks. In this paper, we present a framework for generating weighted networks that satisfy user-defined criteria. Each criterion hierarchically defines a feature of the network and, in doing so, complements existing algorithms in the literature. We use a general example of ecological species dispersal to illustrate the method and provide open-source code for academic purposes.
]]>2017-11-22T00:05:38-08:00info:doi/10.1098/rsos.171227hwp:master-id:royopensci;rsos.1712272017-11-22Mathematics411171227171227<![CDATA[Spatial correlated games]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/11/171361?rss=1
This article studies correlated two-person games constructed from games with independent players as proposed in Iqbal et al. (2016 R. Soc. open sci.3, 150477. (doi:10.1098/rsos.150477)). The games are played in a collective manner, both in a two-dimensional lattice where the players interact with their neighbours, and with players interacting at random. Four game types are scrutinized in iterated games where the players are allowed to change their strategies, adopting that of their best paid mate neighbour. Particular attention is paid in the study to the effect of a variable degree of correlation on Nash equilibrium strategy pairs.
]]>2017-11-15T00:06:00-08:00info:doi/10.1098/rsos.171361hwp:master-id:royopensci;rsos.1713612017-11-15Mathematics411171361171361<![CDATA[Decision landscapes: visualizing mouse-tracking data]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/11/170482?rss=1
Computerized paradigms have enabled gathering rich data on human behaviour, including information on motor execution of a decision, e.g. by tracking mouse cursor trajectories. These trajectories can reveal novel information about ongoing decision processes. As the number and complexity of mouse-tracking studies increase, more sophisticated methods are needed to analyse the decision trajectories. Here, we present a new computational approach to generating decision landscape visualizations based on mouse-tracking data. A decision landscape is an analogue of an energy potential field mathematically derived from the velocity of mouse movement during a decision. Visualized as a three-dimensional surface, it provides a comprehensive overview of decision dynamics. Employing the dynamical systems theory framework, we develop a new method for generating decision landscapes based on arbitrary number of trajectories. This approach not only generates three-dimensional illustration of decision landscapes, but also describes mouse trajectories by a number of interpretable parameters. These parameters characterize dynamics of decisions in more detail compared with conventional measures, and can be compared across experimental conditions, and even across individuals. The decision landscape visualization approach is a novel tool for analysing mouse trajectories during decision execution, which can provide new insights into individual differences in the dynamics of decision making.
]]>2017-11-08T02:01:34-08:00info:doi/10.1098/rsos.170482hwp:master-id:royopensci;rsos.1704822017-11-08Mathematics411170482170482<![CDATA[Multiple steady states and the form of response functions to antigen in a model for the initiation of T-cell activation]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/11/170821?rss=1
The aim of this paper is to study the qualitative behaviour predicted by a mathematical model for the initial stage of T-cell activation. The state variables in the model are the concentrations of phosphorylation states of the T-cell receptor (TCR) complex and the phosphatase SHP-1 in the cell. It is shown that these quantities cannot approach zero and that the model possesses more than one positive steady state for certain values of the parameters. It can also exhibit damped oscillations. It is proved that the chemical concentration which represents the degree of activation of the cell, that of the maximally phosphorylated form of the TCR complex, is, in general, a non-monotone function of the activating signal. In particular, there are cases where there is a value of the dissociation constant of the ligand from the receptor which produces a maximal activation of the T cell. This suggests that mechanisms taking place in the first few minutes after activation and included in the model studied in this paper suffice to explain the optimal dissociation time seen in experiments. In this way, the results of certain simulations in the literature have been confirmed rigorously and some important features which had not previously been seen have been discovered.
]]>2017-11-08T00:05:45-08:00info:doi/10.1098/rsos.170821hwp:master-id:royopensci;rsos.1708212017-11-08Mathematics411170821170821<![CDATA[Modelling the role of correctional services on gangs: insights through a mathematical model]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/4/10/170511?rss=1
Research has shown that gang membership increases the chances of offending, antisocial behaviour and drug use. Gang membership should be acknowledged as part of crime prevention and policy designs, and when developing interventions and preventative programmes. Correctional services are designed to rehabilitate convicted offenders. We formulate a deterministic mathematical model using nonlinear ordinary differential equations to investigate the role of correctional services on the dynamics of gangs. The recruitment into gang membership is assumed to happen through an imitation process. An epidemic threshold value, Rg, termed the gang reproduction number, is proposed and defined herein in the gangs’ context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that gangs may persist in the population even if Rg is less than one. Sensitivity analysis of Rg was performed to determine the relative importance of different parameters in gang initiation. The critical efficacy * is evaluated and the implications of having functional correctional services are discussed.
]]>2017-10-11T01:46:25-07:00info:doi/10.1098/rsos.170511hwp:master-id:royopensci;rsos.1705112017-10-11Mathematics410170511170511