This thesis comprises 51 papers and a book. It is divided into three sections: on statistical methodology, statistical applications and image analysis. Papers in the first section present new methodology on regression with serially correlated errors, computer-intensive inference and clustering methodology on regression with serially correlated errors, computer-intensive inference and clustering criteria. The second section comprises papers on a range of innovative applications of statistical methods. Papers are grouped by application into: combine harvesting, forage conservation, the modelling of climate, estimating and characterising soil properties, specifying and using the distribution of potato sizes and analysing ion channel data. The final section consists of a book and papers on image analysis. Methodology and applications in medical imaging, microscopy and electrophoresis are covered.

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This thesis describes a lattice calculation of the matrix elements of the vector and axial-vector currents which are relevant to the semi-leptonic decays <I>D</I> → <I>K</I> and <I>D → K</I><SUP>*</SUP>. The simulation was performed in the quenched approximation to lattice QCD on a 24<SUP>3</SUP> x 48 space-time lattice at <I>β</I> = 6.2, using an <I>O</I>(<I>a</I>)-improved fermionic action. In the limit of zero lepton masses the <I>D</I> → <I>K</I> and <I>D</I> → <I>K</I><SUP>*</SUP> decays are described by four form factors: <I>f<SUB>K</SUB></I><SUP>+</SUP>, <I>V<SUB>K</SUB></I><SUB>*</SUB>, <I>A<SUB>K</SUB></I><SUB>*</SUB><SUP>1</SUP> and <I>A<SUB>K</SUB></I><SUB>*</SUB><SUP>2</SUP> which are dimensionless functions of <I>q</I><SUP>2</SUP>, where <I>q<SUP>u</SUP></I> is the four-momentum transfer. The main results, for the form factors at <I>q</I><SUP>2</SUP> = 0, are as follows: <I>f<SUB>K</SUB><SUP>+</SUP></I>(0) = 0.67<SUP>+0.05 + 0.03</SUP><SUB>-0.03 - 0.04</SUB> <I>V<SUB>K</SUB></I><SUB>*</SUB>(0) = 1.01<SUP>+0.25 + 0.05</SUP><SUB>-0.05 - 0.06</SUB> <I>A<SUB>K</SUB></I><SUB>*</SUB><SUP>1</SUP>(0) = 0.69<SUP>+0.06 + 0.01</SUP><SUB>- 0.03 - 0.05</SUB> <I>A<SUB>K</SUB></I><SUB>*</SUB><SUP>2</SUP>(0) = 0.63<SUP>+0.12 + 0.01</SUP><SUB>-0.12 - 0.05</SUB> where the first set of errors are statistical and the second are an estimate of the systematic error. These results are in good agreement with experiment. The form factors were determined for different <I>q</I><SUP>2</SUP> values; their <I>q</I><SUP>2</SUP> dependence is found to be reasonably well described by a simple pole-dominance model. The form factors corresponding to the semi-leptonic decays <I>D</I> → π and <I>D</I> → <I>? </I> were also computed.

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