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Karl Popper: Conjectures and Refutations
(1) It is easy to obtain confirmations, or verifications, for nearly every theoryif we look for confirmations. (2) Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in … Continue reading
Some notes on Kalman Filtering
State Space form Measurement Equation Transition Equation Future form
Posted in Statistics, Time Series
Tagged Kalman, State Space, Statistics, Time Series
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Expectation: Useful properties and inequalities
If is a random variable on . The expected value of is defined as Inequalities Jensen’s inequality. If is convex and Holder’s inequality. If with then CauchySchwarz Inequality: For
Big Data for Volatility vs.Trend
So different aspects of Big Data — in this case dense vs. tall — are of different value for different things. Dense data promote accurate volatility estimation, and tall data promote accurate trend estimation. More (No Hesitations blog)
The limitations of randomised controlled trials
In recent years, the use of randomised controlled trials has spread from labour market and welfare programme evaluation to other areas of economics (and to other social sciences), perhaps most prominently in development and health economics. This column argues that … Continue reading
Posted in Statistics, Uncategorized
Tagged Randomised Controlled Trialls, RCT, Statistics
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Very brief notes on measures: From σfields to Carathéodory’s Theorem
Definition 1. A field is a nonempty collection of subsets of the sample space closed under the formation of complements and countable unions (or equivalently of countable intesections – note ). Hence is a field if whenever whenever Definition 2. … Continue reading