Inference and Prediction

Abstract This chapter reviews some basic concepts in statistical inference and prediction. Sufficiency and the likelihood principle are backbones of parametric inference. Method of moments and maximum likelihood are among the most popular methods of point estimation. Finite sample properties of estimators are assessed using bias, variance, or mean squared error, while asymptotic properties pertain to the behavior of estimators when the sample size approaches infinity. Confidence intervals and their relationship to hypothesis testing are described. Additional topics include Bayesian statistics, prediction, and model selection.

[1]  D. Wegner,et al.  Apparent mental causation. Sources of the experience of will. , 1999, The American psychologist.

[2]  R. A. Fisher,et al.  Design of Experiments , 1936 .

[3]  P. J. White,et al.  The ecology of large mammals in central Yellowstone : sixteen years of integrated field studies , 2009 .

[4]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[5]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[6]  P. Haggard.  Conscious intention and motor cognition , 2005, Trends in Cognitive Sciences.

[7]  C. Rahbek,et al.  Potential impacts of climate change on the distributions and diversity patterns of European mammals , 2007, Biodiversity and Conservation.

[8]  W. Thuiller,et al.  Comparing niche- and process-based models to reduce prediction uncertainty in species range shifts under climate change. , 2009, Ecology.

[9]  T. Bayes.  An essay towards solving a problem in the doctrine of chances , 2003 .

[10]  L. Bordignon,et al.  A weak upward elevational shift in the distributions of breeding birds in the Italian Alps , 2009 .

[11]  A. Hoffmann,et al.  Detecting genetic responses to environmental change , 2008, Nature Reviews Genetics.

[12]  F. Ramsey.  Truth and Probability , 2016 .

[13]  U. Cubasch,et al.  A model‐data comparison of European temperatures in the Eemian interglacial , 2005 .

[14]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[15]  Andrew M. Liebhold,et al.  1200 years of regular outbreaks in alpine insects , 2007, Proceedings of the Royal Society B: Biological Sciences.

[16]  J. Peñuelas,et al.  European phenological response to climate change matches the warming pattern , 2006 .

[17]  M. Zappa,et al.  Climate change and plant distribution: local models predict high‐elevation persistence , 2009 .

[18]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[19]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .

[20]  H. Tong,et al.  From patterns to processes: phase and density dependencies in the Canadian lynx cycle. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Wilfried Thuiller,et al.  Predicting potential distributions of invasive species: where to go from here? , 2010 .

[22]  N. Zimmermann,et al.  Predicting future distributions of mountain plants under climate change: does dispersal capacity matter? , 2009 .

[23]  Dean P. Foster,et al.  The risk inflation criterion for multiple regression , 1994 .

[24]  Petter Johansson,et al.  Failure to Detect Mismatches Between Intention and Outcome in a Simple Decision Task , 2005, Science.

[25]  J. S. Hunter,et al.  Statistics for Experimenters: Design, Innovation, and Discovery , 2006 .

[26]  N. Yoccoz,et al.  Demography of small mammals in cold regions: the importance of environmental variability , 1999 .

[27]  J. Räisänen,et al.  How reliable are climate models? , 2007 .

[28]  M. Rebetez.  Summer 2003 maximum and minimum daily temperatures over a 3300 m altitudinal range in the Alps , 2004 .

[29]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[30]  William P. Banks,et al.  Benjamin Libet's work on the neuroscience of free will , 2007 .

[31]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[32]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[33]  B. D. Finetti,et al.  Foresight: Its Logical Laws, Its Subjective Sources , 1992 .

[34]  J. Abatzoglou,et al.  Tracking the rhythm of the seasons in the face of global change: phenological research in the 21st century. , 2009 .

[35]  Wilfried Thuiller,et al.  Sampling in ecology and evolution – bridging the gap between theory and practice , 2010 .

[36]  D. Wolpert,et al.  Abnormalities in the awareness of action , 2002, Trends in Cognitive Sciences.

[37]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[38]  Kung-Sik Chan,et al.  Ecological Effects of Climate Fluctuations , 2002, Science.

[39]  J. Vik,et al.  Rapid Advance of Spring Arrival Dates in Long-Distance Migratory Birds , 2006, Science.

[40]  A. Lehmann,et al.  Using Niche‐Based Models to Improve the Sampling of Rare Species , 2006, Conservation biology : the journal of the Society for Conservation Biology.

[41]  E. Titchener.  Scientific Books: Lectures on the Elementary Psychology of Feeling and Attention , 1909 .

[42]  L. J. Savage,et al.  Probability and the weighing of evidence , 1951 .

[43]  D M Wolpert,et al.  The influence of previous experience on predictive motor control , 2001, Neuroreport.

[44]  Jane Uhd Jepsen,et al.  Shifting altitudinal distribution of outbreak zones of winter moth Operophtera brumata in sub‐arctic birch forest: a response to recent climate warming? , 2007 .

[45]  Sylvain Delzon,et al.  Responses of canopy duration to temperature changes in four temperate tree species: relative contributions of spring and autumn leaf phenology , 2009, Oecologia.

[46]  I. Chuine,et al.  A unified model for budburst of trees. , 2000, Journal of theoretical biology.

[47]  D. Blackwell.  Conditional Expectation and Unbiased Sequential Estimation , 1947 .

[48]  Paul Vos,et al.  Evaluation Criteria for Discrete Confidence Intervals , 2005 .

[49]  P. Haggard,et al.  Voluntary action and conscious awareness , 2002, Nature Neuroscience.

[50]  Antoine Guisan,et al.  Climatic extremes improve predictions of spatial patterns of tree species , 2009, Proceedings of the National Academy of Sciences.

[51]  S. Albon,et al.  Plant phenology and the benefits of migration in a temperate ungulate , 1992 .

[52]  D. Wegner.  The Illusion of Conscious Will , 2018, The MIT Press.

[53]  R. Tibshirani,et al.  An introduction to the bootstrap , 1993 .

[54]  Atle Mysterud,et al.  Linking climate change to lemming cycles , 2008, Nature.

[55]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[56]  M. Sykes,et al.  Climate change threats to plant diversity in Europe. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[57]  Konrad Paul Kording,et al.  Bayesian integration in sensorimotor learning , 2004, Nature.

[58]  Antoine Guisan,et al.  Tree line shifts in the Swiss Alps: Climate change or land abandonment? , 2007 .

[59]  Antoine Guisan,et al.  Are niche-based species distribution models transferable in space? , 2006 .

[60]  Jennifer A. Lau,et al.  Elevated carbon dioxide concentrations indirectly affect plant fitness by altering plant tolerance to herbivory , 2009, Oecologia.

[61]  Sonja Wipf,et al.  A review of snow manipulation experiments in Arctic and alpine tundra ecosystems , 2010 .

[62]  N. Zimmermann,et al.  Predictive mapping of alpine grasslands in Switzerland: Species versus community approach , 1999 .

[63]  Wolfgang Prinz,et al.  Action, binding and awareness , 2002 .

[64]  P. Churchland.  Matter and Consciousness , 1984 .

[65]  J. Tenenbaum,et al.  Special issue on “Probabilistic models of cognition , 2022 .

[66]  B. Libet,et al.  Time of conscious intention to act in relation to onset of cerebral activity (readiness-potential). The unconscious initiation of a freely voluntary act. , 1983 .

[67]  Annette Menzel,et al.  Influence of altitude on phenology of selected plant species in the Alpine region (1971-2000) , 2009 .

[68]  Barbara G. Brown,et al.  Forecast verification: current status and future directions , 2008 .

[69]  V. Ramachandran,et al.  The perception of phantom limbs , 1998 .

[70]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .