A Short Review of Hacking's The Emergence of Probability and Its Implications from the Perspective of a Researcher for Behavioral Decision Making

This paper is a brief introduction to Ian Hacking's (2006) The Emergence of Probability (2nd ed.), a book on the philosophy of science. The book has been a hot topic worldwide and is still quoted even today. It focuses on the emergence of probability before the work of Pascal. Hacking notes that the word “probability” in the Renaissance age meant “something worthy of approval” and that word categorized as “opinion(opinio)” in the medieval technical sense of this term. The meaning changed because the concept of evidence changed and “internal evidence” appeared. Given this prehistory, Hacking argues that probability has had both an epistemological aspect and an aleatory aspect from the time of its emergence. He also shows that probabilities were explicitly mentioned in the added last chapters of The Port Royal Logic and discusses the works of Huygens, Pascal, Leibniz, J. Hudde, Grant, and J. Bernoulli from the perspective of the implication of probability and inductive reasoning. The present paper presents a detailed description of the characteristic parts of The Emergence of Probability that address the concept of probability before the work of Pascal; the subsequent chapters are explained in order. In the last part, the implications of this book's claims for risk research are discussed.

Key words: Epistemic probability, aleatory probability, duality, inductive inference, before Pascal, probability.

Does Philosophical Discussion about Ecological Modelling and Laws Contribute to the Developments of Ecological Studies?

The literature includes ecological papers that have examined philosophical issues in ecology and have been repeatedly cited in both ecological and philosophical journals. This paper discusses two examples. One example is the tradeoff among generality, realism, and precision in population biology modeling. This proposed tradeoff has been criticized by philosophers because of a lack of proof for the existence of a tradeoff relationship and because of unclear usage of the three terms, although the aim of the original paper was to discuss modeling strategies for population biologists. The second example is a paper that asked if there are general laws in ecology. The philosophical literature tends to focus on what the terms “general” and “law” indicate, and some of the discussions diverge from the concerns of ecologists. In addition, very few philosophers have mentioned recent ecological studies that use up-to-date statistical modeling. Even though some philosophical issues have been invariant despite rapid developments in data and computer technologies, philosophical discussions are expected to make ecological issues mature and then feedback to ecological research.

Key words: Ecology, generality, law, philosophy of science, modelling.

Deterministic Nonlinear Prediction of Tree Crops
—Ensemble Reconstruction of Discrete Dynamics and a Lorenz Method for One-year Forward Prediction of Individual Yield—

Deterministic chaos is generated from low-dimensional dynamics with orbital instability. Discriminating chaotic behavior from observed time series is the main objective of nonlinear time series analysis. Deterministic nonlinear prediction is a powerful tool for this purpose but requires large time series sizes. Because crop yields can only be measured once per year, the observed yield time series size is very small. However, the number of crop individuals in a field or orchard is large; thus, the size of the time series sets is large. In addition, the reproductive patterns of many fruit trees can be assumed to have low-dimensional nonlinear dynamics. In this paper, we apply deterministic nonlinear prediction to yield time series sets obtained from orchards and present practical examples of one-year-ahead forecasting of yields for Citrus unshiu and Pistachio (Pistacia vera).

Key words: Chaotic synchronization, deterministic nonlinear prediction, alternate bearing, ensemble reconstruction of dynamics.

Dynamical-system-integrated Variational Autoencoder for Modeling of Time-lapse Microscopy Data: Application to Liverwort Spermatozoid Motion

Microscopy has been one of the most important research methods in biology from the 17th century, when Hooke discovered the cell, to the present day. In recent years, the development of optical technology and fluorescent protein-based tools has revealed various biological phenomena with unprecedented spatio-temporal resolution. However, such microsopic movie data are complex and high-dimensional, and thus it is not always easy to obtain biologically-relevant parameters from them. To address the issue, we propose a framework for modeling of microscopic movie by integrating a dynamical system into a variational autoencoder, a deep-learning model for unsupervised feature extraction. This allows us to extract biological information as state variables and parameters of the integrated dynamical system. In this article, we have validated our framework by analyzing spermatozoid motion of the liverwort Marchantia polymorpha, an emerging model organism for plant biology. Using a phase oscillator, we have succeeded to estimate the phase and speed of spermatozoid rotation from our high-speed dark-field video microscopy.

Key words: Dynamical systems, variational autoencoder, image analysis, plant biology, Marchantia polymorpha.

Quantification of Galaxy Distribution with Topological Data Analysis and Detection of the Baryon Acoustic Oscillation

Galaxies are distributed inhomogeneously in space, with clusters, groups, filaments and voids. This is called the large-scale structure in the Universe. In astronomy, it is customary to refer to the normal matter as baryons. What we directly observe is the large-scale structure made of baryons. The large-scale structure has formed mainly through the gravitational instability, but there is another origin of the structure exists, which is the acoustic oscillation of baryons at the baryon-photon decoupling. This is imprinted on the spatial distribution of galaxies in the Universe, known as the baryon acoustic oscillation (BAO). In this work, we analyzed the spatial distribution of galaxies with a method from the topological data analysis (TDA), in order to examine the BAO signal in the galaxy distribution. The TDA provides a method to treat various types of “holes” in point set data, by constructing the persistent homology group from the geometric structure of data points and handling the topological information of the dataset. We can obtain the information on the size, position, and statistical significance of the holes in the data. A particularly strong point of the persistent homology is that it can classify the holes by their spatial dimension. We first analyzed the simulation datasets with and without the baryon physics to examine the performance of the PH method. We found that the persistent homology is indeed able to detect the BAO signal among the large-scale structures in the Universe: simulation data with baryon physics present a prominent signal from the BAO, while data without baryon physics does not show this signal. Then, we applied the persistent homology to a quasar (a kind of active galaxies) sample at z < 1.0 from extended Baryon Oscillation Spectroscopic Survey in Sloan Digital Sky Survey Data Release 14 (SDSS DR14). We discovered a characteristic hole (a hollow shell) at a scale r ~ 150 [Mpc]. This corresponds exactly to the BAO signature imprinted in the galaxy/quasar distribution. We performed this analysis on a small subsample of 2000 quasars. This clearly demonstrates that the PH analysis is very efficient in finding this type of topological structures even if the sampling is very sparse.

Key words: Topological data analysis (TDA), persistent homology, galaxy distribution, the large-scale structure in the Universe, baryon acoustic oscillation.