Continue reading “A nice chart of univariate distribution relationships”

# Month: November 2016

# 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.

# 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 some of the popularity of such trials rests on misunderstandings about what they are capable of accomplishing, and cautions against simple extrapolations from trials to other contexts.

# Very brief notes on measures: From σ-fields to Carathéodory’s Theorem

**Definition 1.** A -field is a non-empty 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. Set functions and measures**. Let be a set and be an algebra on , and let be a non-negative set function

- is
**additive**if and, for , - The map is called
**countably additive**(or -additive) if and whenever is a sequence of disjoint sets in with union in , then - Let be a measurable space, so that is a -algebra on .
- A map is called a
**measure**on if is countable additive. The triple is called a**measure space**. -
The measure is called

**finite**ifand –

**finite**if, () s.th.

- Measure is called a
**probability measure**if and is then called a**probability triple**. - An element of is called -null if .
- A statement about points of is said to hold
**almost everywhere**(a.s.) if

** Continue reading “Very brief notes on measures: From σ-fields to Carathéodory’s Theorem” **