STA 4273H: Statistical Machine Learning
... • We may also be interested in making predictions for a new input value ...
... • We may also be interested in making predictions for a new input value ...
Basics of Probability — Modules 1. Intro / Examples 2. Set Theory 3
... Two operations are performed one after the other: (a) The first operation can be done in n1 ways. (b) Regardless of the way in which the first operation was performed, the second can be performed in n2 ...
... Two operations are performed one after the other: (a) The first operation can be done in n1 ways. (b) Regardless of the way in which the first operation was performed, the second can be performed in n2 ...
Practical Non-parametric Density Estimation on a Transformation
... estimation [8]. A few authors have also looked at density estimation on group structures [12, 10] (in particular the group SO(n) of n × n rotation matrices), and studied the convergence of Fourier series density estimators from a theoretical perspective. Our approach differs from the previous ones ...
... estimation [8]. A few authors have also looked at density estimation on group structures [12, 10] (in particular the group SO(n) of n × n rotation matrices), and studied the convergence of Fourier series density estimators from a theoretical perspective. Our approach differs from the previous ones ...
ST911 Fundamentals of Statistics
... an answer to the question “Where did the data come from?” – allows a mathematical analysis of many aspects of statistical inference under the assumption that the model is correct. Caveat: – Every model is an idealised simplification of reality. We often assume that our model is adequate for practica ...
... an answer to the question “Where did the data come from?” – allows a mathematical analysis of many aspects of statistical inference under the assumption that the model is correct. Caveat: – Every model is an idealised simplification of reality. We often assume that our model is adequate for practica ...
Giulia Di Nunno - List of publications and scientific works
... 3. “Holder duality for conditional expectations with application to linear monotone operators”. Theory of Probability and its Applications (2003), 48, 194-198; SIAM (2004), 48, pp. 177-181. 4. “Theory and numerical analysis for exact distributions of functionals of a Dirichlet process” (with A. Gugl ...
... 3. “Holder duality for conditional expectations with application to linear monotone operators”. Theory of Probability and its Applications (2003), 48, 194-198; SIAM (2004), 48, pp. 177-181. 4. “Theory and numerical analysis for exact distributions of functionals of a Dirichlet process” (with A. Gugl ...
Chapters 12 and 13 - class notes
... But that percentage will be very close to 50% so we say that when a coin is fair the probability of getting a head (or a tail) is 50%. A random variable is a variable whose value is a numerical outcome of a random phenomenon, or random experiment. Random variables are generally denoted with capital ...
... But that percentage will be very close to 50% so we say that when a coin is fair the probability of getting a head (or a tail) is 50%. A random variable is a variable whose value is a numerical outcome of a random phenomenon, or random experiment. Random variables are generally denoted with capital ...
On random tomography with unobservable projection angles
... i=1 . Several algorithms have been proposed to address this problem, and these are often problem specific, although one may single out broad classes, such as Fourier methods (based on the projection-slice theorem) and back-projection methods (see Natterer [38]). The subject matter and mathematical l ...
... i=1 . Several algorithms have been proposed to address this problem, and these are often problem specific, although one may single out broad classes, such as Fourier methods (based on the projection-slice theorem) and back-projection methods (see Natterer [38]). The subject matter and mathematical l ...
Statistics
Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as ""all persons living in a country"" or ""every atom composing a crystal"". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.Two main statistical methodologies are used in data analysis: descriptive statistics, which summarizes data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draws conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and a synthetic data drawn from idealized model. An hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a ""false positive"") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a ""false negative""). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other important types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data and/or censoring may result in biased estimates and specific techniques have been developed to address these problems.Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. Statistics continues to be an area of active research, for example on the problem of how to analyze Big data.