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Uncertainty Estimation Simon Cousens and Richard Silverwood

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Overview an implementation/coding issue with the Loess approach accounting for within-source correlation increasing uncertainty with increasing sources(?)

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Implementation issue Murray at al. describe incorporation of two sources of uncertainty – random noise in data points through resampling parameter values using point estimates and variance- covariance matrix - (one aspect of) model uncertainty through use of a range of α values Wardlaw subsequently noted surprisingly narrow uncertainty ranges for Belarus, Congo, Cote dIvoire, Ukraine

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Example: Congo

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Example: Belarus

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Accounting for within source correlation Loess and spline approaches have assumed independence of data points In practice multiple data points used in analysis derived from a single source (e.g. DHS) and assumption of independence likely to be violated One approach is to fit a multi-level model. Loess model: log(y ij ) = β 0j + β 1 x ij +β 2 z ij + e ij where β 0j = β 0 + u j and u j ~ N(0,σ u )

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Results In general, little change in point estimates (e.g. 2010)

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Results Uncertainty ranges within period of observed data increase (e.g. 1990)

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Results Pattern less clear outside period of observed data (e.g. 2010)

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Some specific country examples Costa Rica

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Some specific country examples Sierra Leone

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Increasing uncertainty with increasing sources? Eritrea

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Comoros

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The Gambia

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Bangladesh

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No obvious asymtotic pattern – is this useable in any way?

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