Mathematical statisticsMathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling.
Effects of climate changeClimate change affects the physical environment, ecosystems and human societies. Changes in the climate system include an overall warming trend, more extreme weather and rising sea levels. These in turn impact nature and wildlife, as well as human settlements and societies. The effects of human-caused climate change are broad and far-reaching, especially if significant climate action is not taken. The projected and observed negative impacts of climate change are sometimes referred to as the climate crisis.
Climate changeIn common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to Earth's climate. The current rise in global average temperature is more rapid than previous changes, and is primarily caused by humans burning fossil fuels. Fossil fuel use, deforestation, and some agricultural and industrial practices increase greenhouse gases, notably carbon dioxide and methane.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Climate change mitigationClimate change mitigation is action to limit climate change by reducing emissions of greenhouse gases or removing those gases from the atmosphere. The recent rise in global average temperature is mostly due to emissions from burning fossil fuels such as coal, oil, and natural gas. Mitigation can reduce emissions by transitioning to sustainable energy sources, conserving energy, and increasing efficiency. It is possible to remove carbon dioxide () from the atmosphere by enlarging forests, restoring wetlands and using other natural and technical processes.
Student's t-testA t-test is a type of statistical analysis used to compare the averages of two groups and determine if the differences between them are more likely to arise from random chance. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and therefore a nuisance parameter).
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Chi-squared testA chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables (two dimensions of the contingency table) are independent in influencing the test statistic (values within the table). The test is valid when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof.
Climate change denialClimate change denial or global warming denial is dismissal or unwarranted doubt that contradicts the scientific consensus on climate change. Those promoting denial commonly use rhetorical tactics to give the appearance of a scientific controversy where there is none. Climate change denial includes doubts to the extent of how much climate change is caused by humans, its effects on nature and human society, and the potential of adaptation to global warming by human actions.
Probability theoryProbability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.
Bernoulli distributionIn probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability . Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q.
Attribution of recent climate changeEfforts to scientifically ascertain and attribute mechanisms responsible for recent global warming and related climate changes on Earth have found that the main driver is elevated levels of greenhouse gases produced by human activities, with natural forces adding variability. The likely range of human-induced surface-level air warming by 2010–2019 compared to levels in 1850–1900 is 0.8 °C to 1.3 °C, with a best estimate of 1.07 °C. This is close to the observed overall warming during that time of 0.9 °C to 1.
