Computing Entropies With Nested Sampling

The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions, particularly if the probability mass functions or densities cannot be evaluated. This paper introduces a computational approach, based on Nested Sampling, to evaluate entropies of probability distributions that can only be sampled. I demonstrate the method on three examples: a simple gaussian example where the key quantities are available analytically; (ii) an experimental design example about scheduling observations in order to measure the period of an oscillating signal; and (iii) predicting the future from the past in a heavy-tailed scenario.Comment: Accepted for publication in Entropy. 21 pages, 3 figures. Software available at https://github.com/eggplantbren/InfoNes

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Understanding the relativegenerosity of governmentfinancial support to familieswith children

The principal of horizontal equity can be interpreted as requiring that householdswith the same pre-transfer incomes and the same consumption needs should receivethe same post-transfer incomes. We argue the generosity of government financialsupport to families with children should be analysed with respect to such a baseline.Although not without problems, equivalence scales form an important part of such aprocedure. The comparison of financial support to families with children with acorresponding equivalence scale, both over time and between countries, should give amore accurate picture of generosity than comparisons of cash values alone. Wediscuss potential advantages and drawbacks of such comparisons, illustrating withcomparisons of the US and UK systems. The main drawback is that we can onlyevaluate the generosity of support for children relative to that for adults. With thisrestriction, horizontal equity is more likely to be achieved for couples with 1 childthan for those with 2 children. For some groups, the US is more generous to children(relative to adults) than the UK, but this difference is partly generated by the USsystem being less generous to childless households than the UK. The principal of horizontal equity can be interpreted as requiring that householdswith the same pre-transfer incomes and the same consumption needs should receivethe same post-transfer incomes. We argue the generosity of government financialsupport to families with children should be analysed with respect to such a baseline.Although not without problems, equivalence scales form an important part of such aprocedure. The comparison of financial support to families with children with acorresponding equivalence scale, both over time and between countries, should give amore accurate picture of generosity than comparisons of cash values alone. Wediscuss potential advantages and drawbacks of such comparisons, illustrating withcomparisons of the US and UK systems. The main drawback is that we can onlyevaluate the generosity of support for children relative to that for adults. With thisrestriction, horizontal equity is more likely to be achieved for couples with 1 childthan for those with 2 children. For some groups, the US is more generous to children(relative to adults) than the UK, but this difference is partly generated by the USsystem being less generous to childless households than the UK

How many lone parents are receiving tax credits?

When data on child poverty in 2003/04 were released, the fall in child poverty since 2002/03 was smaller than had been expected. Brewer et al. (2005) identified several reasons that might explain this, one of which was that the Family Resources Survey (FRS) - the data-set from which the Households Below Average Income (HBAI) income series is currently derived - may have been under-recording the number of families receiving tax credits (or the equivalent level of support in out-of-work benefits) and therefore underestimating the incomes of some low-income families with children. Brewer et al. (2006), who analyse what happened to child poverty between 1998/99 and 2004/05, show that estimates of spending on tax credits received by families with children based on the FRS have been getting increasingly inaccurate over time compared with estimates made by HM Revenue & Customs (HMRC), with around £5 billion of spending on tax credits received by families with children going unrecorded by the FRS in 2004/05. However, a detailed comparison of estimates of the number of families with children receiving tax credits (or equivalent in out-of-work benefits) based on the FRS with the equivalent estimates based on the government's administrative data is confounded by the fact that HMRC estimates that the government is paying the child tax credit and the equivalent in out-of-work benefits to more lone parents than official statistics suggest live in the UK

The effect of the working families' tax credit on labour market participation

This Briefing Note compares five recent studies that have examined the labour market impact of the Working Families' Tax Credit and related reforms between 1999 and 2002

Families and Children Strategic Analysis Programme (FACSAP): Childcare use and mothers’ employment: a review of British data sources

In this paper we investigate recent trends in childcare use amongst families in Great Britain, and provide a thorough comparison of the different household survey and administrative datasets. The three datasets in questions are Families and Children Study (FACS), Family Resources Survey (FRS), Labour Force Survey (LFS) and Parents’ Demand for Childcare (PDFC)

Can more revenue be raised by increasing income tax rates for the very rich?

This Briefing Note discusses how much scope there is to raise revenue from the very rich by increasing income tax rates and assesses in detail the amount of revenue that is likely to be raised by the government's proposed reforms. It extends analysis presented in the 2009 IFS Green Budget and updates some calculations in a submission to the Mirrlees Review. It also discusses information recently released by HM Treasury and HM Revenue & Customs concerning their methodology for calculating how much revenue these reforms will raise. The Briefing Note shows that there is considerable uncertainty over the revenue that could be raised from the very rich by increasing income tax rates, both because we cannot be certain about the distribution of incomes above £100,000 and because we cannot be certain how those affected will respond to the tax increase. It goes on to discuss under what conditions the measures in PBR 2008 could yield as much revenue as the Treasury is forecasting

Fungal Pathogens Infecting Soybean Aphid and Aphids on Other Crops Grown in Soybean Production Areas of Michigan

Seasonal prevalence of fungal pathogens infecting soybean aphid, Aphis glycines Matsumura (Hemiptera: Aphididae), was assessed from 2004 to 2006 in two Michigan soybean production areas. In 2005 and 2006 field-collected soybean aphids were incubated, and fungal infection was detected at both sites early in August 2005 during soybean pod development and high soybean aphid densities. Significantly higher proportions of winged aphid morphs were infected (20 and 90% infection at the two sites) than wingless aphid morphs (1 and 3% infection). All cases of mycosis examined involved one pathogen species, Pandora neoaphidis (Remaudiére & Hennebert) Humber (Entomophthorales: Entomophthoraceae). In 2004 and 2005, we surveyed for pathogens of the soy- bean aphid in soybean as well as pathogens in other aphid species feeding on other crop plants (alfalfa, clover, corn, and wheat) by inspecting for sporulating aphid cadavers every 2 to 3 wk during the soybean growing season. Aphid ca- davers were most abundant in alfalfa, especially in August; were less common in clover, corn, and soybean; and were not found in wheat. Pandora neoaphidis was associated with cadavers of Acyrthosiphon pisum (Harris) (Hemiptera: Aphididae) in alfalfa and clover during the same period when soybean aphid infection was detected. Overall, mortality of soybean aphid and other aphid species due to fungal infection was confirmed in Michigan. The results also implicate infected winged soybean aphid morphs as potential agents for fungal dispersal, and A. pisum in alfalfa and clover as a source of fungal propagules for soybean aphid

Global Metabolic Shifts in Age and Alzheimer's Disease Mouse Brains Pivot at NAD+/NADH Redox Sites.

Age and Alzheimer's disease (AD) share some common features such as cognitive impairments, memory loss, metabolic disturbances, bioenergetic deficits, and inflammation. Yet little is known on how systematic shifts in metabolic networks depend on age and AD. In this work, we investigated the global metabolomic alterations in non-transgenic (NTg) and triple-transgenic (3xTg-AD) mouse brain hippocampus as a function of age by using untargeted Ultrahigh Performance Liquid Chromatography-tandem Mass Spectroscopy (UPLC-MS/MS). We observed common metabolic patterns with aging in both NTg and 3xTg-AD brains involved in energy-generating pathways, fatty acids oxidation, glutamate, and sphingolipid metabolism. We found age-related downregulation of metabolites from reactions in glycolysis that consumed ATP and in the TCA cycle, especially at NAD+/NADH-dependent redox sites, where age- and AD-associated limitations in the free NADH may alter reactions. Conversely, metabolites increased in glycolytic reactions in which ATP is produced. With age, inputs to the TCA cycle were increased including fatty acid β-oxidation and glutamine. Overall age- and AD-related changes were > 2-fold when comparing the declines of upstream metabolites of NAD+/NADH-dependent reactions to the increases of downstream metabolites (p = 10-5, n = 8 redox reactions). Inflammatory metabolites such as ceramides and sphingosine-1-phosphate also increased with age. Age-related decreases in glutamate, GABA, and sphingolipid were seen which worsened with AD genetic load in 3xTg-AD brains, possibly contributing to synaptic, learning- and memory-related deficits. The data support the novel hypothesis that age- and AD-associated metabolic shifts respond to NAD(P)+/NAD(P)H redox-dependent reactions, which may contribute to decreased energetic capacity